#### ICNPAA 2016 Schedule

#### S4. Control of nonlinear systems under deterministic and stochastic loads

The vibration control of nonlinear engineering systems under deterministic and stochastic loads is a challenging and fascinating field in research and applications.

The aim of the present symposium is . . .Read More

##### S4. Control of nonlinear systems under deterministic and stochastic loads

*Abstract:*

The vibration control of nonlinear engineering systems under deterministic and stochastic loads is a challenging and fascinating field in research and applications.

The aim of the present symposium is to bring together leading scientists and young researchers in applied mathematics, mechanics and engineering sciences to further develop and apply control methods to nonlinear engineering systems.

Topics include, but are are not limited to, passive, active and semi-active control systems, global control, integrity measures in dynamical systems, control of chaos, control algorithms, base isolation and nonlinear vibrations and instabilities of mechanical systems and structures under deterministic and stochastic loads.

**Organizors: J.M. Balthazar and P.B. Gonçalves (Brazil), E. Souza de Cursi (France), ****M. Hajj (USA), S. Lenci (Italy)**

Title | Author | Status | Abstract |
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Polynomial Chaos and Lie Groups: Application in a Gyroscopic System with Uncertainties | Colon | Approved | Stochastic processes in Lie groups is a well-developed theory in the Mathematics community, particularly for the case of rotations (elements of the Lie group SO(3)). This theory finds many application . . . Read More
## Polynomial Chaos and Lie Groups: Application in a Gyroscopic System with Uncertainties
Stochastic processes in Lie groups is a well-developed theory in the Mathematics community, particularly for the case of rotations (elements of the Lie group SO(3)). This theory finds many applications in Mechanical Systems, particularly in the Theory of Mechanisms and Robotics, where the Kinematics and Dynamics can be formulated by using Lie group concepts. We apply this theory for the mathematical model of a gyroscopic system with some stochastic parameters, and use polynomial chaos for the simulation of the resulting stochastic differential system of equations in order to evaluate the uncertainty quantification of the output. We also apply a closed-loop control law in this gyroscopic system and evaluate its robustness by the polynomial chaos method of simulation. |

Automotive Computational Model under Stochastic Disturbances | Colon | Approved | In this work, we present a mathematical (computational) model of a car’s longitudinal and vertical dynamics, with their relevant control systems, and assume that certain parameters and random variable . . . Read More
## Automotive Computational Model under Stochastic Disturbances
In this work, we present a mathematical (computational) model of a car’s longitudinal and vertical dynamics, with their relevant control systems, and assume that certain parameters and random variables and some inputs are stochastic processes. In order to evaluate the performance of the control systems, we apply the Polynomial Chaos method, using the nonintrusive approach, which is more eficiente than the plain Monte Carlo method. In particular, we evaluate the performance of an active suspension system designed to achieve good disturbance attenuation in the chassis, in order to maximize passengers comfort. Several different types of stochastic disturbances are tested and simulation results are presented. |

Computational Analysis of Unmanned Aerial Vehicle (UAV) | ABU DARAG | Approved | A computational exercise has been performed to validate the aerodynamics properties of a novel UAV utilizing a cascade propeller engine. The UAV-SUST has been designed and fabricated at the Department . . . Read More
## Computational Analysis of Unmanned Aerial Vehicle (UAV)
A computational exercise has been performed to validate the aerodynamics properties of a novel UAV utilizing a cascade propeller engine. The UAV-SUST has been designed and fabricated at the Department of Aeronautical Engineering at Sudan University of Science and Technologyin order to meet the specifications required for surveillance and reconnaissance mission. It is classified as a medium range and medium endurance UAV. A commercial CFD solver is used to simulate steady and unsteady aerodynamics characteristics on the entire wing and fuselage of the aircraft. In addition to Lift Coefficient (CL), Drag Coefficient (CD) and Pitching Moment Coefficient (CM), the pressure and velocity contours are illustrated. The aerodynamics parameters are represented a very good agreement with the design consideration at angle of attack ranging from 3 to 20 degrees. Moreover, the visualization of the velocity field and static pressure contours is indicated a satisfactory agreement with the proposed design. The turbulence is predicted by enhancing different turbulence models within the computational fluid dynamics code. |

State of the Art Review of Semi-Active Control for Magnetorheological Dampers | Mughal | Approved | Earthquakes causes severe damage to badly designed structures or buildings to fail or collapse, and also have caused some damage to well-designed structures to malfunction due to the damage or failure . . . Read More
## State of the Art Review of Semi-Active Control for Magnetorheological Dampers
Earthquakes causes severe damage to badly designed structures or buildings to fail or collapse, and also have caused some damage to well-designed structures to malfunction due to the damage or failure of the equipment housed in the structure or building. The use magnetorheological dampers to mitigate the effect of external excitation is increased to resolve this. This article is a state of the art review of nonlinear analytical models to understand the efficacy of semi-active control theory for magnetorheological dampers. A nonlinear semi active control law is desired to be designed which atleast guarantees analytical closed loop stability in order to mitigate the effect of perturbations and drive the desired output to equilibrium. |

Stationary Action and Hamilton-Jacobi Theory | McEneaney | Approved | Stationary-action formulations of conservative dynamical systems are considered. Use of stationary-action formulations allow one to generate fundamental solutions for classes of two-point boundary-val . . . Read More
## Stationary Action and Hamilton-Jacobi Theory
Stationary-action formulations of conservative dynamical systems are considered. Use of stationary-action formulations allow one to generate fundamental solutions for classes of two-point boundary-value problems. For such a problem, one solves for stationary points of the payoff as a function of the input rather than for minima or maxima of the payoff. Nonetheless, a Hamilton-Jacobi partial differential equation (HJ PDE) is obtained for a class of problems subsuming the stationary-action formulation. Although convexity (or concavity) of the payoff is lost as one propagates forward, stationary points continue to exist, and the relationship to the correct solution of the HJ PDE is maintained. The HJ PDE corresponding to stationary action also appears as the semiclassical limit of the Maslov dequantization of the Schrodinger equation. A verification result for solutions of the pre-limit PDE where the system dynamics are driven by a complex-valued stochastic input process is obtained through application of stationary-action techniques. The verification result holds for arbitrary-duration problems, which extends existing results that are valid for limited durations. |

Non-Fragile Observer-Based Controller for Vibration Control of Uncertain Mechanical Systems | Oveisi | Approved | This paper proposes a robust disturbance rejection, non-fragile observer-based controller, for a class of linear systems with structured uncertainty. The robust quadratic stability is guaranteed by th . . . Read More
## Non-Fragile Observer-Based Controller for Vibration Control of Uncertain Mechanical Systems
This paper proposes a robust disturbance rejection, non-fragile observer-based controller, for a class of linear systems with structured uncertainty. The robust quadratic stability is guaranteed by the use of Lyapunov theorem. In order to address the fragility problem, two sets of time-dependent uncertainty sources are considered for the controller and the observer gain in the design procedure. The designed controller is presented in linear matrix equality/inequalities (LME/LMIs) platform. In order to evaluate the performance of the controller, it is implemented in real-time on a mechanical system with the aim of vibration suppression. The plant under study is a multi-input single output (MISO) clamped-free piezo-laminate smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the controller is implemented experimentally on the full-order real system. The results show that the closed-loop system has a robust performance regarding disturbance rejection in the presence of the structured uncertainty and in the presence of the nonlinear/unmodelled dynamics. |

Quasi-Periodic Dynamics of a High Angle of Attack Aircraft | G | Approved | High angle of attack maneuvers closer to stall is a commonly accessed flight regime especially in case of fighter aircrafts. Stall and post-stall dynamics are dominated by nonlinearities which make th . . . Read More
## Quasi-Periodic Dynamics of a High Angle of Attack Aircraft
High angle of attack maneuvers closer to stall is a commonly accessed flight regime especially in case of fighter aircrafts. Stall and post-stall dynamics are dominated by nonlinearities which make the analysis further difficult. Presence of external factors such as wind adds more complexity to the system. Rich nonlinearities point the possibility of existence of chaotic solutions. Past studies in this area confirm the development of such solutions via period doubling. These studies are more concentrated on very high angles of attack which may not be easily accessible practically. This paper examines the possibility of existence of chaotic solutions in the lower, more accessible areas in the post stall domain. The analysis is composed of the study of effect of external wind as an agent to drive the system towards the possibility of a chaotic solution. Investigations reveal presence of quasi-periodic solutions, which are characterized by two incommensurate frequencies. This solution appears when the control parameter, i.e., wind, is varied and time simulation is done. The solution corresponds to the value of angle of attack in the lower region of the angle of attack versus elevator bifurcation curve in the post-stall region. The bifurcation analysis is done for a level flight scenario with elevator deflection as the continuation parameter. A steady wind is considered for the analysis and explores the possibility of chaotic motion by increasing the wind in a step wise manner. It is found that wind adds extra energy to the system which in turn drives the system in to chaos. The analysis is done with the help of phase portrait, Poincare map and amplitude spectrum and a quasi-periodic route to chaos via torus doubling is also presented. |

Damage propagation on a non-ideal vibrating system, with fractional spring and damping | Oliveira | Approved | C Oliveira1,2, J M Balthazar1, A Nabarrete1, M.F. Westin1 , A M Tusset3 and S A David4 1 ITA-Aeronautics Technological Institute, Mechanical-Aeronautics Division, São José dos Campos, SP, Brazil, 2 UF . . . Read More ## Damage propagation on a non-ideal vibrating system, with fractional spring and damping
C Oliveira1,2, J M Balthazar1, A Nabarrete1, M.F. Westin1 , A M Tusset3 and S A David4 Nonlinear physical phenomena are observed in the vibration of different electromechanical systems. This is the main reason for this important topic in engineering investigations. |

Hierarchical Control of Aerial Manipulation Vehicle | Kannan | Approved | Aerial Manipulation can be defined as the technology in which an Aerial Vehicle has the capability to manipulate and interact with its environment. Simple examples of aerial vehicle for active tasking . . . Read More
## Hierarchical Control of Aerial Manipulation Vehicle
Aerial Manipulation can be defined as the technology in which an Aerial Vehicle has the capability to manipulate and interact with its environment. Simple examples of aerial vehicle for active tasking include grasping, manipulation, grasping and transporting etc. The given applications of Aerial Manipulation systems have their own challenges such as highly nonlinear dynamic coupling, instabilities due to load disturbance, nonlinear contact dynamics etc. The Aerial Manipulation Vehicle (AMV) considered here is a Quadrotor with a multilink robotic arm fixed to the base. The quadrotor and the manipulator are dynamically coupled by forming into a multibody system. Theoretically the system can be modelled using Euler-Lagrange techniques where the state vector includes the position and attitude states of the quadrotor along with the joint angles of the robotic arm. The inputs to the AMV include the forces and the torques generated by the four rotors of the quadrotor and manipulator joint torques. The key objective of the control design here is to achieve a reference point in the Cartesian space. That is given a reference point tf=(x,y,z) for the end-effector, the AMV should reach tf starting from initial condition ti=(x0,y0,z0). The control objective is obtained in a hierarchical fashion. The outer most-loop is the reference generator system. This system is a closed-loop inverse kinematic algorithm which generates position, position rates, yaw and yaw rates as well as manipulator joint angle and rates. The quadrotor uses the reference values to perform the outer loop position control, with attitude control (roll, pitch) in inner loop. It must be noted that the position and attitude of the end-effector depends on the position and attitude of the quadrotor itself and the joint angles of the robotic arm. The control of the highly complex hierarchical control involves a combination of Proportional, Integral and Derivative Action. The closed loop stability analysis of the hierarchical control structure is performed using Input-to-State Stability method applied to a cascade system. The performance of the control structure is evaluated for different end-effector reference scenarios in the SimMechanics simulation environment of Matlab/SIMULINK. |

Nonlinear Model Predictive Control for Cooperative Control of Space Robots | Kannan | Approved | Advancement of space needs has challenged human capabilities to perform advanced on-orbit tasks such as construction, maintenance, inspection, astronaut assistance, debris manipulation etc. In order . . . Read More
## Nonlinear Model Predictive Control for Cooperative Control of Space Robots
Advancement of space needs has challenged human capabilities to perform advanced on-orbit tasks such as construction, maintenance, inspection, astronaut assistance, debris manipulation etc. In order to perform these tasks spacecraft with manipulators can be employed. In the current problem we consider the scenario where two space robots are collectively manipulating a passive object. The passive objects include space structures for assembly or space debris etc. Here the two manipulators have to move the passive object from one position to another position in orbit. At the same time the two space manipulators should avoid colliding with each other and the passive object while not applying excessive force on the passive object and the second robot. The given space problem can be simplified as a multi-agent problem with 2 space manipulators and a passive body. Here the satellite dynamic is considered as a point mass |

Mathematical modeling of a Bridge Crane | Bueno | Approved | The problem of transportation and movimentation of heavy loads have allways been found in ports, airports, industrial complexes and construction sites. Cranes are mechanical systems that move heavy lo . . . Read More
## Mathematical modeling of a Bridge Crane
The problem of transportation and movimentation of heavy loads have allways been found in ports, airports, industrial complexes and construction sites. Cranes are mechanical systems that move heavy loads both vertically and horizontally. In the recent years the cranes are becoming bigger, higher and faster and, due to the cables flexibility, the car movements can cause slightly damped oscillations, making the cranes operation slow. In this work, a bridge crane is modelled, and the nonlinear mathematical model is validated experimentally, attempting to develop a better understanding of the complex cranes dynamics. |

Study of effects due to elimination and resources downgrade of sensors in control techniques applied to a two-wheeled inverted pendulum | Bueno | Approved | This paper presents comparisons considering the main characteristics of modeling methodologies and control techniques for a system based on operation of a two wheels inverted pendulum (TWIP), namely, . . . Read More
## Study of effects due to elimination and resources downgrade of sensors in control techniques applied to a two-wheeled inverted pendulum
This paper presents comparisons considering the main characteristics of modeling methodologies and control techniques for a system based on operation of a two wheels inverted pendulum (TWIP), namely, the method of obtaining the model mathematical equations, the type of driver used, number of required sensors and control objectives. Firstly, a robust control strategy is applied to control TWIP’s velocity and displacement considering the use of six sensors. After, a project of a state observer is performed in order to reduce the number of sensors required in the application. The Matlab / Simulink environment is adopted to develop computer simulations considering the use of one of the TWIP models and a robust control strategy to control the speed and vehicle speed. Through the simulation results of the system operation aspects are analyzed considering the influence on the stability of the system caused by the resolution and sampling rate of the sensors, the presence of noise on the sensor readings, general failure of sensors, by providing a conjugated feature oscillating engine for the system and the change of height values and user mass. |

Total Abstracts: 12

#### S17. New Methods and Applications in Aeroelasticity and Structural Mechanics/Dynamics

Abstract: New methods and applications are explored and tackled in order to realize future aircraft. A representative example is the coupling of sophisticated computational fluid dynamics (CFD) and th . . .

##### S17. New Methods and Applications in Aeroelasticity and Structural Mechanics/Dynamics

*Abstract:*

**Abstract:** New methods and applications are explored and tackled in order to realize future aircraft. A representative example is the coupling of sophisticated computational fluid dynamics (CFD) and the nonlinear computational structural dynamics (CSD) which is inevitable in the design of very light flexible aircraft structure undergoing large deformation. The aim of this session is to provide a unique opportunity to researchers to share cutting-edge information of the recent research activities on these issues. Methods in aeroelasticity and mechanics/dynamics, coupling with flight dynamics and applications are within the scope including optimization or inverse analysis.

**Organizers:** Toshiya Nakamura, Masato Tamayama, Jiro Nakamichi , Next Generation Aeronautical Innovation Hub Center, Japan Aerospace Exploration Agency (JAXA)

Title | Author | Status | Abstract |
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Dynamic Load Estimation for a Beam using Central-Difference Scheme and FEM | Nakamura | Approved | Operational load monitoring is very useful in estimating the internal load and hence the usage of the structure based on the actual data. Today there is a strong background of the development of sensi . . . Read More
## Dynamic Load Estimation for a Beam using Central-Difference Scheme and FEM
Operational load monitoring is very useful in estimating the internal load and hence the usage of the structure based on the actual data. Today there is a strong background of the development of sensing technology such as optical fibers (FBG) and data processing, enabling the application of inverse analysis with large degree of freedom. In the present study a method is proposed to estimate the dynamic load on a beam from measured strain data. The FE method is used to model the beam with the central-difference scheme for time-integration. If both the deflection and the slope (a derivative of the deflection) are given at all nodes, the problem is trivial. But since we do not have enough data, the problem becomes mathematically ill-posed and then a technique of inverse analysis is employed. Furthermore, because it is very hard to measure the deflection and slope directly in actual cases, we introduce an operation to transform the strain data, which is usually measured, into the deflection and slope in the numerical scheme of the load identification. The numerical study is not comprehensive at this time but the validity of the present method will be demonstrated. |

Stabilizing effects on 2D channel flow due to longitudinal wall oscillation | Atobe | Approved | Influence of wall oscillation on laminar-turbulent transition of the plane Poiseuille flow is investigated analytically. The Floquet analysis using a time-dependent Orr-Sommerfeld equation expects tha . . . Read More
## Stabilizing effects on 2D channel flow due to longitudinal wall oscillation
Influence of wall oscillation on laminar-turbulent transition of the plane Poiseuille flow is investigated analytically. The Floquet analysis using a time-dependent Orr-Sommerfeld equation expects that the flow is stabilized or destabilized depending on the parameters. The velocity profiles for the analysis are assumed as the superposition of the plane Poiseuille flow and the Stokes layer. Also the collocation method is used in the wall-normal direction for making the monodromy matrix. Depending on the parameters, namely frequency Ω and amplitude Uw of the wall-oscillation, there is the stable region in Ω-Uw plane even though the Reynolod number is of supercritical. |

Reduced Order Modeling of Aeroelasticity Analysis for a Wing under Static Deformation Effect | Tamayama | Approved | The full order analysis of aeroelasticity system, which solves Euler or Navier Stokes equations in time domain, is usually expensive in a sense of time consumed. To improve this defect arisen in the f . . . Read More
## Reduced Order Modeling of Aeroelasticity Analysis for a Wing under Static Deformation Effect
The full order analysis of aeroelasticity system, which solves Euler or Navier Stokes equations in time domain, is usually expensive in a sense of time consumed. To improve this defect arisen in the full order analysis, the Reduced Order Modeling (ROM) method has been developed. If there is a pressure difference between upper and lower surfaces of a wing, aerodynamic forces loaded on the wing cause the wing static deformation. The ROM method, therefore, should have the capability to simulate the wing vibrations under static deformation effect. Some previous researches proposed that this capability is given by applying biases to the unsteady aerodynamic forces which are identified from the aerodynamic response caused by forced wing motions about the rigid wing, i.e. the wing stayed without its static deformation. And, here, the biases are corresponding to the static aerodynamic forces. This implies that the wing motion applied to the wing in order to acquire the aerodynamic response should be large enough to cover the range of wing static deformation. To conduct the full order aerodynamic analysis under a large wing motion is unstable in the CFD code used in this study. Then, another procedure is proposed in this study. The forced unsteady CFD simulation by the full order analysis is conducted about the wing deformed statically. On the other hand, the static deformation varies according to the free stream dynamic pressure, and, therefore, it is strongly sought to identify the aerodynamic model around the flutter dynamic pressure. In this study, this flutter dynamic pressure is initially predicted by the aeroelasticity ROM model composed of the aerodynamic model identified from the full order CFD results simulated around the rigid wing without static deformation. Then, the aerodynamic model is identified from the full order CFD results around the wing model deformed statically at the initially predicted flutter dynamic pressure stated above. At the venue, the simulation results acquired with the method described above will be presented. |

Simulation of Transonic Limit Cycle Oscillations using Nonlinear Aerodynamic Modeling | Arizono | Approved | Limit cycle oscillations (LCO) are usually defined as self-sustained oscillations with limited amplitudes. The type of LCO are categorized as follows: (1) airfoils with stiffness nonlinearities, (2) d . . . Read More
## Simulation of Transonic Limit Cycle Oscillations using Nonlinear Aerodynamic Modeling
Limit cycle oscillations (LCO) are usually defined as self-sustained oscillations with limited amplitudes. The type of LCO are categorized as follows: (1) airfoils with stiffness nonlinearities, (2) delta wings with geometrical plate nonlinearities, (3) very high aspect ratio wings with both structural and aerodynamic nonlinearities, (4) nonlinear structural damping and (5) aerodynamic flows with large shock motions and flow separation. In the transonic region, the presence of shocks on the wing surface introduces strong aerodynamic nonlinearities. The prediction of LCO amplitudes is much more difficult than the related problem of predicting the linear flutter boundary. Stickan et al. presented the LCO simulations of Aerostabil wing. The amplitudes of LCO by the simulation could not meet with the results of experiments. Recent Computational Fluid Dynamics (CFD) solver can estimate the drag and the complicated flow such as the high lift configuration. This paper presents the prediction of LCO amplitude of Aerostabil wind tunnel model using the state-of-the-art CFD solver which is developed at JAXA. |

Total Abstracts: 4

#### S1. Analysis of Fractional Differential, Integral and Difference equations with Applications

Abstract: It has been demonstrated that fractional Dynamic systems equations represent better and more economical models than their counterpart of integer derivative models. Also, due to their applica . . .Read More

##### S1. Analysis of Fractional Differential, Integral and Difference equations with Applications

*Abstract:*

**Abstract**: It has been demonstrated that fractional Dynamic systems equations represent better and more economical models than their counterpart of integer derivative models. Also, due to their applications in various branches of sciences and engineering, the theoretical and numerical study of fractional dynamic systems has gained increased importance. In addition, differential equations involving Riemann Liouville derivatives have a special role in applications in Physics, Biological Sciences and Engineering. Qualitative and quantitative properties of Riemann Liouville and Caputo types of differential and integral and integro-differential equations are very useful in applications. Fractional differential equations are also referred to as equations with memory. Thus the study of fractional differential equations takes care of the global effect rather than the local effect as in the integer derivatives.

**Organizer**: **Aghalaya S. Vatsala****, University of Louisiana at Lafayette, Louisiana 70504, USA**

Title | Author | Status | Abstract |
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New trends on Fractional operators and Applications | Atangana | Approved | In this talk, we present a new direction of fractional calculus with some new definitions of fractional derivatives. New results in connection of the new calculus are presented together with some appl . . . Read More
## New trends on Fractional operators and Applications
In this talk, we present a new direction of fractional calculus with some new definitions of fractional derivatives. New results in connection of the new calculus are presented together with some applications. In addition, we propose a new interpretation to the concept of fractional derivative. |

Global solvability of a class of fractional integro-differential equations with applications | Oukouomi Noutchie | Approved | In this talk, we consider a class of fractional differential equations arising in natural science and engineering. Semi-linear abstract Cauchy theory will be used to investigate the existence and uniq . . . Read More
## Global solvability of a class of fractional integro-differential equations with applications
In this talk, we consider a class of fractional differential equations arising in natural science and engineering. Semi-linear abstract Cauchy theory will be used to investigate the existence and uniqueness of solutions. In particular, perturbation methods will be developed to predict the asymptotic behaviour of solutions. |

Existence of solution for a higher order fractional differential equation | Assia | Approved | In this talk, we establish sufficient conditions for the existence and uniqueness of solution for a class of higher order Caputo fractional initial value problems. We transform the posed problem to a . . . Read More
## Existence of solution for a higher order fractional differential equation
In this talk, we establish sufficient conditions for the existence and uniqueness of solution for a class of higher order Caputo fractional initial value problems. We transform the posed problem to a Volterra integral equation, then under Krasnoselskii-Krein type conditions and by using successive approximations, we discuss the existence and uniqueness questions. A numerical example is given to illustrate the obtained results. |

Generalized Monotone Method and Numerical Approach for Coupled Reaction Diffusion Systems | Muniswamy | Approved | Study of coupled reaction diffusion systems are very useful in engineering and science. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, w . . . Read More
## Generalized Monotone Method and Numerical Approach for Coupled Reaction Diffusion Systems
Study of coupled reaction diffusion systems are very useful in engineering and science. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, with initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to a unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical approach. |

Riemann Lioville Dynamic Systems Versus Sequential Caputo dynamic Systems with Applications | Vatsala | Approved | It is well known that dynamic models represented by fractional derivatives are more efficient and cost effective compared with its counterpart of dynamic models using integer derivatives. The most com . . . Read More
## Riemann Lioville Dynamic Systems Versus Sequential Caputo dynamic Systems with Applications
It is well known that dynamic models represented by fractional derivatives are more efficient and cost effective compared with its counterpart of dynamic models using integer derivatives. The most common fractional derivatives that are used currently are the Riemann-Liouville and the Caputo derivative. The basic idea of fractional dynamic system is to use ‘q’ the order of the derivative as a parameter to improve the model. The order ‘q’ plays an important role as a parameter in the initial and boundary conditions of Riemann-Liouville dynamic systems, but not in the Caputo dynamic systems. In this talk, we bring the salient features of this parameter ‘q’ in the initial and boundary conditions in the sequential Caputo dynamic systems. We develop several results of Sequential Caputo derivative with initial and boundary conditions. As an application of this approach, we demonstrate that sequential Caputo sub and super hyperbolic equations yields the classical reaction diffusion equation and the wave equations as special cases. Also, we present some numerical results. |

Haar based numerical solution of Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions | SETIA | Approved | Fractional integro-differential equations have many applications in different fields of science and engineering like aerospace, nuclear engineering, chemistry, astronomy, biology, economics, potential . . . Read More
## Haar based numerical solution of Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions
Fractional integro-differential equations have many applications in different fields of science and engineering like aerospace, nuclear engineering, chemistry, astronomy, biology, economics, potential theory and electrostatics. One may find the exact solution of such fractional integro-differential equation but in some special cases only. This point has taken attention of lot of researchers and different methods have been proposed time-to-time like transform methods, homotopy analysis, Adomain decomposition method, variational iteration method etc. In this paper, a numerical method is proposed to solve the Fredholm-Volterra fractional integro-differential equation with non local boundary conditions by using Haar wavelets. A collocation based Galerkin’s method is applied by using Haar wavelets as basis functions over the interval [0,1). It converts the Fredholm-Volterra fractional integro-differential equation into a system of k linear equations. We need to incorporate m nonlocal boundary conditions in the same way. So all together it will give a system of (k+m) linear equations in (k+m) variables which can be solved. A variety of test examples are considered to illustrate the proposed method. In first and last examples, the order of fractional differential operator is considered 1/2 and 1/3 respectively which are less than 1. In second example, the order of fractional differential operator is considered 5/4 which is more than 1. First and last examples require only one nonlocal boundary condition while the second example needs two nonlocal boundary conditions. The error bounds have also been explored in all the test examples. The actual error is also measured with respect to a norm and the results are validated through error bounds. |

Numerical method to solve cauchy type singular integral equation with error bounds | SETIA | Approved | Cauchy type singular integral equations with index zero naturally occur in the field of aerodynamics. Literature is very much developed for these equations and Chebyshev’s polynomials are most frequen . . . Read More
## Numerical method to solve cauchy type singular integral equation with error bounds
Cauchy type singular integral equations with index zero naturally occur in the field of aerodynamics. Literature is very much developed for these equations and Chebyshev’s polynomials are most frequently used to solve these integral equations. In this paper, a residual based Galerkin’s method has been proposed by using Legendre polynomial as basis functions to solve Cauchy singular integral equation of index zero. It converts the Cauchy singular integral equation into system of equations which can be easily solved. The test examples are given for illustration of proposed numerical method. Error bounds are derived as well as implemented in all the test examples. |

Integral equation in functional spaces / Generalized Lebesgue space()() | firouz | Approved | The aim of this work is the study: the problem of existence of solutions for integral equation in different functional spaces. Then it is imperative to pass by an assumptional property: the compactnes . . . Read More ## Integral equation in functional spaces / Generalized Lebesgue space()()
The aim of this work is the study: the problem of existence of solutions for integral equation in different |

On a nonlinear fractional boundary value problem | TOREBEK | Approved | In this work we prove the existence and uniqueness of solutions for a class of the nonlinear third order fractional differential equation with boundary condition. An example is given to illustrate the . . . Read More
## On a nonlinear fractional boundary value problem
In this work we prove the existence and uniqueness of solutions for a class of the nonlinear third order fractional differential equation with boundary condition. An example is given to illustrate the main results. |

Total Abstracts: 9

#### Applications on fractional operators to real world problems

Abstract: The concept of derivative with fractional order has attracted attention of many researchers in many branches of sciences, technology and engineering as it was found suitable mathematical too . . .Read More

##### Applications on fractional operators to real world problems

*Abstract:*

**Abstract:** The concept of derivative with fractional order has attracted attention of many researchers in many branches of sciences, technology and engineering as it was found suitable mathematical tools for modeling real world problems. Many researchers around the globe are devoting their attention in proposing a better derivative with fractional order that can be used in almost all real world problems. For each definition proposed, new theory and applications need to be developed. This special section is therefore devoted to the discussion underpinning the latex development on theory, methods and applications of fractional calculus. The special section will include talks on: Theory on recent definitions of fractional derivative, modeling real world problems with fractional derivative, theory on fractional differential equations, numerical methods for fractional differential equations, analytical methods for differential equations and iterative methods.

**Organizer**: Abdon Atangana, Institute for groundwater studies

University of the Free State, Bloemfontein, South Africa

#### S3. Control and Estimation: Theory and Applications

Abstract: Feedback and control systems are all pervasive in nature as well as in human endeavors. The theory of control systems is a mature field in the minds of many; however, it continues to evolve . . .

##### S3. Control and Estimation: Theory and Applications

*Abstract:*

**Abstract:** Feedback and control systems are all pervasive in nature as well as in human endeavors. The theory of control systems is a mature field in the minds of many; however, it continues to evolve as new technologies are seen as areas to which it can be applied. Since the middle of the last century, the field of estimation has become inextricably entwined with control system theory, thus combining the two fields in the literature has become quite common. The purpose of this session is to bring together researchers who are working to advance the theory of control and estimation and those who are advancing the field of control and estimation through the application of the theory to new and advanced technologies.

**Organizers: ** Stephen C. Stubberud, Oakridge Technology, Del Mar, CA, USA , Allen R. Stubberud, University of California, Irvine, Irvine, CA USA

** **

Title | Author | Status | Abstract |
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Submarine Harbor Navigation Using Image Data | Stubberud | Approved | The process of ingress and egress of a United States Navy submarine is a human-intensive process that takes numerous individuals to monitor locations and for hazards. Sailors pass vocal information to . . . Read More
## Submarine Harbor Navigation Using Image Data
The process of ingress and egress of a United States Navy submarine is a human-intensive process that takes numerous individuals to monitor locations and for hazards. Sailors pass vocal information to bridge where it is processed manually. There is interest in using video imaging of the periscope view to more automatically provide navigation within harbors. In this paper, video-based navigation is examined as a target-tracking problem. While some image-processing methods claim to provide range information, the moving platform problem and weather concerns, such as fog, reduce the effectiveness of these range estimates. The video-navigation problem then becomes an angle-only tracking problem. Angle-only tracking is known to be fraught with difficulties, due to the fact that the unobservable space is not the null space. When using a Kalman filter estimator to perform the tracking, significant errors arise which could endanger the submarine. This work analyzes the performance of the Kalman filter when angle-only measurements are used to provide the target tracks. This paper addresses estimation unobservability and the minimal set of requirements that are needed to address it in this complex but real-world problem. Four major issues are addressed: the knowledge of navigation beacons’ locations, the minimal number of these beacons needed to maintain the course, levels of obscuration of these navigation beacons, and update rates of the angles of the beacons as the periscope rotates to monitor the actions in the harbor around the submarine. The goal is to address the problem of navigation to and from the docks, while maintaining the traversing of the harbor channel based on maritime rules relying solely on the image-based data. The minimal number of beacons will be considered. For this effort, the image correlation from frame to frame is assumed to be perfectly achieved. Variation in the update rates and the dropping of data due to rotation and obscuration is considered. The example problem will address a simulated simple-harbor scenario of San Diego harbor. A set of reasonable initial conditions are assumed based on whether the submarine is in ingress or egress operations. Obscuration due to military and commercial traffic will reduce the use of certain beacons. |

A Unified Kalman Filter | Stubberud | Approved | When considering problems of linear sequential estimation, two versions of the Kalman filter, the continuous-time version and the discrete-time version, are often used. (A hybrid filter also exists.) . . . Read More
## A Unified Kalman Filter
When considering problems of linear sequential estimation, two versions of the Kalman filter, the continuous-time version and the discrete-time version, are often used. (A hybrid filter also exists.) In many applications in which the Kalman filter is used, the system to which the filter is applied is a linear continuous-time system, but the Kalman filter is implemented on a digital computer, a discrete-time device. The two general approaches for developing a discrete-time filter for implementation on a digital computer are: (1) approximate the continuous-time system by a discrete-time system (called discretization of the continuous-time system) and develop a filter for the discrete-time approximation; and (2) develop a continuous-time filter for the system and then discretize the continuous-time filter. Generally, the two discrete-time filters will be different, that is, it can be said that discretization and filter generation are not, in general, commutative operations. As a result, any relationship between a discrete-time filter and the continuous-time filter for the same continuous-time system may be obfuscated. This is particularly true when an attempt is made to generate the continuous-time version of the Kalman filter through a simple limiting process (the sample period going to zero) applied to the discrete-time filter. The correct result is, generally, not obtained. |

Integration of Bio-Inspired, Control-Based Visual and Olfactory Data for the Detection of an Elusive Target | Duong | Approved | In this paper, a technique is presented for integrating bio-inspired visual and olfactory receptor systems to search for elusive targets in practical environments in which the targets cannot be detect . . . Read More
## Integration of Bio-Inspired, Control-Based Visual and Olfactory Data for the Detection of an Elusive Target
In this paper, a technique is presented for integrating bio-inspired visual and olfactory receptor systems to search for elusive targets in practical environments in which the targets cannot be detected by either data sensor individually. The bio-inspired Visual System is based on a model of the extended visual pathway which consists of saccadic eye movements and the visual pathway. This model enables powerful target detections from noisy and partially incomplete visual data. The Olfactory receptor algorithm is based on a spatial invariant independent component analysis, that was developed from a receptor-electronic nose (enose) at Caltech. It has been adapted to enable the detection of an odorant target in an unknown environment. The integration of these two systems provides an important approach to detecting unknown targets for many applications. In particular it may provide a cornerstone for developing effective and low cost intelliegnt system-on-a-chip for miniaturized UAVs or flying robots for future DOD and NASA missions. |

Observer based fault diagnostics for networked control systems in presence of delay | Abdollahi Biron | Approved | The concept of wireless communication, provides the ability of remote controlling for large scale systems in industries. Therefore, each large scale system can be divided into (1) physical part contai . . . Read More
## Observer based fault diagnostics for networked control systems in presence of delay
The concept of wireless communication, provides the ability of remote controlling for large scale systems in industries. Therefore, each large scale system can be divided into (1) physical part containing the hardware, plants, sensors and actuators and (2) cyber part containing the software, controllers and communication network. Usually, for a large scale system, controller is a decentralized controller containing several local controllers communicating to each other through the shared network. Also, sensors and actuators of the physical part of a large scale system, can communicate with the controller via communication network to send and receive information from the controllers. Hence, the whole system can be considered as a networked control system (NCS). The communication among different parts of the network system happens with delay effected which is one of the communication network inherent characteristics. A long with the network delay, there are always possibility to physical failures in sensors and actuators of the physical part of the system. |

MODEL PREDICTIVE CONTROL: A NEW APPROACH | Nagy | Approved | New methods are proposed in the paper for solution of the model predictive control problem. Nonlinear state space design techniques are also treated. For nonlinear state prediction (state evolution co . . . Read More
## MODEL PREDICTIVE CONTROL: A NEW APPROACH
New methods are proposed in the paper for solution of the model predictive control problem. Nonlinear state space design techniques are also treated. For nonlinear state prediction (state evolution computation) a newly established predictor, given in the form of an operator, is introduced and tested. Settling the problem may be obtained through application of the principle “direct stochastic optimum tracking” with a simple algorithm. The principle states that a predicted optimum stochastic trajectory (or output sequence) can be obtained by step-by-step optimum extension of a part of the trajectory (output sequence). The optimization method which implements the principle is called “optimized stochastic trajectory / output sequence tracking”. The model predictive control problem with I/O equations or state equations can be solved with this method through a sequence of two-stage optimizations and iteration in an optimum manner, even for linearizable nonlinear plants. Although concrete values of future disturbances are not known, the future nonlinear process, too, is considered as stochastic. Precondition for the optimum nonlinear solution is optimum state prediction, which is based in the paper on definition of virtual intersample points and linearization at these points. Increasing the number of intersample points may give better approximation of the evolving nonlinear trajectory of states, improving the accuracy of prediction. State estimation on virtual intersample sections between virtual intersample points may be done with linear predictor. The predicted state difference between two real sampling instants can be given with a sum, which may be replaced with an integral for the case of infinite virtual intersample points. This integral defines the so-called M-operator, which may be considered as optimum state predictor for linearizable nonlinear plants. Simulations show that applying the described techniques, exact following with estimated outputs is possible on a whole finite horizon (not regarding slight computational errors) with the derived algorithms, even for linearizable nonlinear plants, if the control signals are not constrained. Simulations also demonstrate the advantages of the M-operator based solution in comparison with application of the extended Kalman filter predictor. |

Total Abstracts: 5

#### S5. Delay Differential Equations Models in Life Sciences, Engineering and Economics

Abstract. The Session is dedicated to recent models from biology, medicine, technology and socio-economics that use differential equations with time lag. A major topic in this context is the study of . . .Read More

##### S5. Delay Differential Equations Models in Life Sciences, Engineering and Economics

*Abstract:*

Abstract. The Session is dedicated to recent models from biology, medicine, technology and socio-economics that use differential equations with time lag. A major topic in this context is the study of equilibria and of the existence of periodic solutions, including Hopf bifurcations. Talks presenting oscillatory phenomena in hematology, aircraft control (including Pilot Induced Oscillations) or economics are particularlly encouraged for submission.

Organisers:

Andrei Halanay, University Politehnica of Bucharest

Mihaela Neamtu, West University of Timisoara

Title | Author | Status | Abstract |
---|---|---|---|

On qualitative properties in nonlinear Volterra integro-differential equations with delay | TUNC | Approved | This paper considers a class of scalar and vector non-linear Volterra integro-differential equations of first order with constant delay. We show stability, uniformly stability, boundedness, convergenc . . . Read More
## On qualitative properties in nonlinear Volterra integro-differential equations with delay
This paper considers a class of scalar and vector non-linear Volterra integro-differential equations of first order with constant delay. We show stability, uniformly stability, boundedness, convergence and square integrability of solutions. The technique of proof involves defining appropriate Lyapunov functionals. Our results improve the results obtained in literature. |

The stability analysis of a hypothalamic pituitary adrenal axis model with inclusion of the glucocorticoid receptor and memory | Neamtu | Approved | This paper analyzes a model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the glucocorticoid receptor in the pituitary. Due to the spatial separation between hypothalamus, pituitary a . . . Read More
## The stability analysis of a hypothalamic pituitary adrenal axis model with inclusion of the glucocorticoid receptor and memory
This paper analyzes a model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the glucocorticoid receptor in the pituitary. Due to the spatial separation between hypothalamus, pituitary and adrenal glands, we introduce distributed time delays. The existence of the positive equilibrium point is proved and a local stability analysis with several types of delay kernels is provided. Also, the fractional model is taken into account. The last part contains some numerical simulations to illustrate the effectiveness of our theoretical findings. |

Stability analysis for a delay differential equations model of a hydraulic turbine speed governor | SAFTA | Approved | The paper aims to model the dynamic behavior of a speed governor for a hydraulic turbine using an associated mathematical model. The nonlinear mathematical model newly introduced consists of a system . . . Read More
## Stability analysis for a delay differential equations model of a hydraulic turbine speed governor
The paper aims to model the dynamic behavior of a speed governor for a hydraulic turbine using an associated mathematical model. The nonlinear mathematical model newly introduced consists of a system of delay differential equations (DDE) and will be compared to some already in use mathematical models that use ordinary differential equations (ODE). A new kind of nonlinearity is introduced through the time delay. The delays can characterize different running conditions of the speed governor. For example, it can happen that the spool displacement of the hydraulic amplifier is blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay. Stability analysis of the equilibria of the model for the hydraulic control system is performed. Numerical simulations are presented to illustrate the characteristics of the new model as compared to the classical one. |

Dynamics of complex-valued fractional-order neuronal networks | Radulescu | Approved | The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability, Hopf bifurcations and chaos. Sufficient conditions for the asymptotic stability . . . Read More
## Dynamics of complex-valued fractional-order neuronal networks
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability, Hopf bifurcations and chaos. Sufficient conditions for the asymptotic stability and instability of a steady state of the network are derived, based on the complex system parameters and the fractional order of the system, considering simplified neuronal connectivity structures (hub and ring). In some specific cases, it is possible to identify the critical values of the fractional order for which Hopf bifurcations may occur. Numerical simulations results are presented to illustrate the theoretical findings and to investigate the stability of the limit cycles which appear due to Hopf bifurcations. Potential routes towards the onset of chaotic behavior are also explored numerically, when the fractional order of the system increases. (joint work with Eva Kaslik) |

Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia | Candea | Approved | D. Candea, A. Halanay, R. Radulescu We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-l . . . Read More ## Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia
D. Candea, A. Halanay, R. Radulescu We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. We aim to estimate the realistic values of the most significant parameters of the model which affect the evolution of CML during Imatinib treatment using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted. |

Influence of Delay on Dynamical Behaviour of Nonideal Pendulum Systems | Shvets | Approved | Influence of Delay on Dynamical Behaviour of Nonideal Pendulum Systems A.Yu. Shvets National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine (e-mail: alex.shvets@bigmir.ne . . . Read More ## Influence of Delay on Dynamical Behaviour of Nonideal Pendulum Systems
Influence of Delay on Dynamical Behaviour of Nonideal Pendulum Systems A.Yu. Shvets In mathematical modelling of oscillatory processes a mathematical model of The mathematical models of nonideal (in sense of Sommerfeld-Kononenko) spherical pendulum systems, keywords: nonideal pendulum systems; delay factors, regular and chaotic attractors |

New results on the stability, boundedness and periodic solutions of some third-order delay nonlinear differential equations with multiple deviating arguments | Adesina | Approved | A.T. Ademola, B.S.Ogundare, M.O. Ogundiran and O.A.Adesina Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria In this paper, sufficient conditions for solutions that are periodic, . . . Read More ## New results on the stability, boundedness and periodic solutions of some third-order delay nonlinear differential equations with multiple deviating arguments
A.T. Ademola, B.S.Ogundare, M.O. Ogundiran and O.A.Adesina In this paper, sufficient conditions for solutions that are periodic, uniformly asymptotically stable and uniformly ultimately bounded are established for some third-order nonlinear differential equations with multiple deviating arguments. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish novel results that made relevant results on the subject matter in the literature to be particular cases of our results. Finally, the correctness and effectiveness of the results are tested with illustrations. |

Nonlinear dynamics in a fractional-order Morris-Lecar neuronal model | Brandibur | Approved | A two-dimensional fractional-order Morris-Lecar neuronal model is analyzed, focusing on stability and instability properties. Moreover, we discuss the occurrence of Hopf bifurcations with respect to t . . . Read More
## Nonlinear dynamics in a fractional-order Morris-Lecar neuronal model
A two-dimensional fractional-order Morris-Lecar neuronal model is analyzed, focusing on stability and instability properties. Moreover, we discuss the occurrence of Hopf bifurcations with respect to the fractional order of the system, which is chosen as bifurcation parameter. Numerical simulations exemplify the theoretical results, revealing rich spiking behavior. We also compare the results to similar ones obtained for the classical integer-order Morris-Lecar neuronal models. (joint work with Eva Kaslik) |

Stability and oscillations in a CML model | Badralexi | Approved | We capture the evolution in competition of healthy and leukemic cells in Chronic Myelogenous Leukemia (CML) taking into consideration the response of the immune system. Delay-differential equations in . . . Read More
## Stability and oscillations in a CML model
We capture the evolution in competition of healthy and leukemic cells in Chronic Myelogenous Leukemia (CML) taking into consideration the response of the immune system. Delay-differential equations in a Mackey-Glass approach are used. One starts with the study of stability of the equilibrium points of the system. Conditions on parameters for the local stability are given. Oscillatory behaviors occur naturally in biological phenomena. Thus, we investigate the periodic behavior of solutions and we obtain conditions for periodic solutions to appear through a Hopf bifurcation. |

Total Abstracts: 9

#### S6. Integral Equations and Their Applications in Science and Technology

Abstract: The aim of the session is to discuss both the theory of integral equations and their applications in engineering, mechanics, mathematical physics and so on. In particular, talks presenting t . . .Read More

##### S6. Integral Equations and Their Applications in Science and Technology

*Abstract:*

**Abstract**: The aim of the session is to discuss both the theory of integral equations and their applications in engineering, mechanics, mathematical physics and so on. In particular, talks presenting the use of integral equations in the areas of aerodynamics, fluid mechanics and wave diffraction are especially welcomed. Special emphasis is also paid to nonlinear integral equations, functional integral equations and systems of integral equations. The theory of fractional integral equations and their numerous applications is also included. Thus, various topics of the theory of integral equations which have a wide range of applications will be considered.

**Organizers:** **Jozef Banas, Department of Mathematics, Rzeszów University of Technology, Rzeszów, (Poland)**

**Luis Castro,CIDMA – Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Aveiro, (Portugal)**

Title | Author | Status | Abstract |
---|---|---|---|

A Fast Computational Technique for Solving General Nonlinear Integral Equations | Fattahzadeh | Approved | In this work we propose a fast scheme for solving general nonlinear Integral equation by using Chebyshev fast method of Fourier transform (FFT). This method is based on replacement of unknown function . . . Read More
## A Fast Computational Technique for Solving General Nonlinear Integral Equations
In this work we propose a fast scheme for solving general nonlinear Integral equation by using Chebyshev fast method of Fourier transform (FFT). This method is based on replacement of unknown function by truncated series of well known Chebyshev polynomials. The quadrature formulas which we use to calculate integral terms have been estimated by FFT. This is a grate advantages of this method which has lowest operation count in contrast to other works which use multi production of operational matrices which raise computational complexity or involve intermediate numerical techniques. Also convergence of this method is given and the numerical experiments show the applicability and accuracy of this method. |

Hyers-Ulam-Rassias stability for a class of Hammerstein integral equations | Simões | Approved | We obtain sufficient conditions for the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations within both cases of finite and infinite intervals. These sta . . . Read More
## Hyers-Ulam-Rassias stability for a class of Hammerstein integral equations
We obtain sufficient conditions for the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations within both cases of finite and infinite intervals. These stabilities are analysed upon the consideration of fixed point arguments and weighted metrics. Some concrete examples will be presented to illustrate the theoretical results. |

Invertibility of Wiener-Hopf plus Hankel integral equations | Silva | Approved | We will study operators arising in Wiener-Hopf plus Hankel integral equations. Invertibility and Fredholm criteria for those operators are obtained in the framework of variable exponent Lebesgue spac . . . Read More ## Invertibility of Wiener-Hopf plus Hankel integral equations
We will study operators arising in Wiener-Hopf plus Hankel integral equations. Invertibility and Fredholm criteria for those operators are obtained in the framework of variable exponent Lebesgue spaces on the real line. The main technique is based on appropriate factorizations of the corresponding Fourier symbols. |

Fourier cosine and Fourier sine integral equations and their convolutions | Guerra | Approved | We will present a study for a class of integral equations associated with the Fourier cosine and Fourier sine transforms. The solvability of those equations is analysed. In addition, a Parseval type f . . . Read More
## Fourier cosine and Fourier sine integral equations and their convolutions
We will present a study for a class of integral equations associated with the Fourier cosine and Fourier sine transforms. The solvability of those equations is analysed. In addition, a Parseval type formula and a Plancherel type theorem are obtained. Heisenberg uncertainty principles are also obtained, and new convolutions are derived for the integral equations under study. |

Some new properties and applications of a fractional Fourier transform | Rodrigues | Approved | In this talk, we deal with the fractional Fourier transform in the form introduced a little while ago by Yuri Luchko. This transform is closely connected with the FC operators and has been already emp . . . Read More
## Some new properties and applications of a fractional Fourier transform
In this talk, we deal with the fractional Fourier transform in the form introduced a little while ago by Yuri Luchko. This transform is closely connected with the FC operators and has been already employed for solving of both the fractional diffusion equation and the fractional Schr\”odinger equation. In this paper, we continue investigation of the fractional Fourier transform and in particular prove some new operational relations for a linear combination of the left- and right-hand sided fractional derivatives. As an application of the obtained results, we provide a schema for solving the fractional differential equations with both left- and right-hand sided fractional derivatives without and with delays and give some examples of realization of our method for several fractional differential equations. |

On the solvability of a class of convolution integral equations with symmetry | Castro | Approved | Convolution integral equations with symmetry appear naturally in boundary value problems for elliptic partial differential equations in symmetric or symmetrizable domains. We will be concentrated on a . . . Read More
## On the solvability of a class of convolution integral equations with symmetry
Convolution integral equations with symmetry appear naturally in boundary value problems for elliptic partial differential equations in symmetric or symmetrizable domains. We will be concentrated on a class of those equations which is associated with the Helmholtz equation in a quadrant, where a possible solution is symmetrically extended to a half-plane. Characterizations of the normal solvability, Fredholm property, one-sided invertibility will be obtained for the consequent integral operators within a framework of Bessel potential spaces. Moreover, explicit factorization methods for such operators will be presented. The talk is based on joint works with F.-O. Speck. |

Some asymptotic properties of Fourier-Laplace transform of the Green’s Tensor for coupled thermoelastodynamics in 2D and 3D case | Alipova | Approved | The dynamics of thermoelastic medium under the action of concentrated transient heat sources and mass forces is considered. It is known that the effect of such sources is modeled by representation of . . . Read More
## Some asymptotic properties of Fourier-Laplace transform of the Green’s Tensor for coupled thermoelastodynamics in 2D and 3D case
The dynamics of thermoelastic medium under the action of concentrated transient heat sources and mass forces is considered. It is known that the effect of such sources is modeled by representation of the body force F, or heat source Q through the singular generalized functions. Fourier transformation in space coor-dinates and Laplace transformation in time were done for components of Green’s Tensor. Some asymptotic properties and symmetrical properties of Green’s Tensor for coupled Thermoelastodynamics in 2-dimensional case are considered: by approaching to infinity and zero, and symmetry properties by indexes and by ar-guments. Several Lemmas are proved: logarithmic singularities of the type ln p at p approaching to zero. The proved inequalities for parameters of Bessel’s function are valid for real p>0 and inequalities of Bessel functions in dynamical functions are proved also. It is obviously the confir-mation of physical statement of isotropic thermoelstic medium in 2D and 3D case. |

Shock Waves As Generalized Solutons Of Thermoelastodynamics Equations. On The Uniqueness Of Boundary Value Problems Solutions | Alipova | Approved | Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energ . . . Read More
## Shock Waves As Generalized Solutons Of Thermoelastodynamics Equations. On The Uniqueness Of Boundary Value Problems Solutions
Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energy density on their fronts are received. The statements of four non-stationary boundary value problems of coupled thermoelasticity are given, for which uniqueness of decisions are proved taking into account shock thermoelastic waves. |

Total Abstracts: 8

#### S7. Inverse Problems: Theory and Application to Science and Engineering

Abstract: Inverse problems arise naturally in many branches of science and engineering where the values of some model parameters must be obtained from the observed data.

This sort of question is of gr . . .Read More

##### S7. Inverse Problems: Theory and Application to Science and Engineering

*Abstract:*

**Abstract**: Inverse problems arise naturally in many branches of science and engineering where the values of some model parameters must be obtained from the observed data.

This sort of question is of great interest in many application areas in science and engineering including acoustics, aerodynamics, electromagnets, hydrological engineering, image analysis, shape design, structural dynamic modification and reconstruction, tomography, etc.

In the recent years, theory and applications of inverse problems have undergone a tremendous growth: They can be formulated in many mathematical areas and analyzed by different theoretical and computational techniques.

This session focuses on theory and application of inverse problems and includes talks on Inverse problems for differential and integral equations, Inverse problems and homogenization techniques, Regularization techniques, Statistical inverse problems, Numerical analysis of inverse problems, Computational Inverse Problems, and related areas.

**Organizers**: **Prof. Herb Kunze, University of Guelph (Canada), ****Prof. Davide La Torre, University of Milan (Italy) and Khalifa University (UAE).**

Title | Author | Status | Abstract |
---|---|---|---|

An inverse problem for a system of steady-state reaction-diffusion equations acting on a perforated domain | Kunze | Approved | A perforated domain (or porous medium) is a material characterized by a partitioning of the total volume into a solid portion often called the matrix and a pore space usually referred to as holes. Mat . . . Read More
## An inverse problem for a system of steady-state reaction-diffusion equations acting on a perforated domain
A perforated domain (or porous medium) is a material characterized by a partitioning of the total volume into a solid portion often called the matrix and a pore space usually referred to as holes. Mathematically speaking, these holes can be either materials different from that of the matrix or real physical holes. The treatment of an inverse problem on a perforated domain is complicated heavily by the presence of the perforations or holes. In this work, we consider a coupled system of reaction-diffusion equations at steady-state acting on a perforated domain. Given observation data of the system components, we seek to estimate the coefficients/parameters in the model. We build on past work in which we established and demonstrated results for solving the related inverse problem for a single equation. The method relies on relating the problem on the domain with holes to the problem on the domain with no holes. As we will see, the extension to a system of equations adds extra complexity and complications to the problem. |

An inverse problem for a mathematical model of aquaponic agriculture. | Bobak | Approved | Aquaponics is a closed-loop agricultural system which uses a symbiotic relationship between aquatic organisms and aquatic macrophytes. The two major populations of interest are fish and plants, howe . . . Read More
## An inverse problem for a mathematical model of aquaponic agriculture.
Aquaponics is a closed-loop agricultural system which uses a symbiotic relationship between aquatic organisms and aquatic macrophytes. The two major populations of interest are fish and plants, however the system is dependent on ammonia concentrations and nitrate concentrations to function sustainably. Organic nitrogen in fish waste naturally converts to ammonia through biological degradation. Ammonia is highly toxic to fish, and is an inefficient nutrient source for plants. In order for ammonia to be used as fertilizer for the plants, it must go through a natural microbial process called the Nitrogen Cycle and be transformed to Nitrate. Nitrate is a nutrient rich food source for plants and essential to the nutrient uptake process. Academic research into the aquaponics is just beginning to get momentum. To our knowledge, there is a distinct lack of reliable mathematical models and simulations available to analyze the stability of an aquaponic system. In this work, we present an aquaponic system model and discuss solution behaviour. A sensitivity analysis helps us to identify the most impactful parameters in the model. Researchers at John Hopkins Center for a Liveable Future have provided us with a large set of data from their aquaponic lab; the data contains information about fish population, major concentrations present in the tank water, as well as harvesting information regarding the plant populations. We approach the parameter estimation inverse problem in several ways. By using simulated data, with low-amplitude noise added, we first demonstrate that the “collage method” for ODEs inverse problems works well for our model. We then discuss how the real-world data can be used to address the inverse problem, both with this mathematical machinery and via appropriate statistical analyses. |

Signal processing with Circle Inversion Map Systems | Boreland | Approved | Given a circle C with centre o and radius r, inversion with respect to C transforms the point p to the point p’ such that p and p’ lie on the same radial half-line from o and d(o,p)d(o,p’)=r*r, where . . . Read More ## Signal processing with Circle Inversion Map Systems
Given a circle C with centre o and radius r, inversion with In this talk, we establish that a system of circle inversion maps has |

Collage-based Approaches for Elliptic Partial Differential Equations Inverse Problems | Yodzis | Approved | The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach’s fixed point theorem, for treating i . . . Read More
## Collage-based Approaches for Elliptic Partial Differential Equations Inverse Problems
The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach’s fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this work, we explore and compare how the two different approaches perform for selected problems: the estimation of the diffusivity for a steady-state heat equation and the estimation of the flexural rigidity for an Euler-Bernoulli beam problem. We include complicating factors, such as observational noise, point sources, and only having boundary measurements. |

Addaptive model reduction approach in optimal control applied to solve Transfer Equations | Oulghelou | Approved | Optimal control of dynamical systems is of much interest in a wide range of applications, such us aeronautics, design and mechanical systems. However, the main fear often encoun- tered is the huge tim . . . Read More ## Addaptive model reduction approach in optimal control applied to solve Transfer Equations
Optimal control of dynamical systems is of much interest in a wide range of applications, |

Stability Problem for Singular Dirac Equation System on Finite Interval | ERCAN | Approved | In this study, we show the stability spectral problem for the singular Dirac system respect to two spectra on a finite interval. The meaning of the stability problem of differential operators is to . . . Read More
## Stability Problem for Singular Dirac Equation System on Finite Interval
In this study, we show the stability spectral problem for the singular Dirac system respect to two spectra on a finite interval. The meaning of the stability problem of differential operators is to estimate the difference of their spectral functions when finite numbers of eigenvalues of operator overlap. The method is based on work by Ryabushko [12]. The paper [12] studied to what extent only finitely many eigenvalues in one or both spectra determine the potential. We obtain a bound for difference of the spectral functions for Singular Dirac equation system. |

Surface Pressure Sensitivities for the Measurement of the Mach Number and Angle of Attack of Supersonic Flows | Stoia-Djeska | Approved | In this paper we present a method for the calculation of the sensitivities in the case of supersonic flows over a bi-splopes wedge. The sensitivities are of the pressures determined at some locations . . . Read More
## Surface Pressure Sensitivities for the Measurement of the Mach Number and Angle of Attack of Supersonic Flows
In this paper we present a method for the calculation of the sensitivities in the case of supersonic flows over a bi-splopes wedge. The sensitivities are of the pressures determined at some locations on the wedge surface and are determined with respect to the time-dependent Mach number and to the angle of attack. Both of these parameters are included in the upstream boundary conditions in the numerical simulations. These sensitivities are necessary for the solution of the inverse problems in which the angle of attack and the Mach number are determined from the surface pressures measurements. The goal is the development of an air data sensor for a test vehicle which is intended to be used for drop tests from very high altitudes (Fukiba, 2012). The feasibility of the concept of such measurements was first demonstrated by (Cooper and Webster, 1951). Bibliography 1. K. Fukiba and all. Numerical Study of Flow Angles and Mach number Measurement Using the Surface Pressure of a Supersonic Aircraft with Nose Cone. Tran. Japan Soc. Aero. Space. Sci. Vol. 55, No. 2, pp. 81-88, (2012). 2. M. Cooper, R.A. Webster. The Use of an Uncalibrated Cone for Determination of Flow Angles and mach Numbers at Supersonic Speeds. NACA Technical Note 2190. (1951). |

IFSM Fractal Image Compression, Sparsity, and Total Variation Minimization: A Multiobjective Approach | La Torre | Approved | We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its invariant fixed point f is sufficiently close to f in the Lp distance. Forte and Vrscay (1 . . . Read More ## IFSM Fractal Image Compression, Sparsity, and Total Variation Minimization: A Multiobjective Approach
We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its invariant fixed point f |

Total Variation Minimization for Measure-valued Images | La Torre | Approved | We present a notion of total variation for measure-valued images. We introduce the total variation denoising problem and show an application to the case of fractal transforms on the space of measure-v . . . Read More ## Total Variation Minimization for Measure-valued Images
We present a notion of total variation for measure-valued images. We introduce the total variation denoising problem and show an application |

Total Abstracts: 9

#### Mathematical Modeling of Tires

Abstract: This session invites papers that deal with mathematical modeling and testing of tires. The force and moment generation mechanism of tires depends on the tire-road interaction and tire struct . . .Read More

##### Mathematical Modeling of Tires

*Abstract:*

**Abstract:** This session invites papers that deal with mathematical modeling and testing of tires. The force and moment generation mechanism of tires depends on the tire-road interaction and tire structure and materials properties. Authors who have developed models and test equipment simulating the behavior of the tire noise, vibration, handling, and wear are encouraged to submit their paper for this session.

**Organizer :** Saied Taheri, Virginia Tech, Blacksburg, VA 24060, USA

#### S8. Mathematical Problems in Combustion and Fire Science

Abstract: The session solicits papers on wide range of mathematical problems emerging in studies of combustion, and fires as its special case. Combustion systems in general exhibit extremely complex b . . .Read More

##### S8. Mathematical Problems in Combustion and Fire Science

*Abstract:*

**Abstract:** The session solicits papers on wide range of mathematical problems emerging in studies of combustion, and fires as its special case. Combustion systems in general exhibit extremely complex behavior, resulting from interactions of various physical and chemical phenomena over a wide range of spatial and temporal scales.

Presentations on both theoretical and numerical studies are most welcome.

Particular topics of interest include, but not limited to

reaction-diffusion systems

theoretical analysis of relevant ODE and PDEs

asymptotic analysis

instabilities, bifurcations and chaos in combustion systems

efficient and novel numerical methods (such as Lattice Boltzmann methods)

stochastic methods

mathematical models and approaches for specific applied problems

One of driving objectives for this session is to identify mathematical problems that are important for progress, but not yet receiving deserved attention from mathematical community.

The session aims to provide enjoyable open forum for interaction of theoreticians, applied mathematicians, as well as industry users. Contributions revealing new, stimulating and controversial ideas are highly encouraged.

**Organizer; Prof. Vasily Novozhilov, Victoria University (Australia)**

Title | Author | Status | Abstract |
---|---|---|---|

Fire Suppression as a Thermal Implosion | Novozhilov | Approved | The paper considers an inversion of a thermal explosion concept which we call thermal implosion. One of natural applications of the proposed concept is a phenomenon of fire suppression. Equations des . . . Read More ## Fire Suppression as a Thermal Implosion
The paper considers an inversion of a thermal explosion concept which we call thermal implosion. One of natural applications of the proposed concept is a phenomenon of fire suppression. Equations describing thermal implosion will be proposed, and their analysis presented for some of the most fundamental cases. |

APPLICATION OF FRACTIONAL CALCULUS TO MODELLING TRANSIENT COMBUSTION OF SOLID PROPELLANTS | KULISH | Approved | It was Zel’dovich, who first considered the transient combustion problem of solid propellants. Some more detailed models of that process have been developed afterwards. However, until today, numerical . . . Read More
## APPLICATION OF FRACTIONAL CALCULUS TO MODELLING TRANSIENT COMBUSTION OF SOLID PROPELLANTS
It was Zel’dovich, who first considered the transient combustion problem of solid propellants. Some more detailed models of that process have been developed afterwards. However, until today, numerical methods remain the prevailing tool for modelling unsteady combustion processes. In this work, we demonstrate that at least one of the problems of the unsteady combustion theory, which previously investigated numerically, can be treated analytically by means of fractional calculus. The solution for the unsteady speed of combustion thus derived is then compared with the solution obtained by numerical means in previous studies. The comparison shows a good agreement between those results, especially for small values of time. |

ON THE POSSIBILITY TO DEVELOP AN ADVANCED NON-EQUILIBRIUM MODEL OF DEPRESSURISATION IN TWO-PHASE FLUIDS | KULISH | Approved | Carbon dioxide is widely used as the power gas in the gas guns community due to its ease of handling, storability at room temperature, and high vapour pressure depending only upon temperature, but not . . . Read More
## ON THE POSSIBILITY TO DEVELOP AN ADVANCED NON-EQUILIBRIUM MODEL OF DEPRESSURISATION IN TWO-PHASE FLUIDS
Carbon dioxide is widely used as the power gas in the gas guns community due to its ease of handling, storability at room temperature, and high vapour pressure depending only upon temperature, but not a tank size, as long as some liquid carbon dioxide remains in the tank. This high vapour pressure can be used as the pressurant, making it what is referred to as a self-pressurising propellant. However, as a two-phase substance, carbon dioxide does have its drawbacks: (1) vaporisation of liquefied CO2 inside a tank when shooting rapidly or a lot causes the tank to get cool, resulting in pressure fluctuations that makes the gun’s performance and accuracy worse, (2) solid carbon dioxide that is also known as dry ice can appear on the output valve of the tank while shooting and it can cause damage or slow the gun’s performance down, if it works its way into some control components, including the barrel of the gun. Hence, it is crucial to obtain a scientific understanding of carbon dioxide behaviour and further the discharge characteristics of a wide range of pressure-tank configurations. For the purpose of satisfying this goal, a comprehensive discharge mathematical model for carbon dioxide tank dynamics is required. In this paper, the possibility to develop an advanced non-equilibrium model of depressurisation in two-phase fluids is discussed. |

Effects of Initial and Boundary Conditions on Thermal Explosion Development | Novozhilov | Approved | The paper presents some recent results concerning thermal explosion (autoigniiton) development. The two problems are considered 1) Effects of initial temperature non-uniformities in the mixture. This . . . Read More ## Effects of Initial and Boundary Conditions on Thermal Explosion Development
The paper presents some recent results concerning thermal explosion (autoigniiton) development. The two problems are considered 1) Effects of initial temperature non-uniformities in the mixture. This effect is considered both in steady mixtures, In both cases, final results are critical conditions (boundaries) for thermal explosion, which are found using numerical modeling. |

How simulating wildland fires: the multiphase approach ? | MORVAN | Approved | This communication demonstrates how the behaviour of wildland fires can be simulated using a multiphase formulation. This approach consists in solving the coupled system formed by the vegetation and t . . . Read More
## How simulating wildland fires: the multiphase approach ?
This communication demonstrates how the behaviour of wildland fires can be simulated using a multiphase formulation. This approach consists in solving the coupled system formed by the vegetation and the surrounding atmosphere, in assimilating the vegetation as a sparse porous media and performing a homogenization-like procedure. After a presentation of the physical and mathematical model, some numerical simulations are presented, illustrating various configurations of fires (surface fire, backfire, counter fire …), in various ecosystems (grass, shrubs), and under various external conditions (slope, wind) (Morvan et al 2009, Dupuy et al 2005, Morvan 2014). An analysis of the main scales associated with the physical mechanisms (radiation and convective heat transfer, atmospheric turbulence, combustion …) contributing to the ignition and the propagation of a forest fire (Morvan 2011) has been also proposed, with the identification of two modes of propagation, namely wind driven fire and plume dominated fire. References D. MORVAN, S. MERADJI, G. ACCARY “Physical modelling of fire spread in grasslands” Fire Safety Journal, Vol.44, pp. 50-61, 2009. J.L. DUPUY, D. MORVAN “Physical modelling of forest fire behaviour in a fuel break” Int. J. Wildland Fire Vol.14, pp.141-151, 2005. D. MORVAN “Wind effects, unsteady behaviours and regimes of propagation of surface fires in open field”, 2014, Combustion Science and Technology, Vol.186(7), pp.869-888. D. MORVAN “Physical phenomena and length scales governing the behaviour of wildfires: a case for physical modelling”, 2011, Fire Tech. Vol.47, pp.437-460. |

Modelling Emission Turbulence-Radiation Interaction by using a Hybrid Flamelet/Stochastic Eulerian Field Method | CONSALVI | Approved | The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as ‘absorption Turbulence Radiation Interaction (TRI)’ and ‘emission TRI’. Emission TRI is related to the non-l . . . Read More
## Modelling Emission Turbulence-Radiation Interaction by using a Hybrid Flamelet/Stochastic Eulerian Field Method
The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as ‘absorption Turbulence Radiation Interaction (TRI)’ and ‘emission TRI’. Emission TRI is related to the non-linear coupling between fluctuations of the absorption coefficient and fluctuations of the Planck function and can be described without introduction any approximation by using a transported PDF method. In this study, a hybrid flamelet/ Stochastic Eulerian Field Model is used to solve the transport equation of the one-point one-time PDF. In this formulation, the steady laminar flamelet model (SLF) is coupled to a joint Probability Density Function (PDF) of mixture fraction, enthalpy defect, scalar dissipation rate, and soot quantities and the PDF transport equation is solved by using a Stochastic Eulerian Field (SEF) method. Soot production is modeled by a semi-empirical model and the spectral dependence of the radiatively participating species, namely combustion products and soot, are computed by using a Narrow Band Correlated-k (NBCK) model. The model is applied to simulate an ethylene/methane turbulent jet flame burning in an oxygen-enriched environment. Model results are compared with the experiments and the effects of taken into account Emission TRI on flame structure, soot production and radiative loss are discussed. |

Total Abstracts: 6

#### S10. Nonlinear analysis, optimal design and guidance of space systems with low thrust

Abstract: The scope of the special session covers all areas of the mathematical problems of the nonlinear analysis, optimal design and guidance of space systems equipped with low thrust engines and it . . .Read More

##### S10. Nonlinear analysis, optimal design and guidance of space systems with low thrust

*Abstract:*

**Abstract: **The scope of the special session covers all areas of the mathematical problems of the nonlinear analysis, optimal design and guidance of space systems equipped with low thrust engines and its practical implementations in the aerospace engineering.

The development of new space exploration missions requires creation of space systems with improved mass-power characteristics and economic indicators. One of possible problem solutions is the use of prospective power systems based on new physical principles that provides high technical characteristics. Such systems include, for example, electric rocket propulsion system and spacecraft with solar sail. It is also noteworthy that existing classical methods of multi-objective optimization are not efficient enough for the synthesis of such space systems. We dedicate our attention to development of new mathematical methods in this field.

The main directions of this special section:

– the mechanics and the dynamics of the space flight with low thrust, including electric propulsion and a solar sailing;

– the application of the optimal control theory to the synthesis control of spacecraft;

– the analysis of the control peculiarities of large spacecrafts;

– the guidance of spacecraft with low thrust, including functioning in conditions of gravitational fields of complex configuration;

– the methods development of complex polyoptimization of the trajectories and design parameters of spacecraft.

Special session request authors to participate

**Organizers: **Prof. Olga Starinova, Samara State Aerospace University (Russia), Prof. Cui Naigang, Harbin Institute of Technology (China).

Title | Author | Status | Abstract |
---|---|---|---|

Methods of Optimal Control Choice of Non-Keplerian Orbits | Starinova | Approved | The developed method of iterative optimization of interplanetary missions with the low thrust, using sequence of movement specified mathematical models and design shape spacecraft, is realised. The ne . . . Read More
## Methods of Optimal Control Choice of Non-Keplerian Orbits
The developed method of iterative optimization of interplanetary missions with the low thrust, using sequence of movement specified mathematical models and design shape spacecraft, is realised. The new articular analytical decision describing planar movement of spacecraft with solar electric propulsion is described, allowing to construct initial approach in the iterative scheme of optimization. Developed a method of modelling and optimization of interplanetary missions ballistic schemes, based on a combination of Pontryagin’s maximum principle formalism conditions of transversality and methods of the mathematical programming, allowing to consider restrictions characteristic for concrete interplanetary missions. Recommendations for choice design-ballistic parameters of the interplanetary missions spacecraft, received taking into account features nuclear and solar power plant for missions on delivery of a payload to orbits of Mars, expeditions the Earth–Mars–Earth are received. |

Boundary problem solution of an optimal control transfer between circular orbits for an electric propulsion spacecraft in an irregular gravitational field of an asteroid | Shornikov | Approved | The paper deals with a two-point boundary problem of optimal control transfer between circular orbits for a spacecraft with an electric propulsion engine. The spacecraft manoeuvres in vicinity of the . . . Read More
## Boundary problem solution of an optimal control transfer between circular orbits for an electric propulsion spacecraft in an irregular gravitational field of an asteroid
The paper deals with a two-point boundary problem of optimal control transfer between circular orbits for a spacecraft with an electric propulsion engine. The spacecraft manoeuvres in vicinity of the asteroid Gaspra 951 with an irregular gravitational field. We propose to consider the irregular gravitational field of the asteroid as a superposition of relative gravitate points rotating near a single barycenter of the system. Consequently, the idea is to reduce the gravitational field simulation to the n-body problem. We use the proposed method for boundary value problem formalization. The task of control spacecraft’s transfer between circular orbits from 200 km to 100 km is considered. Authors propose a combination of the Pontryagin’s maximum principle and the Newton’s step by step approximation as solutions methods for the boundary problem. Authors developed a software for the boundary problem solution where operator is able to intervene in the calculation process: changing international step and increment. The main advantage of the introduced method is a remarkable increase of the solution’s convergence. |

Pulse-width control of electro-reaction engines for a station-keeping of land-survey satellite on sun-synchronous orbit | Somov | Approved | We present a method for a station-keeping of a small land-survey satellite on a sun-synchronous orbit. We have developed mathematical models of the spacecraft orbital motion taking into account princi . . . Read More
## Pulse-width control of electro-reaction engines for a station-keeping of land-survey satellite on sun-synchronous orbit
We present a method for a station-keeping of a small land-survey satellite on a sun-synchronous orbit. We have developed mathematical models of the spacecraft orbital motion taking into account principal disturbances and original scheme of the correcting engine unit (CEU) based on eight electro-reaction engines with pulse-width control of their thrust. The CEU is applied simultaneously for both correction of the satellite orbital motion and an unloading of onboard electromechanical driver from accumulated angular momentum. |

An approach for the control method’s determination for an interplanetary mission with solar sail | Gorbunova | Approved | This article is devoted to an interplanetary flight of a spacecraft with a solar sail. Model of solar sail spacecraft called Helios is designed by students of Samara State Aerospace University. We def . . . Read More
## An approach for the control method’s determination for an interplanetary mission with solar sail
This article is devoted to an interplanetary flight of a spacecraft with a solar sail. Model of solar sail spacecraft called Helios is designed by students of Samara State Aerospace University. We define heliocentric motion of the solar sail spacecraft via Keplerian elements. Authors propose to use locally-optimal control laws for the solar sail control model. The obtained laws can provide rapid change of Keplerian elements or stabilize its values. Authors used combination technique for locally-optimal control laws to obtained several trajectories for interplanetary missions. The distinctive feature of the proposed method that parameters of osculating elements are used as destination phase coordinates. Authors have received the main ballistic parameters and the trajectories of the flights to libration points of Venus and Mercury. The exact optimal control is close to obtained solution by application locally-optimal control laws, and the difference in duration of the flight is only 10 %. |

Optimization methods of near-Earth and interplanetary flights with low thrust | Salmin | Approved | The problem of improving the efficiency of space transport operations and control modes of the orbits of spacecraft now is particularly relevant. The problem of improving the efficiency of space tran . . . Read More ## Optimization methods of near-Earth and interplanetary flights with low thrust
The problem of improving the efficiency of space transport operations and control modes of the orbits of spacecraft now is particularly relevant. |

Approximate approach for optimization space flights with a small thrust on the basis of sufficient optimality conditions | Salmin | Approved | Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of sp . . . Read More
## Approximate approach for optimization space flights with a small thrust on the basis of sufficient optimality conditions
Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of spacecraft. |

Control geostationary spacecraft in orbital plane using a low thrust engine | Chetverikov | Approved | The control algorithm the parameters of the geostationary spacecraft’s orbit using low-thrust engine. We consider the only flat parameters, determining the geostationary spacecraft’s position in the o . . . Read More
## Control geostationary spacecraft in orbital plane using a low thrust engine
The control algorithm the parameters of the geostationary spacecraft’s orbit using low-thrust engine. We consider the only flat parameters, determining the geostationary spacecraft’s position in the orbit plane, namely, orbital period, eccentricity and longitude point of standing. Formulated plane problem of terminal control geostationary spacecraft. It is assumed that the corrective maneuver is implemented by creating a small transversal acceleration using electric low-thruster. Developed a discrete model of the geostationary spacecraft motion in the orbit plane under the influence of small transversal acceleration. The solution of this problem using traditional dynamic programming method based on the use of Bellman equation, is difficult to obtain, because the discrete model of geostationary spacecraft motion is a nonlinear system of equations. Therefore, the proposed approximate scheme of solving the problem based on the three-step algorithm of terminal control the orbital period, eccentricity and longitude point of standing. The result is solution flat problem of the terminal control in the analytical form. Analytical expressions for the cost estimate characteristic velocity of corrective maneuver. When modeling the motion of a geostationary spacecraft under the influence of a small transversal acceleration, algorithm showed high accuracy of solving the terminal control problem. |

Total Abstracts: 7

#### S11. Nonlinear Engineering Problems with Singularities

Abstract: The scope of Session may include but not limited to following scientific directions: Mechanical systems with critical parameters. Mechanical systems with configuration manifold having self- . . .

Organizers: Dr. Yury Selyutskiy, Dr. Oleg Cherkasov and me, Dr. Marat Dosaev. Lomonosov Moscow State University.

##### S11. Nonlinear Engineering Problems with Singularities

*Abstract:*

**Abstract: **The scope of Session may include but not limited to following scientific directions: Mechanical systems with critical parameters. Mechanical systems with configuration manifold having self-intersections. Auto-oscillations, instability and shock inspired by dry friction. Problems of body motion in resisting medium. Nonlinear bifurcation problems in wind engineering.** **

** Organizers: **Dr. Yury Selyutskiy, Dr. Oleg Cherkasov and me, Dr. Marat Dosaev. Lomonosov Moscow State University.

Title | Author | Status | Abstract |
---|---|---|---|

Helicopter Flight Control by Dynamic Compensator | Yaici | Approved | In a precedent paper a design process is described to achieve eigenstructure assignment using block poles placement. Systems described in state space equations are transformed to systems in matrix fra . . . Read More
## Helicopter Flight Control by Dynamic Compensator
In a precedent paper a design process is described to achieve eigenstructure assignment using block poles placement. Systems described in state space equations are transformed to systems in matrix fractions description (MFD), in which the denominator and the numerator are matrix polynomials. As for systems in state space description (SSD) the behavior is defined by the eigenstructure of its state matrix, the behavior of systems in MFD is defined by the latent structure (latent values and latent vectors) of the denominator. To such matrix polynomials we define block roots (called block poles for the denominator and block zeros for the numerator). From a set of latent values and corresponding latent vectors a block root can be constructed. Thus a desired eigenstructure can transformed to a desired latent structure, which is used to construct desired block poles. The method proposed here allows the assignment of the whole set (and even more) of latent values and vectors obtained. The input-output feedback configuration has been chosen to design the compensator which allows the placement of block poles of a desired denominator constructed from a desired latent structure. In this paper, the proposed design method is applied for attitude stabilization of a Lynx helicopter in hover. Helicopters are inherently unstable, very non-linear and highly cross coupled, and thus must be augmented with feedback control to reduce the pilot workload to an acceptable level. So a presentation of some research works on flight control is given, then the details of the design process of the compensator, starting from a desired eigenstructure, are presented. To validate the results, the output responses are compared to state and output feedback control responses, and some of these shapes are shown. The proposed method results has better parameters: a better peak angle, the initial response delay is more confined, and presents a better damping and shaping of the response. It was shown that the input-output feedback configuration was able to retain the performance of a state-feedback solution while using only measurable information. |

Treatment of flow singularity for exiting liquid jet from a hydrophobic channel | Khayat | Approved | The flow of a slipping fluid jet is examined theoretically as it emerges from a channel at moderate Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The p . . . Read More
## Treatment of flow singularity for exiting liquid jet from a hydrophobic channel
The flow of a slipping fluid jet is examined theoretically as it emerges from a channel at moderate Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. A similarity solution is obtained in the inner layer near the free surface, with the outer layer extending to the jet centerline. A slipping jet is found to contract very near and far from the channel exit but does not have a definite behavior in between, compared to for an adhering jet. Eventually, the jet reaches uniform conditions far downstream. As in the case of entry flow, there is a rapid departure in flow behavior for a slipping jet as the slip length. This rapid change is notably observed in the drop of boundary-layer thickness, increase in exit and relaxation lengths as well as in jet width with slip length. Finally, the connection with microchannel and hydrophobic flows is highlighted. |

Nonlinear Mathematical Models for Paths Maintaining Constant Normal Accelerations | Pakdemirli | Approved | Authors: Mehmet Pakdemirli and Volkan Yıldız Ordinary differential equation models describing paths for which the normal acceleration components of the objects remain constant is derived. The normal . . . Read More ## Nonlinear Mathematical Models for Paths Maintaining Constant Normal Accelerations
Authors: Mehmet Pakdemirli and Volkan Yıldız |

Range Maximization and Brachistochrone Problem with Dry Friction, Viscous Drag and Accelerating Force | Cherkasov | Approved | Cherkasov O.Yu., Zarodnyuk A.V. The range maximization problem and corresponding the brachistochrone problem with Coulomb, viscous friction and accelerating force are considered. A maximum principle . . . Read More ## Range Maximization and Brachistochrone Problem with Dry Friction, Viscous Drag and Accelerating Force
Cherkasov O.Yu., Zarodnyuk A.V. |

Comparison of energy costs for different control laws of a vibratory robot | Kulikovskaya | Approved | In the study there are introduced several control methods that maximize average velocity of the vibratory robot subject to several constraints. The robot is presented by a rigid box with a pendulum in . . . Read More
## Comparison of energy costs for different control laws of a vibratory robot
In the study there are introduced several control methods that maximize average velocity of the vibratory robot subject to several constraints. The robot is presented by a rigid box with a pendulum inside it. It can move forwards and backwards and there is a Coulomb friction between the box and the surface. In the paper it is not only shown the difference and advantages of proposed control laws but there is also done a comparison between works done by motor for different control cases. |

Evolution of rotational motions of a rigid body similar to pseudoregular precession in the Lagrange case | Leshchenko | Approved | Perturbed rotational motions of a rigid body similar to pseudoregular precession in the Lagrange case when perturbation torque slowly varying with time. Conditions are presented for the possibility o . . . Read More
## Evolution of rotational motions of a rigid body similar to pseudoregular precession in the Lagrange case
Perturbed rotational motions of a rigid body similar to pseudoregular precession in the Lagrange case when perturbation torque slowly varying with time. Conditions are presented for the possibility of averaging the equations of motion with respect to the nutation angle is conducted. The averaged system of equations of motion is obtained. A mechanical model of the perturbations, corresponding to the body’s motion in a medium with linear dissipation, is considered. Evolution of the projection of the angular momentum vector onto the vertical, the body’s total energy and the projection of the angular velocity vector onto the axis of dynamic symmetry are determined. The obtained solutions have an independent value for applications. |

Mechanical Systems with Singularities | Vitaly | Approved | Mechanisms with critical parameters are considered. Finding so-called dead center positions is shown. Mechanical systems having self-intersections in configurational manifold are presented. Stability . . . Read More
## Mechanical Systems with Singularities
Mechanisms with critical parameters are considered. Finding so-called dead center positions is shown. Mechanical systems having self-intersections in configurational manifold are presented. Stability and bifurcations of equilibriums of mechanical systems will be discussed. Bifurcations of solutions in the problem of equilibrium of a slipper brake will be considered without and with the presence of an external force. |

On auto-oscillations of a plate in flow | Selyutskiy | Approved | Self-sustaining oscillations (auto-oscillations) of bodies of different shape in flow is a well known phenomenon. It is observed both for streamlined (like plates or wings) or bluff bodies (cylinders) . . . Read More
## On auto-oscillations of a plate in flow
Self-sustaining oscillations (auto-oscillations) of bodies of different shape in flow is a well known phenomenon. It is observed both for streamlined (like plates or wings) or bluff bodies (cylinders). In order to describe this effect and related features, an attached oscillator model is used. Characteristics of limit cycles arising in the resulting dynamical system are analyzed depending on parameters. Evolution of limit cycles with changing flow speed is studied. It is shown that calculations performed in the framework of the model qualitatively agree with available experimental data. |

Electromechanical imitator of antilock braking modes of wheels with pneumatic tire and its application for the runways friction coefficient measurement | Putov | Approved | The towed complex of prelanding control of runways friction coefficient for the purpose of ensuring the safe landing of aircraft runways is discussed. Measuring is carried out by rolling with sliding . . . Read More
## Electromechanical imitator of antilock braking modes of wheels with pneumatic tire and its application for the runways friction coefficient measurement
The towed complex of prelanding control of runways friction coefficient for the purpose of ensuring the safe landing of aircraft runways is discussed. Measuring is carried out by rolling with sliding measuring wheel along the proposed path of the aircraft wheels and calculating the friction coefficient on the measured force of sliding. |

Modeling of indentation into inhomogeneous soft tissues | Lyubicheva | Approved | Lyubicheva A.N., Goryacheva I.G., Dosaev M.Z., Su F.-Ch. A simulation of a contact interaction of the indenter and inhomogeneous soft biological tissues is carried out. The soft tissue is modeled by . . . Read More ## Modeling of indentation into inhomogeneous soft tissues
Lyubicheva A.N., Goryacheva I.G., Dosaev M.Z., Su F.-Ch. |

Stability domains for vane with viscose filling | Dosaev | Approved | The motion of a four-blade axisymmetric vane with fixed point is considered in the constant flow of medium. This is a mechanical system with variable dissipation. Stability of the permanent rotation o . . . Read More
## Stability domains for vane with viscose filling
The motion of a four-blade axisymmetric vane with fixed point is considered in the constant flow of medium. This is a mechanical system with variable dissipation. Stability of the permanent rotation of vane in medium flow is studied. We consider the stability conditions for of this motion. Stability domains are found. |

A Predication model for combustion modes of the scramjet-powered aerospace vehicle based on the nonlinear features of the isolator flow field | YANG | Approved | The supersonic combustion ramjet (scramjet) engine remains the most promising airbreathing engine cycle for hypersonic flight, particularly the high-performance dual-mode scramjet in the range of flig . . . Read More
## A Predication model for combustion modes of the scramjet-powered aerospace vehicle based on the nonlinear features of the isolator flow field
The supersonic combustion ramjet (scramjet) engine remains the most promising airbreathing engine cycle for hypersonic flight, particularly the high-performance dual-mode scramjet in the range of flight Mach number from 4 to 7, because it can operates under different combustion modes. Isolator is a very key component of the dual-mode scramjet engine. |

Total Abstracts: 12

#### S12. Simple and Robust Adaptive Control

Abstract: Theoretical contributions of the 1970s, based on Lyapunov stability theory, led to firstnproofs of stability and had an important role in the development of model reference adaptive control . . .Read More

##### S12. Simple and Robust Adaptive Control

*Abstract:*

**Abstract**: Theoretical contributions of the 1970s, based on Lyapunov stability theory, led to firstnproofs of stability and had an important role in the development of model reference adaptive control (MRAC) methodologies. However, the need to know the order of the controlled plant and also the complexity of the resulting controller make the applicability of these methods difficult in real large order systems. Even if only prior knowledge on an upper bound of this order is needed, this does not help reducing the complexity of the adaptive controller. For example, the order of large flexible systems is theoretically infinite and even if the number of modes in real-world is finite, the order of the resulting controller is larger than anything that can be practically implemented.

The previous decades have seen developments of new adaptive control techniques under such names as “simple adaptive control (SAC)” and similar. Although they use different approaches, all these techniques tend to use adaptive controllers, which try to avoid the need for very large order and complex computations and, therefore, are suitable for application in real world systems.

Last few years have seen quite a few works that, though different, have something in common: each one deals with large realistic plants, such as robot manipulators, planes, missiles, re-entry vehicles, large processes, etc. Application designers have first tried classical design and ended up with less than satisfactory results, whereas the adaptive control techniques performed much better, both with respect to speed of response and accuracy of tracking and even with respect to noise reduction. Some papers treated the fine theoretical issues related to adaptive control dealing with uncertainties, variable environments, nonlinear systems or systems with delays.

The proposed special session invites prospective authors to present both their particular contributions to the theoretical problems related to stability and performance and the detailed presentation of their particular realistically large applications.

**Organizer; Prof Itzhak Barkana**

Title | Author | Status | Abstract |
---|---|---|---|

PASSIFICATION BASED SIMPLE ADAPTIVE CONTROL OF QUADROTOR ATTITUDE: ALGORITHMS AND TESTBED RESULTS | Andrievsky | Approved | In the paper, the results of the Passification Method with the Implicit Reference Model (IRM) application for designing the simple adaptive controller for quadrotor attitude are presented. The IRM de . . . Read More
## PASSIFICATION BASED SIMPLE ADAPTIVE CONTROL OF QUADROTOR ATTITUDE: ALGORITHMS AND TESTBED RESULTS
In the paper, the results of the Passification Method with the Implicit Reference Model (IRM) application for designing the simple adaptive controller for quadrotor attitude are presented. The IRM design technique makes it possible to relax the matching condition, known for habitual MRAC systems, and leads to simple adaptive controllers, ensuring fast tuning the controller gains, high robustness with respect to nonlinearities in the control loop, to the external disturbances and the unmodeled plant dynamics. The simulation results are presented and compared with obtained by the standard PD- and feedback linearization control technique. For experimental evaluation of the adaptive systems performance, the compact laboratory testbed has been created and launched. It is clear that testing the new control algorithms is connected with possibility of serious accidents due to the algorithmic drawbacks, programming mistakes, sensor errors, etc, which may cause quadrotor damage or breaking, and to injury the people, as well. For flight testing, the spacy area, which is free from different obstacles is demanded. Also, flight testing procedure is very time consuming for the researchers. To overcome the mentioned problems at the initial stage of real-world adaptive controllers design the indoor testbed has been used. The testbed allows to safely test new control algorithms in the laboratory area with a small space and promptly make changes in cases of failure. The main part of the testbed is the quadrotor, which is installed on the 2DOF gimbal suspension, allowing the quadrotor to freely rotate on pitch and roll. The outer frame is mounted on the pillars and can rotate about the horizontal axis. The inner gimbal frame can rotate with respect to the outer one. Quadrotor is fixed in the middle of the inner frame. The quadrotor center of mass is fixed, eliminating an opportunity of unforeseen changes and the dangerous trajectory. Pillars are mounted on the square support. Whole construction is made from wood and metal angle braces. The tested quadrotor is based on radiating frame DJI 450 and supplied with Ardupilot Mega 2.6 autopilot with the IMU, the GPS the satellite navigation system. The brushless motors with external rotor DJI 2213 (250 W each) are used as actuators. The device is supplied with the Electronic Speed Controllers (ESC) DJI 30A Opto with current output up to 30 A and with operating voltages up to 14.8 V, rotors left and right rotation with the size 10 x 4.5 or 8 x 4.5 inches. The real-time data exchange with the operator’s PC is fulfilled by means of WiFi XBee modems. The testing results of simple adaptive control of quadrotor pitch and roll angles, their comparison with ones, obtained via the simulations, and the parameter identification results are presented. The work was performed in the IPME RAS, supported by RSF (grant 14-29-00142). |

Implementation of SAC in Target Tracking Loop | Rusnak | Approved | The existing SAC architecture requires the knowledge of a model whose output is followed by the controlled system. This control architecture is suitable for motion control applications where the requi . . . Read More
## Implementation of SAC in Target Tracking Loop
The existing SAC architecture requires the knowledge of a model whose output is followed by the controlled system. This control architecture is suitable for motion control applications where the required trajectory of the controller plant is known. The SAC algorithm uses the input of the trajectory generator, its state and output to drive the tracking error to zero (in the deterministic case). |

The new Theorem of Stability and Gain Convergence in Simple Adaptive Control | Barkana | Approved | Convergence of the adaptive control gains when the presence of sufficient excitation is not available has remained an open question for more than 30 years. The rather common opinion that in these case . . . Read More ## The new Theorem of Stability and Gain Convergence in Simple Adaptive Control
Convergence of the adaptive control gains when the presence of sufficient excitation is not available |

Simple Adaptive Control for Quadcopters with Saturated Actuators | Borisov | Approved | The stabilization problem for quadcopters with saturated actuators is considered. A simple adaptive output control approach is proposed. The control law “consecutive compensator” is augmented with the . . . Read More
## Simple Adaptive Control for Quadcopters with Saturated Actuators
The stabilization problem for quadcopters with saturated actuators is considered. A simple adaptive output control approach is proposed. The control law “consecutive compensator” is augmented with the auxiliary integral loop and anti-windup scheme. Efficiency of the obtained regulator was confirmed by simulation of the quadcopter control problem. The authors of this work are Oleg Borisov, Alexey Bobtsov, Anton Pyrkin, Vladislav Gromov. |

Adaptive sliding mode control for nonlinear systems with unknown time-varying uncertainties | Liao | Approved | This paper proposes a new adaptation methodology for the control of a class of nonlinear systems with unknown time-varying bounded uncertainties. The proposed method does not require any prior knowled . . . Read More
## Adaptive sliding mode control for nonlinear systems with unknown time-varying uncertainties
This paper proposes a new adaptation methodology for the control of a class of nonlinear systems with unknown time-varying bounded uncertainties. The proposed method does not require any prior knowledge of the uncertainties, including their bounds. Reference: |

Adaptive control of an unmanned aerial vehicle | Putov | Approved | The paper deals with development and investigation of searchless adaptive control systems for unmanned aerial vehicle (UAV) in conditions of nonlinearity and uncertainty of dynamic characteristics and . . . Read More
## Adaptive control of an unmanned aerial vehicle
The paper deals with development and investigation of searchless adaptive control systems for unmanned aerial vehicle (UAV) in conditions of nonlinearity and uncertainty of dynamic characteristics and effect of atmospheric turbulence and wind disturbances. |

A Dynamic Controller Guaranteeing Almost Strict Positive Realness of the Interconnected System | Kim | Approved | This paper addresses the problem of designing a dynamic controller for a given MIMO LTI system (not necessarily being strictly positive real) such that their interconnection becomes almost strictly p . . . Read More
## A Dynamic Controller Guaranteeing Almost Strict Positive Realness of the Interconnected System
This paper addresses the problem of designing a dynamic controller for a given MIMO LTI system (not necessarily being strictly positive real) such that their interconnection becomes almost strictly positive real (ASPR), i.e., the interconnected system can be rendered strictly positive real by a static output feedback controller. A Riccati-type characterization is given to guarantee the ASPRness of such interconnection, and is shown to be equivalent to the minimum phaseness of the interconnected system having vector relative degree {1,…,1}. Based on this, a particular interconnection structure of a system and controller is considered, i.e., dynamic controller interconnected in parallel with the system. Then, a sufficient condition is given for the existence of such dynamic controller, termed as parallel feedforward compensator (PFC), which guarantees the minimum phaseness and vector relative degree {1,…,1} of the parallel interconnected system. Finally, an observer-based construction of such PFC is given with the additional ability of assigning the zeros of the interconnected system. |

On the Synthesis of Nonlinear Sliding Mode Controller for the Autopilot Design of Free Flight System | K B | Approved | Today’s rapid growth in air transportation demand leads to the problem of congestion in air traffic routes. Free flight concept is widely discussed as the solution to this problem in recent years. Fre . . . Read More
## On the Synthesis of Nonlinear Sliding Mode Controller for the Autopilot Design of Free Flight System
Today’s rapid growth in air transportation demand leads to the problem of congestion in air traffic routes. Free flight concept is widely discussed as the solution to this problem in recent years. Free flight is a decentralized method of air traffic management, in which each aircraft has the freedom to self-optimize its own route. Conflict detection and its subsequent resolution are the major challenges in the realization of this concept. Today’s modern navigation and surveillance equipment like Global Positioning System (GPS), Automatic Dependent Surveillance- Broadcast ADS-B, etc. can ensure accurate conflict predictions. Once a conflict is detected, it should be avoided through suitable conflict avoidance maneuvers. An autopilot capable of initiating these conflict free maneuvers should be thus a necessary component of any aircraft in free flight to ensure conflict avoided flight. Autopilot design for this purpose based on Sliding Mode Control (SMC) strategy is presented in this paper since SMC can guarantee the property of robustness which results in a highly confident autopilot design. SMC design based on a nonlinear aircraft model is being encompassed so that the drawbacks associated with linear SMC design are overcome. Four different approaches of SMC control law for nonlinear systems viz., 1) Linear feedback control with switched gains, 2) Augmented equivalent plus relay control, 3) Constant plus proportional reaching law method, 4) Power rate reaching law method, are considered here for the implementation of free flight autopilot system. The performances of all these four methods are validated through simulation studies using MATLAB considering typical free flight conflict avoidance scenarios. The four control laws are compared based on their ability to reduce chattering, maximum tolerance to parametric uncertainties and improved settling time so as to select the best controller among the four considered methods, which can be used for the autopilot implementation. Keywords: Air Traffic Control, Chattering, Conflict, Free Flight, Resolution, Robustness, Sliding Mode Control |

A Direct Implicit Reference Model Adaptive Control for SIMO Linear Time Invariant Systems with Super-Twisting-Like Terms | Popov | Approved | Alexander Popov, Vladimir Salikhov The Implicit Reference Model (IRM) is a well-known approach simple adaptive control of linear and some nonlinear systems. IRM adaptive control is used for linear t . . . Read More ## A Direct Implicit Reference Model Adaptive Control for SIMO Linear Time Invariant Systems with Super-Twisting-Like Terms
Alexander Popov, Vladimir Salikhov The Implicit Reference Model (IRM) is a well-known approach simple |

Bifurcation Analysis and Control of Aircraft Dynamics in Constrained Trims – A Direct Approach | Vora | Approved | Dynamical systems theory has been applied to provide intuitive understanding of nonlinear dynamics of multi-parametric non-linear systems such as an aircraft. A Bifurcation Analysis and Continuation T . . . Read More
## Bifurcation Analysis and Control of Aircraft Dynamics in Constrained Trims – A Direct Approach
Dynamical systems theory has been applied to provide intuitive understanding of nonlinear dynamics of multi-parametric non-linear systems such as an aircraft. A Bifurcation Analysis and Continuation Theory Methodology (BACTM) has been instrumental in studying nonlinear behavior of aircraft associated with onset of instabilities and loss of control. Numerical continuation, an integral part of the BACTM, is used to compute the steady state solutions and their local stability as function of a changing parameter of the system. While a single parameter continuation and bifurcation analysis is in-vogue to study bifurcations of an aircraft model, constrained conditions in which aircraft usually operate and call for deployment of two or more controls simultaneously, for example cruise flight conditions, require a two step Extended Bifurcation Analysis (EBA) technique for computation of trim and stability. The first step of EBA requiring computation of constrained equilibrium solutions and the second step for computing stability of constrained equilibrium solutions and bifurcations from constrained solutions. The EBA technique based on a continuation algorithm such as AUTO2000 has its own limitations and shortcomings when applied to analysis of dynamical systems under constraints. |

Adaptive synchronization of robot-manipulators for tracking problem | Popov | Approved | Alexander Popov, Vladimir Salikhov, Dmitriy Lisin, Tagir Nigmatulin It is an important issue to coordinate multiple robotsin carrying out assembly tasks in modern manufacturing and space applicat . . . Read More ## Adaptive synchronization of robot-manipulators for tracking problem
Alexander Popov, Vladimir Salikhov, Dmitriy Lisin, Tagir Nigmatulin It is an important issue to coordinate multiple robotsin carrying out |

Total Abstracts: 11

#### S15. Stochastic Processes and Fields in Engineering

Abstract: This special session is devoted to applications of random functions of one or more variables to physical and engineering problems. We plan to discuss the newest applications to continuum phy . . .Read More

##### S15. Stochastic Processes and Fields in Engineering

*Abstract:*

**Abstract:** This special session is devoted to applications of random functions of one or more variables to physical and engineering problems. We plan to discuss the newest applications to continuum physics, earthquake engineering, financial engineering, partial differential equations with random initial conditions, etc. Researchers having various mathematical, physical, and engineering background, will participate in the session.

**Organizer**: Professor Anatoliy Malyarenko, Mälardalen University, Sweden.

Title | Author | Status | Abstract |
---|---|---|---|

Spectral expansions of tensor-valued random fields (invited talk) | Malyarenko | Approved | Many physical quantities, like the temperature, the velocity of a turbulent fluid, the strain and the elasticity tensors of a deformable body, can be modelled as a homogeneous and isotropic tensor-val . . . Read More
## Spectral expansions of tensor-valued random fields (invited talk)
Many physical quantities, like the temperature, the velocity of a turbulent fluid, the strain and the elasticity tensors of a deformable body, can be modelled as a homogeneous and isotropic tensor-valued random field. Calculating the spectral expansion of such a field is an interesting task, and such expansions have alot of practical applications. We give an overview of the current state of art in the area. In particular, we show how various parts of mathematics, including Group Representations, Special Functions, Invariant Theory, and Geometry of Convex Compacta, interplay in obtaining mathematically interesting expansions. |

Scaling to RVE in Viscoelastic Random Composites | Ostoja-Starzewski | Approved | This paper investigates the scaling from a mesoscale level to Representative Volume Element (RVE) of spatially random linear viscoelastic materials, focusing on the quasi-static properties. Requiring . . . Read More
## Scaling to RVE in Viscoelastic Random Composites
This paper investigates the scaling from a mesoscale level to Representative Volume Element (RVE) of spatially random linear viscoelastic materials, focusing on the quasi-static properties. Requiring the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on RVE response are developed from the Hill-Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The scalings (or scale dependencies) of mesoscale bounds, in time and frequency domains, are obtained through computational mechanics for composites with planar random checkerboard microstructures. In general, the frequency dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random checkerboards and, essentially, is only a function of the microstructure and mesoscale. |

Randomly Stopped Stochastic Processes | Silvestrov | Approved | Dmitrii Silvestrov Stockholm University E-mail: silvestrov@math.su.se A survey of models, problems and methods of asymptotic analysis for randomly stopped stochastic processes is presented in context . . . Read More ## Randomly Stopped Stochastic Processes
Dmitrii Silvestrov A survey of models, problems and methods of asymptotic analysis for randomly stopped stochastic processes is presented in context of various applications in statistics, engineering, finance and insurance. References [1] Silvestrov, D.S. (2004). Limit Theorems for Randomly Stopped Stochastic Processes. |

Anatoliy Malyarenko and Martin Ostoja-Starzewski. Random fields related to the symmetry classes of second-order symmetric tensors | Malyarenko | Approved | A second-order symmetric tensor can either be orthotropic, transverse isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed . . . Read More
## Anatoliy Malyarenko and Martin Ostoja-Starzewski. Random fields related to the symmetry classes of second-order symmetric tensors
A second-order symmetric tensor can either be orthotropic, transverse isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed point set of the class that is isotropic with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields. |

Approximation methods of European option pricing in multiscale stochastic volatility model | Ni | Approved | Approximation methods of European option pricing in multiscale stochastic volatility model Ying Ni, Betuel Canhanga, Anatoliy Malyarenko, Sergei Silvestrov In the classical Black-Scholes model for fin . . . Read More ## Approximation methods of European option pricing in multiscale stochastic volatility model
Approximation methods of European option pricing in multiscale stochastic volatility model Ying Ni, Betuel Canhanga, Anatoliy Malyarenko, Sergei Silvestrov In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be more effective in terms of capturing the empirical facts. However in order to capture more features of the volatility smile, researchers have suggested a multiscale stochastic volatility model which contains two volatility factors. These two volatility factors follow mean-reverting processes but at different reverting rates, with one factor reverting fast and the other one reverting slowly. In the present paper we consider the European option pricing problem under one type of the multiscale stochastic volatility model. Whereas an analytical solution to such problem is still missing there are several approximation methods using different approaches. We examine the properties of two existing approximation methods, namely the method by Chiarella and Ziveyi [2] using characteristics of PDEs, Fourier and Laplace transforms and the method by Canhanga et al. [1] using asymptotic expansions. Monte Carlo simulation with variance reduction techniques is implemented as a reference method. [1] Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. “Perturbation methods [2] Chiarella, C., and Ziveyi, J. “American option pricing under two stochastic volatility |

Fractional Poisson Random Fields | Leonenko | Approved | We present new properties for the Fractional Poisson process and the Fractional Poisson fields on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this res . . . Read More ## Fractional Poisson Random Fields
We present new properties for the Fractional Poisson process and the Fractional Poisson fields on the plane. A martingale characterization |

Total Abstracts: 6

#### S14. Statistics and Modeling

Abstract: We focuses on good practices in both modelling and statistics for engineering, Reliability, testing and physical sciences. Both applied and theoretical aspects are considered. In particular . . .Read More

##### S14. Statistics and Modeling

*Abstract:*

Abstract: We focuses on good practices in both modelling and statistics for engineering, Reliability, testing and physical sciences. Both applied and theoretical aspects are considered. In particular, several issues important for mathematical Problems in Engineering, Aerospace and Science from statistical point of view will be covered, e.g. Quantization Dimension of Distributions, testing for reliability among others.

Organizers: Milan Stehlik, Professor at Institute of Statistics, University of Valparaíso, V Región, Valparaíso, Chile and Assoc. Professor at Johannes Kepler University, Linz, Austria

Title | Author | Status | Abstract |
---|---|---|---|

Recognition of human activities from situation based model | SALIMA | Approved | The notion of learning includes many methods to build a model of reality from data or improving a partial model less general or by creating a new model. There are two main learning trends: (i) Artific . . . Read More
## Recognition of human activities from situation based model
The notion of learning includes many methods to build a model of reality from data or improving a partial model less general or by creating a new model. There are two main learning trends: (i) Artificial intelligence methods which are qualified as symbolic, (ii) the statistical methods, qualified as digital. The cognitive model proposed in this paper combine the two approaches for a better perception and context analysis in ambient intelligent environments to achieve human activities recognition. |

Estimating The Quantization Dimension of Distributions | Poetzelberger | Approved | We present estimators of the dimension of the support of a probability distribution. These estimators are derived from the concept of quantization dimension. For the general case consistency results . . . Read More
## Estimating The Quantization Dimension of Distributions
We present estimators of the dimension of the support of a probability distribution. These estimators are derived from the concept of quantization dimension. For the general case consistency results are discussed. Versions of the estimators may be applied for instance to estimate the dimension of the driving Brownian motion of Itô processes or the dimension of the attractor of a dynamical system. A second application of estimators of dimension is the analysis of high-dimensional data X where the stochastic properties of X are explained by a vector of factors W in the sense that for a sufficiently smooth (Lipschitz) mapping f, X=f(W) and s:=\mbox{dim}(W)<<\mbox{dim}(X)=:d. |

Control charts and differentiation of sampling schemes among Phase I and Phase II | Economou | Approved | Statistical process monitoring (SPM) is extensively used in order to secure not only the quality of the output of industrial processes but also to determine the state of processes. One of the main cha . . . Read More
## Control charts and differentiation of sampling schemes among Phase I and Phase II
Statistical process monitoring (SPM) is extensively used in order to secure not only the quality of the output of industrial processes but also to determine the state of processes. One of the main challenges in SPM is the differentiation of sampling schemes among Phase I and Phase II that appears in many practical problems. A characteristic example of such a situation arises when we monitor measurements taken for example from a car repair station (Phase II) using control limits that were calculated using samples taken during the vehicle testing procedure carried out by the car manufacturer (Phase I). In the present work a new approach is proposed in order to overcome this change when passing from Phase I to Phase II without loosing all the available information from Phase I. |

IMPORTANCE ASSESMENT OF AGING MULTI-STATE WATER COOLING SYSTEM BY LZ-TPANSFORM METHOD | Frenkel | Approved | Modern high-tech equipment requires precise temperature control and effective cooling below the ambient temperature. Greater cooling efficiencies will allow equipment to be operated for longer period . . . Read More
## IMPORTANCE ASSESMENT OF AGING MULTI-STATE WATER COOLING SYSTEM BY LZ-TPANSFORM METHOD
Modern high-tech equipment requires precise temperature control and effective cooling below the ambient temperature. Greater cooling efficiencies will allow equipment to be operated for longer periods without overheating, providing a greater return on investment and increased in availability of the equipment. This paper presents application of the Lz-transform method to importance assessment of aging multi-state water cooling system used in one of Israeli hospitals. The water cooling system consists of 3 principal sub-systems: chillers, heat exchanger and pumps. The performance of the system and the sub-systems is measured by their produced cooling capacity. Heat exchanger is an aging component. Straightforward Markov method applied to solve this problem will require building of a system model with numerous numbers of states and solving a corresponding system of multiple differential equations. Lz-transform method, which is used for calculation of the system elements importance, drastically simplified the solution. Numerical example is presented to illustrate the described approach. |

Total Abstracts: 4

#### S13. Soliton Theory and Integrability in Mathematical Physics

Abstract: In recent years, nonlinear differential equations have been extensively used to mathematical models of interesting and important phenomena that have been observed in broad science and techno . . .Read More

##### S13. Soliton Theory and Integrability in Mathematical Physics

*Abstract:*

Abstract: In recent years, nonlinear differential equations have been extensively used to mathematical models of interesting and important phenomena that have been observed in broad science and technology area. In the last decades, many powerful methods to construct exact and analytical solutions of nonlinear differential equations have been established and developed, which lead to one of the most excited advances of nonlinear science and theoretical physics. These relatively new methods proved to be fully synchronized with the complexities of the physical problems. Investigating integrability and finding exact solutions for nonlinear evolution equations also plays an important role in the study of nonlinear physical phenomena.

This special session aims to combine contributions across a variety of exact and analytical solutions of nonlinear differential equations, understanding integrability of system and dynamical behaviors (properties) of solutions for nonlinear evolutions and invite authors to submit original research and/or domain reviews in various methods. This session will become an international forum for researchers to present the most recent research and ideas about soliton theory and integrability in mathematical physics. Original research that reflects the recent theoretical advances and experimental results as well as new topics are invited on all aspects of object tracking.

Potential topics include, but are not limited to:

• Soliton Theory

• Conservation laws

• Painleve Analysis

• Fractional Differential equations

• Nonlinear Evolution equations

• Further equations in physics and applied mathematics.

Organizer: Abdelouahab Kadem Setif University Algeria ,Ahmet Bekir, Eskisehir Osmangazi University, Turkey, Melike Kaplan, Eskisehir Osmangazi University,Turkey Omer Unsal, Eskisehir Osmangazi University,, Turkey

Title | Author | Status | Abstract |
---|---|---|---|

Conservation laws and exact solutions of Boussinesq-Burger equation | KAPLAN | Approved | The conservation laws play an important role in the solution and reduction of partial differential equations. Also obtaining exact solutions of these equations is a significant topic. In . . . Read More ## Conservation laws and exact solutions of Boussinesq-Burger equation
The conservation laws play an important role in the solution and reduction of partial differential equations. Also obtaining exact solutions of these equations is a significant topic. |

The Auto- Bäcklund transformations for the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation | KAPLAN | Approved | More and more physical structures of nonlinear partial differential equations have attracted a lot of interests due to their applications in many important scientific problems. Apart from their theore . . . Read More
## The Auto- Bäcklund transformations for the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation
More and more physical structures of nonlinear partial differential equations have attracted a lot of interests due to their applications in many important scientific problems. Apart from their theoretical importance, they have remarkable applications to many physical systems such as mechanics, hydrodynamics, nonlinear optics, plasma and field theories and so on. |

Multiple Scales Analysis and Travelling Wave Solutions for KdV Type Nonlinear Evolution Equations | Ayhan | Approved | Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years . . . Read More
## Multiple Scales Analysis and Travelling Wave Solutions for KdV Type Nonlinear Evolution Equations
Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics. |

A Family of Exact Travelling Wave Solutions of (2+1)-dimensional KdV4 Equation | Ayhan | Approved | Nonlinear evolution equations have a wide range of applications in science and engineering. In recent years many powerful methods to construct exact solutions of nonlinear evolution equations. In this . . . Read More
## A Family of Exact Travelling Wave Solutions of (2+1)-dimensional KdV4 Equation
Nonlinear evolution equations have a wide range of applications in science and engineering. In recent years many powerful methods to construct exact solutions of nonlinear evolution equations. In this paper we present extended simplest equation method (SEM) and the modification of the truncated expansion (MTEM) method for (2+1)-dimensional KdV4 equation to establish new exact solutions. So periodic and hyperbolic function solutions are obtained for this equation. The efficiency of the these methods for finding travelling wave solutions of the high order nonlinear evolution equations is demonstrated. |

The (G’/G)-expansion method for the nonlinear time fractional differential equations | Ünsal | Approved | Fractional differential equations have been used nowadays frequently in various applications for modelling heat transfer, seismic wave analysis, signal processing, control theory and many other fract . . . Read More
## The (G’/G)-expansion method for the nonlinear time fractional differential equations
Fractional differential equations have been used nowadays frequently in various applications for modelling heat transfer, seismic wave analysis, signal processing, control theory and many other fractional dynamical systems. |

Singular 1-solution of the nonlinear variable-coefficient diffusion–reaction and mKdV equations | Ünsal | Approved | The study of nonlinear evolution equations (NLEEs) is very important in various areas of applied mathematics and theoretical physics. Searching for exact soliton solutions of these equations plays an . . . Read More
## Singular 1-solution of the nonlinear variable-coefficient diffusion–reaction and mKdV equations
The study of nonlinear evolution equations (NLEEs) is very important in various areas of applied mathematics and theoretical physics. Searching for exact soliton solutions of these equations plays an important role in the study on the dynamics of those phenomena. |

Soliton solutions and other solutions to a nonlinear fractional differential equations | Abdelouahab | Approved | Ömer ÜNSAL, Ahmet BEKİR, Özkan Güner Abstract: In the last decades, fractional calculus found many applications in various fields of applied mathematics, theoretical physics and engineering such as co . . . Read More ## Soliton solutions and other solutions to a nonlinear fractional differential equations
Ömer ÜNSAL, Ahmet BEKİR, Özkan Güner Abstract: |

A Novel Generalized Kudryashov Method for Exact Solutions of Nonlinear Evolution Equations | Koparan | Approved | Nonlinear evolution equations (NLEEs) and systems form the most fundamental theme in mathematical physics. Exact solutions of these equations play a crucial role in the suitable understanding of mecha . . . Read More
## A Novel Generalized Kudryashov Method for Exact Solutions of Nonlinear Evolution Equations
Nonlinear evolution equations (NLEEs) and systems form the most fundamental theme in mathematical physics. Exact solutions of these equations play a crucial role in the suitable understanding of mechanisms of the various physical phenomena modeled by these NLEEs. For this reason, searching exact solutions of these equations have taken interest in recent years. In this paper, we have obtained new exact solutions of the Kaup-Boussinesq and Wu-Zhang systems by using the generalized Kudryashov method. |

Total Abstracts: 8

#### S9. New Era in Mathematics

Abstract: The session aims to present the latest advances in the field of Santilli

iso-, geno- and hyper-mathematics and their applications in mathematics, physics, mechanics, chemistry, biology, eng . . .Read More

##### S9. New Era in Mathematics

*Abstract:*

Abstract: The session aims to present the latest advances in the field of Santilli

iso-, geno- and hyper-mathematics and their applications in mathematics, physics, mechanics, chemistry, biology, engineering and other applied sciences. The proposed session intends to gather experts working on various actually important aspects of Santilli iso-, geno-, hyper- mathematics and to explore new connections between different research areas. We expect a fruitful exchange of new ideas and collaboration regarding the research development of these disciplines among the participants.

Organizer: Svetlin Georgiev, Sorbonne University, Paris, France

E-mail; sgg2000bg@yahoo.com,svetlingeorgiev1@gmail.com

Title | Author | Status | Abstract |
---|---|---|---|

How Can One Look at if Gravitational Wave Generation Has Semi Classical Features, and What This Implies About Compression of Vacuum Wave States, and Coherence/de Coherence? | Beckwith | Approved | We argue in this document that initial vacuum state values possibly responsible for GW(Gravitational wave) generation in relic conditions in the initial onset of inflation may have a temporary un squ . . . Read More
## How Can One Look at if Gravitational Wave Generation Has Semi Classical Features, and What This Implies About Compression of Vacuum Wave States, and Coherence/de Coherence?
We argue in this document that initial vacuum state values possibly responsible for GW(Gravitational wave) generation in relic conditions in the initial onset of inflation may have a temporary un squeezed , possibly even coherent initial value, which would permit in certain models classical coherent initial gravitational wave states. The coherent states would be amendable to nucleation by classical/ highly non linear processes which would be almost immediately eliminated by compression and squeezing. Even though that the general background of incoherency for relic GW is a given. Furthermore, several arguments pro and con as to if or not initial relic GW should be high frequency will be presented, with the reason given why earlier string models did NOT favor low relic GW from the big bang. |

The influence of Latin squares autotopisms on the rocket propellant problem and the radar detection experiment | Falcon | Approved | Latin square design is used as a statistical model in Engineering whose analysis of variance makes clear differences among distinct nuisance sources of variability. This model depends on the Latin squ . . . Read More
## The influence of Latin squares autotopisms on the rocket propellant problem and the radar detection experiment
Latin square design is used as a statistical model in Engineering whose analysis of variance makes clear differences among distinct nuisance sources of variability. This model depends on the Latin square that is used in the experiment and that is selected at random among a predetermined set of squares of a given order. In this work, we study the role that plays the autotopism group of a Latin square in the corresponding analysis of variance. Particularly, we focus on the effect that right-multiplication autotopisms of Latin squares produces on the rocket propellant problem and the radar detection experiment introduced by Montgomery in his fundamental monograph. |

The Cube in Art and Mathematics | Trell | Approved | The Cube in Art and Universe Erik TRELL, Alexander ANIMALU. Samuel EDEAGU Starting with the mathematical roots of Cubism, a survey of the cube as eigenunit and generator in artistic and physical assem . . . Read More ## The Cube in Art and Mathematics
The Cube in Art and Universe Erik TRELL, Alexander ANIMALU. Samuel EDEAGU Starting with the mathematical roots of Cubism, a survey of the cube as eigenunit and generator in artistic and physical assemblies and projections from the infinitesimal to the cosmic scale is made which involves the Euclidean space, the Diophantine equations, Fermat’s Last Theorem, and the isometric vector matrix realization of the electron and crystallization of the primordial Universe and periodic system of the elements. |

Some aspects of iso-differential calculus | Georgiev | Approved | In this talk we define iso-derivative and deduct some of its properties. They are given some applications. Read More ## Some aspects of iso-differential calculus
In this talk we define iso-derivative and deduct some of its properties. They are given some applications. |

On the iso-hyper-representation theory | Dramalidis | Approved | Abstract The hyper-representation theory appeared in mid 80’s. Nowdays, it is clear that this theory is refered to the very large class of hyperstructures since the Hv-structures are used. The main pr . . . Read More ## On the iso-hyper-representation theory
Abstract |

Helix hopes in Lie-Santilli addmissibility | Dramalidis | Approved | Abstract On ordinary non-square matrices of type mn one can define a hypermultiplication by using the so called hope: helix multiplication. We face the problem of the general Lie-Santilli admissibili . . . Read More ## Helix hopes in Lie-Santilli addmissibility
Abstract |

Small Hypernumbers | Dramalidis | Approved | Abstract With the term “Small Hypernumbers” we mean that we have elements of an Hv-field of very thin type, weak associative, weak commutative and with finite fundamental field. Especially, we focus o . . . Read More ## Small Hypernumbers
Abstract |

1. Small Hypernumbers, 2. On the iso-hyper-representation theory, 3. Helix hopes in Lie-Santilli addmissibility, 4. The LV-hyperstructures in Santilli’s iso-theory | Vougiouklis | Approved | 1. Small Hypernumbers T. Vougiouklis Democritus University of Thrace, School of Education 68100 Alexandroupolis, Greece, tvougiou@eled.duth.gr Abstract With the term “Small Hypernumbers” we mean that . . . Read More ## 1. Small Hypernumbers, 2. On the iso-hyper-representation theory, 3. Helix hopes in Lie-Santilli addmissibility, 4. The LV-hyperstructures in Santilli’s iso-theory
1. Small Hypernumbers Abstract Basic References 2. On the iso-hyper-representation theory Abstract 3. Abstract 4. Abstract |

Trajectories of antimatter asteroids in our Solar system | Beghella Bartoli | Approved | The innovative Isodual Theory of Antimatter proposed by R. M. Santilli is able to provide a classical representation of neutral or charged antimatter bodies in a way compatible with available classica . . . Read More
## Trajectories of antimatter asteroids in our Solar system
The innovative Isodual Theory of Antimatter proposed by R. M. Santilli is able to provide a classical representation of neutral or charged antimatter bodies in a way compatible with available classical experimental evidence on antimatter. Since Earth appears to have been hit in the past by antimatter asteroids (as it seems to be the case for the 1908 Tunguska explosion in Siberia), the author presents in this paper an analysis of possible trajectories of an antimatter asteroid in our Solar System and the possibilities of collision with our planet under the assumption of the repulsive gravitational interaction between Earth and the antimatter asteroid. Moreover, an estimate of the minimum approach speed required for an antimatter asteroid to impact with Earth is theoretically and numerically identified at different distances from our planet, along with other considerations about the trajectories. |

Apparent need of antimatter galaxies for the stability of the universe | Beghella Bartoli | Approved | Fritz Zwicky’s hypothesis, according to which the cosmological redshift is due to galactic light losing energy to intergalactic media, without need of Universe expansion, seems to have been recently c . . . Read More
## Apparent need of antimatter galaxies for the stability of the universe
Fritz Zwicky’s hypothesis, according to which the cosmological redshift is due to galactic light losing energy to intergalactic media, without need of Universe expansion, seems to have been recently confirmed by recent mathematical, theoretical and experimental studies via measurements on Earth. |

EXACT AND INVARIANT REPRESENTATION OF NUCLEAR SPINS VIA ISOMATHEMATICS AND ISOMECHANICS | BHALEKAR | Approved | EXACT AND INVARIANT REPRESENTATION OF NUCLEAR SPINS VIA ISOMATHEMATICS AND ISOMECHANICS A. A. Bhalekar(1,2) and R. M. Santilli(1) (1)Thunder Energies Corporation, Tarpon Springs, Florida, U. S. A. (2 . . . Read More ## EXACT AND INVARIANT REPRESENTATION OF NUCLEAR SPINS VIA ISOMATHEMATICS AND ISOMECHANICS
EXACT AND INVARIANT REPRESENTATION OF NUCLEAR SPINS VIA ISOMATHEMATICS AND ISOMECHANICS A. A. Bhalekar(1,2) and R. M. Santilli(1) In the preceding talk at this conference R. M. Santilli has outlined the rudiments of the covering isomathematics and related isomechanics with particular reference to the time invariant representation of nucleons as extended, non-spherical and deformable particles, and indicated the fundamental relevance of the Lie-Santilli isotheory for the nuclear structure in terms of isonucleons (isoelectrons, isoprotons and isoneutrons) and based on it he described the nuclear magnetic moments of all stable nuclides starting from deuteron as isodeuteron. As discussed in the preceding talk a neutron and a deuteron, indeed, are constituted of isoprotons and isoneutrons that are the mutual penetrated states of the wavepackets of protons and electrons. We have extended this description to higher atomic number stable nuclides (upto Z= 82). The approach adopted has been to develop nuclear configurations which are commensurate with the observed nuclear spins. Since in our proposal we use only the isoelectrons, isoneutrons and isoprotons as basic constituents we are indeed incorporating isomathematics and isomechanics. However, the details of the quantitative hadronic mechanics of each isonuclides has not been completely investigated so far. But these nuclear configurations we believe would substantially assist in our future attempts. We have developed two approaches. The first one builds nuclear configurations taking isodeuterons, isoneutrons and isoprotons as basic constituents whereas the second one uses only the isoprotons and isoelectrons as basic nuclear constituents. Notice that when we use isodeuterons as basic nuclear constituents there is no room to speak of isoelectrons separately because each isodeuteron consists of two isoprotons and one isoelectron. It turns out that isoelectrons, indeed, serve as effective nuclear glue. Some preliminary generalizations of both the models would be discussed. Reference: |

Mathematics of Space vs. Spaces of Hadronic Mathematics | Johansen | Approved | While there is no astrophysics without the notion of space, there still is much dispute in theoretical physics about the basic architecture of space. Does ‘mind’ exist outside or inside space? Is spac . . . Read More
## Mathematics of Space vs. Spaces of Hadronic Mathematics
While there is no astrophysics without the notion of space, there still is much dispute in theoretical physics about the basic architecture of space. Does ‘mind’ exist outside or inside space? Is space a container for matter, is matter bending space, or is space itself built by an ‘organic’ algorithm? Does space have a dual nature including a subspace of antimatter? Is ‘vacuum’ to be understood as some underpinning subspace with inherent kinetics? Does there exist parallel universes or multiverses inside space? Does space have a layered structure, with laws for traffic of energy and information between layers, yet to become discovered? Viewed from the more abstract angle, answers to such questions can become stimulated from relevant and consistent ontological philosophy. Viewed from the more concrete angle, answers can become stimulated from significant observations and experiments. In between these two angles dwells the connecting body of mathematical physics, encompassing paradigmatic key notions of theoretical physics and related reservoirs of mathematical concepts and techniques. The paper will approach such questions in relation to the theory of hadronic mechanics, initiated by Ruggero Maria Santilli, and related hadronic mathematics (and geometry) establishing novel fields of isonumbers, genonumbers and hyperstructural numbers, with their respective isoduals. Hadronic mathematics has developed by contributions from several mathematicians, in recent years including extensive contributions to isocalculus from Svetlin Georgiev. The discussion in the paper will also present some reflections on recently published claims of discoveries of various macroscopic structures of antimatter by means of a novel kind of telescope, including claimed observations of so-called ITE-1 (dark) and ITE-2 (light) kinds of antimatter objects/”entities” close to Earth. |

Isomathematics and IsoAlgebras | Muktibodh | Approved | Mathematics of 20th century is solely applicable to the dynamical systems wherein point like particles are moving in a vacuum under Hamiltonian interactions; known as Exterior Dynamical Systems. Appr . . . Read More
## Isomathematics and IsoAlgebras
Mathematics of 20th century is solely applicable to the dynamical systems wherein point like particles are moving in a vacuum under Hamiltonian interactions; known as Exterior Dynamical Systems. Appropriate generalization of 20th century mathematics , today known as Santilli isomathematics is applicable to the dynamical systems wherein the particles are extended, non-spherical and deformable, moving within a physical medium under Hamiltonian and non-Hamiltonian interactions; known as Interior Dynamical systems. IsoAlgebras play an important role in the development of Lie-Santill isotheory. In this paper we deal with the development of the central problem of construction of regular and irregular isorepresentations of Li-Santilli isotheory and its applications. |

Total Abstracts: 13

#### S16. Modelling, Simulation and Optimization in Engineering

Abstract:

In recent years, the use of Modelling, Simulation and Optimization techniques in engineering has accelerated with the advances in computational methods and resources. Modelling, Simulation . . .Read More

##### S16. Modelling, Simulation and Optimization in Engineering

*Abstract:*

Abstract:

In recent years, the use of Modelling, Simulation and Optimization techniques in engineering has accelerated with the advances in computational methods and resources. Modelling, Simulation and Optimization has become an important part of the research repertoire, supplementing and in some cases replacing lengthy experimentation procedures.

Engineering parameters are difficult to predict and analyze before prototyping but modern modelling, simulation and optimization packages can replicate the actual phenomena in less time and cost. Modelling and simulation focuses on optimizing and predicting the performance and reducing the costs of complex systems that may involve multiple interacting disciplines, such as those found in automobiles, aircrafts, spacecrafts, industrial and manufacturing equipment, engineering operations and various consumer products.

The purpose of this session is to bring together users, developers, and researchers to present the latest theoretical and computational developments, applications, ideas, and problems related to Modelling, Simulation and Optimization. Papers may present innovative models, methods or the problem of solving engineering problems.

The multidisciplinary nature of this session invites papers on Modelling, Simulation and Optimization models, methods and approaches with applications in the various disciplines of engineering including but not limited to Mechanical Engineering, Manufacturing Engineering, Industrial Engineering, Engineering Operations, Aerospace Engineering, Electronics Engineering, Electrical Engineering, Bio-Medical Engineering, Computer Science and Engineering, Optimization Applications, and Renewable energy.

Organizers: Dr. Amer Farhan Rafique Faculty of Engineering, King Abdulaziz University,

Jeddah, Kingdom of Saudi Arabia , E-mail: afrafique@kau.edu.sa

Dr. Qasim Zeeshan , Faculty of Engineering Eastern Mediterranean University, Mersin, Turkey

E-mail: qasim.zeeshan@emu.edu.tr

Title | Author | Status | Abstract |
---|---|---|---|

A Survey of Multidisciplinary Design and Optimization in UAVs | Rafique | Approved | As UAV Industry is a growing industry, designs developed by the traditional methods does not provide valid solutions or efficient designs. It was this time, MDO was suggested overtaking the existing s . . . Read More
## A Survey of Multidisciplinary Design and Optimization in UAVs
As UAV Industry is a growing industry, designs developed by the traditional methods does not provide valid solutions or efficient designs. It was this time, MDO was suggested overtaking the existing single disciplinary optimization. This paper is focusing on Multidisciplinary design and optimization methods in UAVs covering the hierarchy of methods. It also goes through main methods developed from its origin. Some of algorithms are also explained into an understanding level. Pros & Cons of each methods and algorithms are discussed and characterized according to their convergence, consistency of solution, computation speed etc. Next step was to analyze documents on UAVs and their achievements and what has been done and up to what level. |

Total Abstracts: 1

#### S2. Clifford algebras, Clifford analysis and their applications

Abstract: We plan to have a special session on Clifford algebras, Clifford analysis and their applications. It aims to present the latest advances in the field of Clifford (geometric) algebras and t . . .Read More

##### S2. Clifford algebras, Clifford analysis and their applications

*Abstract:*

Abstract: We plan to have a special session on Clifford algebras, Clifford analysis and their applications. It aims to present the latest advances in the field of Clifford (geometric) algebras and their applications in mathematics, physics, engineering and other applied sciences. The proposed session intends to gather experts working on various actually important aspects of Clifford algebras and to explore new connections between different research areas. We expect a fruitful exchange of new ideas and collaboration regarding the research development of this discipline among the participants

Title | Author | Status | Abstract |
---|---|---|---|

New Aspects on Moisil-Teodorescu System | Georgiev | Approved | In this talk is considered the Moisil-Teodorescu system. It is investigated for existence of classical solutions. It is proposed new integral representation of the classical solutions. As an appli . . . Read More
## New Aspects on Moisil-Teodorescu System
In this talk is considered the Moisil-Teodorescu system. It is investigated for existence of classical solutions. It is proposed new integral representation of the classical solutions. As an application, they are given continuous dependence and differentiability of the solutions with respect to the initial data and parameters. |

Uncertainty Principles For The Clifford-Fourier transform | Jday | Approved | Many works are devoted to generalize the classical Fourier transform. In 2005, Sommen and Brackx introduce a generalization of the classical Fourier transform in the setting of Clifford analysis c . . . Read More
## Uncertainty Principles For The Clifford-Fourier transform
Many works are devoted to generalize the classical Fourier transform. In 2005, Sommen and Brackx introduce a generalization of the classical Fourier transform in the setting of Clifford analysis called the Clifford-Fourier transform. Considering the integral expression of this Fourier transform, De Bie and Xu establish several properties for the Clifford-Fourier transform.\\ |

Computational aspects of quaternionic polynomials | Falcão | Approved | The processes of evaluating and factoring real or complex polynomials are very important problems and had received a lot of attention over the years. In the ring of quaternionic polynomials new proble . . . Read More
## Computational aspects of quaternionic polynomials
The processes of evaluating and factoring real or complex polynomials are very important problems and had received a lot of attention over the years. In the ring of quaternionic polynomials new problems arise: the evaluation map at a quaternion is not a ring homomorphism and the structure of the zero-set of quaternionic polynomials is quite different from the complex case. This is a joint work with F. Miranda, R. Severino and J. Soares. |

Recurrence relations for hypercomplex orthogonal polynomials | Cacao | Approved | The theory of orthogonal polynomials of one real or complex variable and its generalization to higher dimensions is well established. Hypercomplex function theory (or Clifford analysis) provides an al . . . Read More
## Recurrence relations for hypercomplex orthogonal polynomials
The theory of orthogonal polynomials of one real or complex variable and its generalization to higher dimensions is well established. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with arbitrary dimensions. In this context, we construct orthogonal polynomial systems of a hypercomplex variable and study some of their properties, including three-term recurrence relations. |

Quaternionic polynomials with multiple zeros: a numerical point of view | Miranda | Approved | There are a lot of rootfinding algorithms especially designed for real or complex polynomials. Most of these methods however face difficulties in dealing with multiple roots or clusters of roots. The . . . Read More ## Quaternionic polynomials with multiple zeros: a numerical point of view
There are a lot of rootfinding algorithms especially designed for real or complex polynomials. Most of these methods however face difficulties in dealing with multiple roots or clusters of roots. |

Zeros and singularities of slice regular functions over alternative *-algebras | Stoppato | Approved | The theory of slice regular functions over real alternative ∗-algebras has been introduced in [Ghiloni, Perotti, 2011] as a higher-dimensional generalization of the theories of: holomorphic complex fu . . . Read More
## Zeros and singularities of slice regular functions over alternative *-algebras
The theory of slice regular functions over real alternative ∗-algebras has been introduced in [Ghiloni, Perotti, 2011] as a higher-dimensional generalization of the theories of: holomorphic complex functions; slice regular quaternionic functions [Gentili, Struppa, 2006]; slice monogenic functions [Colombo, Sabadini, Struppa, 2009]. Along with this generalization step, the larger class of slice functions has been defined. Some recent developments in the theory concern the algebraic structure and the zero sets of slice functions, as well as the classification of the singularities of slice regular functions. Peculiar phenomena arise, which were not present in the complex or quaternionic case. The talk will provide examples of these phenomena and, time permitting, put them into context with the statement of general results. This is joint work with Riccardo Ghiloni and Alessandro Perotti. |

Constructing multivariate polynomials in function theories over non-commutative algebras | Malonek | Approved | The theory of polynomials in one or several variables is, in general, divided into three main parts, namely algebra, analysis, and geometry of polynomials. However, the division lines between these ar . . . Read More
## Constructing multivariate polynomials in function theories over non-commutative algebras
The theory of polynomials in one or several variables is, in general, divided into three main parts, namely algebra, analysis, and geometry of polynomials. However, the division lines between these areas are quite blurred. The algebraic aspect of the theory has close connections with special functions and combinatorics. In turn, the analytical aspect of the theory deals with questions that are typical in analysis concerning sometimes very subtle quantitative as well as qualitative properties. Needless to mention that besides of seeming a very old subject, polynomials did not loose their place in what are called modern mathematical theories. Among them those which are heavily relying on the use of non-commutative algebras also emerged in the last five or six decades for solving problems in the most diversified areas of application. Analytical methods in generalizing complex function theory to higher dimensions by means of the use of non-commutative algebras, for example Clifford algebras, immediately implies the revision of the concept of a polynomial expressed as function of the chosen variables. In particular, dealing with polynomials as, in some sense, generalized holomorphic functions requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. This is caused by the fact that, in general, neither multiplication nor composition are operations closed in the set of generalized holomorphic functions. Naturally the question arises whether besides the peculiarities of the non-commutative algebras there exist sufficiently general approaches for constructing Clifford algebra valued polynomials defined in higher dimensional Euclidean spaces. After a short historical overview on how polynomials are used in hypercomplex function theory, our survey tries to give partial answers to some general questions, stressing at the same time a new matrix approach to the representation of generalized holomorphic polynomials. |

Towards a quaternionic function theory linked with the Zernike spherical polynomials | Morais | Approved | It is truly uncommon that a paper that has been set aside for almost eighty years finds its way back to scientific spotlight. Yet this is exactly what the 1934 paper by F. Zernike’s Nobel prize has ac . . . Read More
## Towards a quaternionic function theory linked with the Zernike spherical polynomials
It is truly uncommon that a paper that has been set aside for almost eighty years finds its way back to scientific spotlight. Yet this is exactly what the 1934 paper by F. Zernike’s Nobel prize has accomplished in the last decade. As a matter of fact, in the last years considerable attention has been paid to the role played by the Zernike Polynomials (ZPs) in many different fields of geometrical optics, optical engineering, and astronomy. The ZPs are the product of a normalization constant by radial polynomials and a pair of trigonometric functions (sine and cosine). These polynomials form a complete orthogonal set over the unit circle and are commonly used to describe balanced aberrations. In this talk, we give a brief description of the theory and properties of the 3D Quaternionic Zernike Spherical Polynomials (QZSPs). A generalization and refinement of the QZSPs to functions vanishing outside the unit ball leads to the computation of the Weighted Quaternionic Zernike Spherical Functions (WQZSFs). In particular, the underlying functions are of three real variables and take on values in the quaternions (identified with $\mathbb{R}^4$). Also, in this talk, we prove that the WQZSFs are orthonormal over the unit ball with respect to a suitable weight function and allow, inside an embedding sphere, to be decomposed into 3D spherical monogenics. The representation of these functions are given explicitly and a summary of their fundamental properties is also discussed. The talk is based on joint work with I. Ca{\c c}{\~a}o (University of Aveiro, Portugal). |

Poster on: Double Conformal Space Time Algebra | Hitzer | Approved | First author: Robert Benjamin Easter. We introduce the double conformal version of space-time algebra based multivector modeling of quartic and general quadric surfaces, Darboux cyclides, Dupin cycli . . . Read More ## Poster on: Double Conformal Space Time Algebra
First author: Robert Benjamin Easter. We introduce the double conformal version of space-time algebra based multivector modeling of quartic and general quadric surfaces, Darboux cyclides, Dupin cyclides, tori and pairs of standard conformal space-time algebra objects in Minkowski space. We can use extended Lorentz boost transformations and projections to three-dimensional Euclidean space to directionally dilate objects. |

Total Abstracts: 9

#### S18. Recent Integral Transforms Advances (RITA)

The papers in this session are expected to cover new and recent developmental advances in the theory of Integral transforms and consequent application aspects in mathematics areas as well as in variou . . .Read More

##### S18. Recent Integral Transforms Advances (RITA)

*Abstract:*

The papers in this session are expected to cover new and recent developmental advances in the theory of Integral transforms and consequent application aspects in mathematics areas as well as in various fields of Engineering and Science. Full papers in this session can be considered on a case by case basis, and appropriate journals may be suggested by organizers as feasible.

Organizers:

Fethi Bin Muhammad Belgacem, Seenith Sivasundaram, Xiao-Jun Yang.

E-mail: fbmbelgacem@gmail.com

Title | Author | Status | Abstract |
---|---|---|---|

New approach for accelerating the non linear Schwarz iterations | Nagid | Approved | A new approach using the vector epsilon algorithm is considered to accelerate the convergence of vector sequences derived from the discretization of non linear PDEs in the context of domain decomposit . . . Read More
## New approach for accelerating the non linear Schwarz iterations
A new approach using the vector epsilon algorithm is considered to accelerate the convergence of vector sequences derived from the discretization of non linear PDEs in the context of domain decomposition. This |

Applications of the Sumudu Transform to Bernoulli Numbers and Polynomials | Ahmed | Approved | In the present paper, we apply the Sumudu transform to the Bernoulli generic function (BGF), then the properties of this transformation are examined, in the goal of re-extract some properties of Berno . . . Read More ## Applications of the Sumudu Transform to Bernoulli Numbers and Polynomials
In the present paper, we apply the Sumudu transform to the Bernoulli generic function (BGF), then the properties of this transformation are examined, in the goal of |

Applications of the Sumudu Transform to Euler Numbers and Polynomials | Ahmed | Approved | The aim of this paper is to derive some properties of Euler numbers and Polynomials using the Sumudu transformation, we apply this transformation to the Euler generic function (EGF), then we used the . . . Read More ## Applications of the Sumudu Transform to Euler Numbers and Polynomials
The aim of this paper is to derive some properties of Euler numbers and Polynomials using the Sumudu transformation, we apply this transformation to the Euler |

Total Abstracts: 3

#### S19. Wavelets Analysis, Fractional Advances and Applications (WAFAA)

Abstract:

The papers in this session are expected to cover recent and state of the art computational techniques and schemes pertaining to applications with waves, wavelets, fractals and fractional cal . . .Read More

##### S19. Wavelets Analysis, Fractional Advances and Applications (WAFAA)

*Abstract:*

Abstract:

The papers in this session are expected to cover recent and state of the art computational techniques and schemes pertaining to applications with waves, wavelets, fractals and fractional calculus. Full papers in this session can be considered on a case by case basis, and appropriate journals may be suggested by organizers as feasible.

Organizers:

Fethi Bin Muhammad Belgacem, Zakia Hammouch, Carlo Cattani.

E-mail: fbmbelgacem@gmail.com

Title | Author | Status | Abstract |
---|---|---|---|

Numerical Solution of Linear Quadratic Optimal Control Problems using CAS Wavelet Operational Matrix of Derivative | Ahmed | Approved | In the present paper, a new CAS wavelet operational matrix of derivative is presented. After presenting relevant properties of the CAS wavelet, we apply its connected operational matrix to differentia . . . Read More ## Numerical Solution of Linear Quadratic Optimal Control Problems using CAS Wavelet Operational Matrix of Derivative
In the present paper, a new CAS wavelet operational matrix of derivative is presented. After presenting relevant properties of the CAS wavelet, we apply its connected |

Total Abstracts: 1

#### Aspects Integres dans les Mathematiques de Abbas Bahri- a Loving Eulogy II. (AIMABLE II)

In this this session presenters are welcome to present any aspects or connections to the Mathematics of the late Abbas Bahri, whether be of technical, professional, respect or simply of feeling and eu . . .Read More

##### Aspects Integres dans les Mathematiques de Abbas Bahri- a Loving Eulogy II. (AIMABLE II)

*Abstract:*

In this this session presenters are welcome to present any aspects or connections to the Mathematics of the late Abbas Bahri, whether be of technical, professional, respect or simply of feeling and eulogical nature. Ideas and proposals on how to further commemorate the life and legacy of Abbas Bahri woulkd be most welcome. Full papers in this session can be considered on a case by case basis, and appropriate journals may be suggested by organizers as feasible.

Organizers:

Fethi Bin Muhammad Belgacem, and Yomna Rebai,

E-mail: fbmbelgacem@gmail.com

#### M4: Modern approximation methodologies for functions and arrays in science and engineering computions

This mini symposium welcomes the contributions for the following topics mainly. However, some other areas which are closely related to the title issue and not listed below can also be considered to ha . . .Read More

##### M4: Modern approximation methodologies for functions and arrays in science and engineering computions

*Abstract:*

This mini symposium welcomes the contributions for the following topics mainly. However, some other areas which are closely related to the title issue and not listed below can also be considered to have foci for paper submissions.

* Univariate and/or multivariate function decompositions or approximations

* Decompositions of ordinary linear algebraic vectors and/or matrices

* Decompositions of multilinear algebraic structures like folvecs, folmats, multiway arrays

* Approximating the ODE and/or ODE Set solutions

* Approximating the PDE and/or PDE Set solutions

* Approximating the linear univariate and/or multivariate integral operators

* High Dimensional Model Representation Varieties

* Enhanced Multivariance Products Representation Varieties

**Organizer****:** Metin Demiralp, İstanbul Technical University, Informatics Institute, Maslak, 34469, İstanbul, Türkiye (Turkey)

Title | Author | Status | Abstract |
---|---|---|---|

A Numerical Comparision between Bivariate Enhanced Multivariance Products Representation and Smoothing Bicubic Spline Method | Tuna | Approved | \documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\evensidemargin}{-0.6in} \addtolength{\textwidth}{1.2in} \addtolength{\topmargin}{-.875in} \addtolength{\textheight}{1.7 . . . |

High Dimensional Model Representation (HDMR) with Clustering for Image Retrieval | Tunga | Approved | \documentclass{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\evensidemargin}{-0.6in} \addtolength{\textwidth}{1.2in} \addtolength{\topmargin}{-.875in} \addtolength{\textheight}{1.75in} \ . . . Read More ## High Dimensional Model Representation (HDMR) with Clustering for Image Retrieval
\documentclass{article} \addtolength{\topmargin}{-.875in} \title{High Dimensional Model Representation (HDMR) with Clustering for Image Retrieval} \date{} %% if you don’t need date to appear In this study, we deal with image retrieval and use Columbia Object Image Library (COIL100). This database has $7200$ color images of $100$ different objects that is, \end{document} |

A TMEMPR Based Approach for Transforming Arrowheaded Matrices to Tridiagonal Forms | OKAN | Approved | \documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\evensidemargin}{-0.6in} \addtolength{\textwidth}{1.2in} \addtolength{\topmargin}{-.875in} \addtolength{\textheight}{1.7 . . . Read More ## A TMEMPR Based Approach for Transforming Arrowheaded Matrices to Tridiagonal Forms
\documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\topmargin}{-.875in} \usepackage{amssymb} %\newcommand{\sss}[1]{\sum\limits_{i_{#1}=1}^{n_{#1}}} \begin{document} \begin{center} \thispagestyle{empty} |

Certain Implementative Applications of Separate Node Ascending Derivatives Expansion (SNADE) | Bodur | Approved | \documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\evensidemargin}{-0.6in} \addtolength{\textwidth}{1.2in} \addtolength{\topmargin}{-.875in} \addtolength{\textheight}{1.7 . . . Read More ## Certain Implementative Applications of Separate Node Ascending Derivatives Expansion (SNADE)
\documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\topmargin}{-.875in} \usepackage{amssymb} %\newcommand{\sss}[1]{\sum\limits_{i_{#1}=1}^{n_{#1}}} \begin{document} \begin{center} This work is designed to emphasize the method’s interpolatory nature. % |

Transformational Tridiagonal Folmat Enhanced Multivariance Products Representation (TTFEMPR) Possibilities in Multivariate Array Decomposition | Gündoğar | Approved | \documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\evensidemargin}{-0.6in} \addtolength{\textwidth}{1.2in} \addtolength{\topmargin}{-.875in} \addtolength{\textheight}{1.7 . . . Read More ## Transformational Tridiagonal Folmat Enhanced Multivariance Products Representation (TTFEMPR) Possibilities in Multivariate Array Decomposition
\documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\topmargin}{-.875in} \usepackage{amssymb} \begin{document} \begin{center} Transformational Enhanced Multivariance Products Respresentation (TEMPR), % General component of a multiway array such as % Tridiagonal Matrix Enhanced Multivariance Product Representation (TMEMPR) method % In this work we will focus on Transformational TFEMPR, relatively new method in % |

Face Recognition using Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) | Korkmaz Özay | Approved | This study aims to retrieve face images from a database according to a target face image. For this purpose, Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) is taken into con . . . Read More ## Face Recognition using Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR)
This study aims to retrieve face images from a database according to |

An Implementative Application of Probabilistic Evolution Theory : A Case Study for Two Particles Celestical Mechanical System | TATAROGLU | Approved | \begin{center} {\bf{Elif Tataro\u glu and Metin Demiralp}} \\ {\textit{\.Istanbul Technical University, Informatics Institute, % 34469, Turkey (T\”URK\.IYE)}} % \end{center} \vskip1cm \noindent In thi . . . Read More ## An Implementative Application of Probabilistic Evolution Theory : A Case Study for Two Particles Celestical Mechanical System
\begin{center} \noindent In this work, we apply Probabilistic Evolution Theory % One of the most important facts in the probabilistic evolution theo% Amongst other space extensions the constancy addition plays an impor% By using this structure and the analytic probabilistic evolution % \end{document} |

A Wavefunction Free Exponential Function Expectation Value Determination Based ODE Construction and Solution to Get Spectral Entities For the Systems Having Coulombic Attractions | Kalay | Approved | \documentclass[12pt]{article} \addtolength{\oddsidemargin}{-0.6in} \addtolength{\evensidemargin}{-0.6in} \addtolength{\textwidth}{1.2in} \addtolength{\topmargin}{-.875in} \addtolength{\textheight}{1.7 . . . Read More ## A Wavefunction Free Exponential Function Expectation Value Determination Based ODE Construction and Solution to Get Spectral Entities For the Systems Having Coulombic Attractions
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%\newcommand{\sss}[1]{\sum\limits_{i_{#1}=1}^{n_{#1}}} \begin{document} \begin{center} By setting $f$ equal to a natural number power of position opera% In this work we extend this analysis to more comprehensive potenti% This work is based on private communications with Professor Demiralp. |

Recovery of Missing Data via Wavelets Followed by High-Dimensional Modeling | Gürvit | Approved | In a scientiﬁc research missing observations can pose serious problems, aﬀect the bias and can lead to misleading conclusions. Moreover missing data can make the construction of a mathematical model i . . . Read More
## Recovery of Missing Data via Wavelets Followed by High-Dimensional Modeling
In a scientiﬁc research missing observations can pose serious problems, aﬀect the bias and can lead to misleading conclusions. Moreover missing data can make the construction of a mathematical model impossible. The major objective is ﬁrst to complete a matrix with missing data and then to construct a mathematical model based on the new prediction. In this article univariable case in data recovery is taken into consideration and without losing from the generality it is intended to be extended to multivariable case followed by a high dimensional modeling. Supposing that a portion of a data vector is missing in such a way that we have a minimal prior knowledge about the data structure, missing part must be recovered from the existing part of the data set. The only prerequisite information needed is the knowledge that would allow us to guess a matrix called a frame. As an example in image processing an inverse discrete cosine transform matrix would be a suitable frame. The main purpose here is to guess such a sparse frame that can represent complete data vector f. By a sparse representation we mean the majority of components being close to zero. In the present article the data imputation using the expected sparse representation is intended to be done in a wavelet or lifting scheme basis. Numerical implementation and the tabulation of the results will be given and the generalization to multivariate case will be discussed. |

Multivariate Numerical Integration via Fluctuationlessness Theorem: Case Study | Baykara | Approved | In this work we come up with the statement of the Fluctuationlessness theorem recently conjectured and proven by M. Demiralp and its application to numerical integration of univariate functions by res . . . Read More
## Multivariate Numerical Integration via Fluctuationlessness Theorem: Case Study
In this work we come up with the statement of the Fluctuationlessness theorem recently conjectured and proven by M. Demiralp and its application to numerical integration of univariate functions by restructuring the Taylor expansion with explicit remainder term. The Fluctuationlessness theorem states that the matrix representation of an algebraic operator which multiplies its argument by a scalar univariate function, is identical to the image of the independent variable’s matrix representation over the same subspace via the same basis set, under that univariate function, when the ﬂuctuation terms are ignored. Following this step an orthonormal basis set is formed and the necessary formulas for calculating the coeﬃcients of the three term recursion formula are constructed. Then for multivariate numerical integration, instead of dealing with a single formula for multiple remainder terms, a new approach that is already mentioned for bivariate functions is taken into consideration. At every step of a multivariate integration one variable is considered and the others are held constant. In such a way, this gives us the possibility to get rid of the complexity of calculations. The trivariate case is taken into account and its generalization is step by step explained. At the ﬁnal stage the implementation is done for some trivariate functions and the results are tabulated together with the implementation times. As a conclusion it can be said that the trivariate case as in the case of bivariate case gives us good results in precision as well as in duration. All the numerical calculations are done in Mathematica. |

A Novel Compression Algorithm for Hyperspectral Images Using Enhanced Multivariance Products Representation | Tuna | Approved | A Novel Compression Algorithm for Hyperspectral Images Using Enhanced Multivariance Products Representation Aleksei Sukhanov, Süha Tuna, Behçet Uğur Töreyin İstanbul Technical University, Informatics . . . Read More ## A Novel Compression Algorithm for Hyperspectral Images Using Enhanced Multivariance Products Representation
A Novel Compression Algorithm for Hyperspectral Images Using Aleksei Sukhanov, Süha Tuna, Behçet Uğur Töreyin İstanbul Technical University, Informatics Institute, 34469, Hyperspectral images, typically comprising hundreds of narrow Ack.: The second author is grateful to Professor Demiralp for |

More Practicalization of Probabilistic Evolution Theory: Case Studies for the Squariﬁcation of Telescope Matrices | Kırkın | Approved | \begin{center} {\bf{Melike Ebru K\i rk\i n and Metin Demiralp}} \\ {\textit{\.Istanbul Technical University, Informatics Institute, % 34469, Turkey (T\”URK\.IYE)}} % \end{center} \vspace{0.5cm} %%% Th . . . Read More ## More Practicalization of Probabilistic Evolution Theory: Case Studies for the Squariﬁcation of Telescope Matrices
\begin{center} \end{document} |

A Space Pruning Approach to the Determination of Spectral Entities for a Quantum System Described by a Singular Potential | Kalay | Approved | The space pruning approach is not a newly proposed idea and it finds its roots in late 1980s when it was first proposed by M. Demiralp for the determination of spectral entities for certain Coulombic . . . Read More ## A Space Pruning Approach to the Determination of Spectral Entities for a Quantum System Described by a Singular Potential
The space pruning approach is not a newly proposed idea and it finds its roots in late 1980s 1 |

Squarification of Telescope Matrices in the Probabilistic Evolution Theoretical Approach to the Two Particle Classical Mechanics as an Illustrative Implementation | Gozukirmizi | Approved | There has been an increasing tendency in the Group for Science and Methods of Computing (Demiralp’s group) to develop an analytical method for the construction of solutions to the explicit ordinary di . . . Read More ## Squarification of Telescope Matrices in the Probabilistic Evolution Theoretical Approach to the Two Particle Classical Mechanics as an Illustrative Implementation
There has been an increasing tendency in the Group for Science and Methods of Computing |

Classical Symmetric Fourth Degree Potential Systems In Probabilistic Evolution Theoretical Perspective: Most Facilitative Conicalization and Squarification of Telescope Matrices | Gozukirmizi | Approved | The companion paper of the second author includes a sufficiently comprehensive introduction to the quite recently developed Probabilistic Evolution Theory. Therein, the basic issues in this theory are . . . Read More ## Classical Symmetric Fourth Degree Potential Systems In Probabilistic Evolution Theoretical Perspective: Most Facilitative Conicalization and Squarification of Telescope Matrices
The companion paper of the second author includes a sufficiently comprehensive introduction |

Overflow Removal from the Images of an Infinite Linear Combination Over a Basis Function Set Under the Quantum System Hamiltonian to Evaluate the System’s Spectral Entities | Abdulbaki Baykara | Approved | We focus on a single particle quantum system having one degree of freedom such that the particle’s position can vary only in a finite interval of the real axis. This means that the wave function of th . . . Read More ## Overflow Removal from the Images of an Infinite Linear Combination Over a Basis Function Set Under the Quantum System Hamiltonian to Evaluate the System’s Spectral Entities
We focus on a single particle quantum system having one degree of freedom such that the |

Total Abstracts: 16

#### M2: Engineering Mathematics: wavelets, fractals, networks and matrices in computational electromagnetics, antennas, fluid dynamics and biomathematics.

Abstract: This special section is devoted to Engineering Mathematics. Special focus is on the theory and applications of wavelets, fractals and networks. The fundamental role of applied matrix analy . . .Read More

##### M2: Engineering Mathematics: wavelets, fractals, networks and matrices in computational electromagnetics, antennas, fluid dynamics and biomathematics.

*Abstract:*

** **

**Abstract:** This special section is devoted to Engineering Mathematics. Special focus is on the theory and applications of wavelets, fractals and networks. The fundamental role of applied matrix analysis, operator methods, iterated function systems, attractors and analysis of fractals will be emphasised. Session specially will highlight also the relevant Engineering Mathematics applications in computational electromagnetics, antennas, fluid dynamics, mechanics, materials, communication, information and aerospace technologies, life science and bioinformatics. This section thus will bring together researchers with various mathematical and engineering backgrounds sharing common interests in development of the theory and applications of wavelets, fractals, networks and matrix methods in science and engineering. The participants will present lectures on the newest developments and reviews of the “status of the art”. Complementing informal special meetings and discussions will be organized, where in particular various kinds of applications will be jointly explored and joint publications will be prepared.

** Organizers: **Prof. Sergei Silvestrov, Mälardalen University, Sweden, Dr. Milica Rancic, Mälardalen University, Sweden, Emanuel Guargilia, University of Salerno, Italy and Mälardalen University, Sweden

Title | Author | Status | Abstract |
---|---|---|---|

Double diffusive convection in a Porous Medium Layer Saturated with an Oldroyd Nanofluid | Umavathi | Approved | J.C. Umavathi and Maurizio Sasso Department of Engineering, University of Sannio, Piazza Roma 21, 82100 Benevento, Italy. The onset of double diffusive convection in a horizontal layer of a porous me . . . Read More ## Double diffusive convection in a Porous Medium Layer Saturated with an Oldroyd Nanofluid
J.C. Umavathi and Maurizio Sasso The onset of double diffusive convection in a horizontal layer of a porous medium saturated with an Oldroyd nanofluid is studied using linear and non-linear stability analysis. The modified Darcy- Oldroyd model is used for the momentum equation. The model used for the Oldroyd nanofluid incorporates the effects of Brownian motion and thermophoresis. The thermal energy equations include the diffusion and cross diffusion terms. The linear theory depends on normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The effects of various governing parameters viz., concentration Rayleigh number, nanofluid Lewis number, modified diffusivity ratio, Soret and Dufour parameters, Solutal Rayleigh number, Vadasz number, Lewis number, relaxation, and retardation parameters, viscosity ratio and conductivity ratio on the stationary and oscillatory convections are presented graphically. The non-linear theory based on the representation of Fourier series method is used to find the heat and mass transport. The effect of various parameters on transient heat and mass transfer is also brought out and nonlinear analysis depends on a minimal representation of double Fourier series. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large all the three transient Nusselt values approaches to their steady state values. |

Numerical methods and asymptotic expansions for multi-paramenter stochastic differential equations modeling | Canhanga | Approved | State of art, after Black-Scholes proposed in 1973 a model for pricing European Options under constant volatilities, Christoffersen in 2009 empirically showed “why multi factor stochastic volatility m . . . Read More
## Numerical methods and asymptotic expansions for multi-paramenter stochastic differential equations modeling
State of art, after Black-Scholes proposed in 1973 a model for pricing European Options under constant volatilities, Christoffersen in 2009 empirically showed “why multi factor stochastic volatility models work so well”. Four years late Chiarella and Ziveyi solved the Christoffersen model considering an underlying asset whose price is governed by stochastic volatilities. Using the Duhamel’s principle they derived an integral form solution of the boundary value problem associated to the option price, applying method of characteristics, Fourier transforms and Laplace transforms they computed an approximate formula for pricing American options. Keywords: Option pricing model, asymptotic expansion, numerical studies . |

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes | Silvestrov | Approved | Dmitrii Silvestrov Stockholm University E-mail: silvestrov@math.sus.se Sergei Silvestrov Mälardalen University E-mail: sergei.silvestrov@mdh.se New algorithms for computing asymptotic expansions for s . . . Read More ## Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
Dmitrii Silvestrov Sergei Silvestrov New algorithms for computing asymptotic expansions for stationary and quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and some kind of “operational calculus” for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have an universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of the phase space. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures. |

Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet with viscous dissipation and uniform heat source | Metri | Approved | Prashant G Metri*, Emanuel Guariglia* and Sergei Silvestrov* *Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sweden An analysis for the MHD boundary layer flow and heat transf . . . Read More ## Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet with viscous dissipation and uniform heat source
Prashant G Metri*, Emanuel Guariglia* and Sergei Silvestrov* *Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sweden An analysis for the MHD boundary layer flow and heat transfer towards stretching sheet is carried out via symmetry analysis. A steady two dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow is permeated by a uniform transverse magnetic field. The governing partial differential equations are reduced to a system of ordinary differential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations. The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary differential equation corresponding to momentum equation and second order differential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the effects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed. |

INFLUENCE OF THE MAGNETIZATION VECTOR MISALIGNMENT ON RING PERMANENT MAGNET POSITIONED ABOVE SOFT MAGNETIC CILINDER | Vuckovic | Approved | Ana VUČKOVIĆ*, Nebojša RAIČEVIĆ*, Mirjana PERIĆ*, Željko HEDERIĆ** *University of Niš, Faculty of Electronic Engineering, Niš, Serbia ** J.J. Strossmayer University of Osijek, Faculty of Electrical E . . . Read More ## INFLUENCE OF THE MAGNETIZATION VECTOR MISALIGNMENT ON RING PERMANENT MAGNET POSITIONED ABOVE SOFT MAGNETIC CILINDER
Ana VUČKOVIĆ*, Nebojša RAIČEVIĆ*, Mirjana PERIĆ*, Željko HEDERIĆ** *University of Niš, Faculty of Electronic Engineering, Niš, Serbia e-mail:ana.vuckovic@elfak.ni.ac.rs, nebojsa.raicevic@elfak.ni.ac.rs, mirjana.peric@elfak.ni.ac.rs, zeljko.hederic@etfos.hr Permanent magnetism is one of the oldest continuously studied branches of the science but the utilization of permanent magnets themselves was limited it the past. Reason for this could be low force they could generate at the time. The application of permanent magnets has gained momentum since early ‘80s, thanks to the discovery of rare-earth materials with high energy production. In the past, scientists introduced wide variety of techniques for modelling permanent magnet configurations. Different numerical and analytical methods were proposed for determining the magnetic flux density generated by permanent magnets of various shapes and magnetic force between them. Generally, the Ampere’s current model and the Colombian approach are used. In order to overcome the drawbacks of numerical and analytical methods for permanent magnet modelling the semi-analytical approach is proposed in the paper. |

Influence of metallization thickness on microstrip lines characteristic parameters distribution | Peric | Approved | The effect of microstrip lines metallization thickness is very important for successful monolithic microwave integrated circuits (MMICs) optimization and design. In many cases, due to limitations of m . . . Read More
## Influence of metallization thickness on microstrip lines characteristic parameters distribution
The effect of microstrip lines metallization thickness is very important for successful monolithic microwave integrated circuits (MMICs) optimization and design. In many cases, due to limitations of methods, authors analyze structures with an infinitely thin metallization thickness that does not correspond to the real situation in practice. However, various methods take into account the finite dimension of metal conductors. Some of those methods are: the conformal mapping, the finite element method, the boundary element method, the finite difference method, the variational method, the method of lines, etc. The calculation of characteristic parameters of shielded and covered multilayered microstrip lines, with finite metallization thickness which penetrates into dielectric substrates, will be presented in this paper. Also, the cases when the metallization thickness does not penetrate into substrates will be considered. The hybrid boundary element method (HBEM), developed at the Faculty of Electronic Engineering in Nis, is applied for those calculations. This semi-numerical method is based on combination of the boundary element method, the equivalent electrodes method and the point-matching method for the potential of the perfect electric conductor electrodes and for the normal component of the electric field at the boundary surface between any two dielectric layers. The method is very simple and accurate comparing to the other methods. It is applied until now, by authors of this paper, for microwave transmission lines analysis. The characteristic parameters of open and shielded microstrip lines as well as covered and coupled structures are calculated using this method. Also, the method was successfully applied for electromagnetic field determination in the vicinity of cable terminations and magnetic force calculations of permanent magnets. This paper has an aim to show that HBEM can handle with microstrip lines configurations where the metal conductors penetrate into dielectric layers. The quasi-static TEM approach is applied. Several microstrip lines geometries will be considered. The characteristic parameters results will be presented in tables and graphically. The authors expect a very good results agreement with those obtained by other researchers. Also, it will be shown that the method application does not have any limitation considering the number of dielectric layers. Authors: Mirjana Peric, Slavoljub Aleksic and Ana Vuckovic |

Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet | Narayana | Approved | Mahesha Narayana*, Prashant G Metri** ***, Sergei Silvestrov** *Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India **Division of Applied Mathematics, . . . Read More ## Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet
Mahesha Narayana*, Prashant G Metri** ***, Sergei Silvestrov** *Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Bangalore, Karnataka, India The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nanoliquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with temperature. An effective medium theory (EMT) based model is used for the thermal conductivity of the nanoliquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) – water base liquid. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations with the application of similarity transformations. Resultant two-point boundary value problem is solved numerically using a shooting method together with Runge-Kutta-Fehlberg and Newton-Raphson schemes. The effect of surface tension on the dynamics of the considered problem is presented graphically and analyzed in detail. The clear liquid results which form special case of the present study are in excellent agreement with the results reported in the literature. |

Hypergeometric Steady Solution of Hydromagnetic Nano Liquid Film Flow over an Unsteady Stretching Sheet | Metri | Approved | Prashant G Metri*, Mahesha Narayana** and Sergei Silvestrov* *Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sweden **Department of Mathematics, M. S. Ramaiah University of Ap . . . Read More ## Hypergeometric Steady Solution of Hydromagnetic Nano Liquid Film Flow over an Unsteady Stretching Sheet
Prashant G Metri*, Mahesha Narayana** and Sergei Silvestrov* *Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sweden In this paper, we examine the MHD boundary layer flow and heat transfer characteristics of a laminar nanoliquid film over an unsteady stretching sheet is presented. The highly nonlinear partial differential equations governing flow and heat transport are simplified using similarity transformation. The analytical solutions of the resulting ODEs are obtained for some special case of nano liquid film using hypergeometric functions, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. |

Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents | Rancic | Approved | Karl Lundengård*, Milica Rančić*, Vesna Javor**, Sergei Silvestrov* * Division of Applied Mathematics, UKK, Mälardalen University (MDH), Västerås, Sweden ** Department of Power Engineering, University . . . Read More ## Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents
Karl Lundengård*, Milica Rančić*, Vesna Javor**, Sergei Silvestrov* * Division of Applied Mathematics, UKK, Mälardalen University (MDH), Västerås, Sweden A number of current functions have been proposed in the literature to model the electrostatic discharge (ESD) currents. They are mostly based on exponential functions. Double exponential function or its four-term version, Pulse function or its multiples, two-terms Gaussian function or other functions may be used for this purpose, as well as the analytically extended function (AEF) presented in this paper. AEF gives good approximation of the IEC Standard 61000-4-2 function and experimentally measured ESD currents. Well-defined representation of real ESD currents is needed in order to establish realistic requirements for ESD generators used in testing the equipment and devices, as well as to provide and improve the repeatability of tests. It should be able to approximate the current for various test levels, test set-ups and procedures, and also for various ESD conditions such as approach speeds, types of electrodes, relative arc length, humidity, etc. A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition. |

Data Classifications with Support Vector Machines and Generalized Support Vector Machine | Qi | Approved | In the paper, we study the theory of support vector machine and the using for linear and nonlinear classi
cation of data. And we also used the notion of generalized support vector machine for data cla . . . Read More
## Data Classifications with Support Vector Machines and Generalized Support Vector Machine
In the paper, we study the theory of support vector machine and the using for linear and nonlinear classi cation of data. And we also used the notion of generalized support vector machine for data classi cations. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide several examples to support our results. |

Fractional derivative of the Zeta Functions and Functional Equations | Guariglia | Approved | Emanuel Guariglia*, Sergei Silvestrov** * Department of Physics “E. R. Caianiello”, University of Salerno, Fisciano, Italy ** Division of Applied Mathematics, UKK, Mälardalen University , Västerås, Sw . . . Read More ## Fractional derivative of the Zeta Functions and Functional Equations
Emanuel Guariglia*, Sergei Silvestrov** * Department of Physics “E. R. Caianiello”, University of Salerno, Fisciano, Italy Special functions are described by their functional equation. The case of the Riemann zeta function is one of the most popular. Its functional equation can be achieved by applying the periodic Poisson summation formula. This same procedure may be applied to derive the Hurwitz’s formula for the Hurwitz zeta function. In the attempt to discover the functional equations about their fractional derivatives, new properties of these latter have been discovered. |

INFLUENCE OF NOZZLE SHAPE, REYNOLDS NUMBER AND NOZZLE-TO-PLATE DISTANCE ON FLOW CHARACTERISTICS, WALL SHEAR RATE AND MASS TRANSFER GENERATED BY SUBMERGED ROUND IMPINGING JETS | Montagné | Approved | Brice MONTAGNÉ (1) , Kodjovi SODJAVI (1), Amina MESLEM (2), Vaclav SOBOLIK (1) (1) Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE), Pôle Sciences et Technologie – Avenue Michel Cr . . . Read More ## INFLUENCE OF NOZZLE SHAPE, REYNOLDS NUMBER AND NOZZLE-TO-PLATE DISTANCE ON FLOW CHARACTERISTICS, WALL SHEAR RATE AND MASS TRANSFER GENERATED BY SUBMERGED ROUND IMPINGING JETS
Brice MONTAGNÉ (1) , Kodjovi SODJAVI (1), Amina MESLEM (2), Vaclav SOBOLIK (1) Heat, mass and momentum transfer induced on a wall by an impinging jet are linked to the jet control parameters. This study presents measurements of velocities, wall shear rates (γ) and mass transfer coefficient (Sh) for submerged impinging jets issued from three round nozzles having a same exit diameter D. Convergent nozzle (CONV), round orifice perforated on a flat plate (RO/P) and on a hemispherical surface (RO/H) were compared. Various types of jet control parameters have been used to provide a wide range of data. Apart from the nozzle shape, the jet Reynolds number (Re) and the nozzle-to-plate distance (H) were varied from 500 to 6500 and 2D to 8D, respectively. |

Calculating PageRank in a changing network | Silvestrov | Approved | PageRank is a method which is used to rank the nodes of a network such as the network consisting of the webpages on the Internet and the links between them, other information and communication network . . . Read More
## Calculating PageRank in a changing network
PageRank is a method which is used to rank the nodes of a network such as the network consisting of the webpages on the Internet and the links between them, other information and communication networks or networks in data mining and network analysis of big data. Many real world networks change over time resulting in the need to re-calculate PageRank after a while. In this talk we will show how the old rank can be used to find the ranking in the new network for some simple changes in a network or strongly connected component part of the network. In particular three types of changes will be considered: 1) changes to the personalization vector used in PageRank, 2) adding or removing a single edge and 3) re-scaling the weight of all edges going out of a single vertex. In order to achieve this a non-normalised variation of PageRank will be used based on a sum of random walks on the network. |

Passive control of supplied air jets for thermal comfort improvement in ventilated spaces | Pierre | Approved | Mixing ventilation is commonly used to control thermal comfort in a room by means of air jets generated from diffusers. Diffusers should distribute the fresh air and energy for heating or cooling, in . . . Read More
## Passive control of supplied air jets for thermal comfort improvement in ventilated spaces
Mixing ventilation is commonly used to control thermal comfort in a room by means of air jets generated from diffusers. Diffusers should distribute the fresh air and energy for heating or cooling, in the entire occupied zone. Hence, the design of the diffuser must aim the ability to well mix the jet with the ambient air. The airflow pattern in the occupied zone is highly dependent on the geometry of the diffuser, even if all other factors are the same, such as room configuration, room heat loads levels and locations, position of the diffuser in the room, and supply air conditions. Enhancement of jet entrainment by means of lobes inserted into a diffuser, has been recently proposed as a promising and low-cost solution for improving the performance of HVAC systems. The present study aims the quantification of this effect on room air motion and subsequent thermal comfort. A commercial multi-cone circular ceiling diffuser is used to control indoor thermal conditions. The internal geometry of that diffuser can be arranged to produce either a vertical pattern distribution in heating conditions, or a horizontal pattern distribution in cooling conditions so as the jet attaches to the ceiling and spreads radially along its surface. Experimental investigations are made on jet characteristics and thermal comfort generated in a full scale model room by the multi-cone diffuser and its performance is compared with the innovative diffuser having similar geometry, and including inserted lobes. The impact of the inserted lobes is evaluated under same heating and cooling conditions. |

Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents | Lundengård | Approved | A number of current functions have been proposed in the literature to model the electrostatic discharge (ESD) currents. They are mostly based on exponential functions. Double exponential function or i . . . Read More
## Multi-Peaked Analytically Extended Function Representing Electrostatic Discharge (ESD) Currents
A number of current functions have been proposed in the literature to model the electrostatic discharge (ESD) currents. They are mostly based on exponential functions. Double exponential function or its four-term version, Pulse function or its multiples, two-terms Gaussian function or other functions may be used for this purpose, as well as the analytically extended function (AEF) presented in this paper. AEF gives good approximation of the IEC Standard 61000-4-2 function and experimentally measured ESD currents. Well-defined representation of real ESD currents is needed in order to establish realistic requirements for ESD generators used in testing the equipment and devices, as well as to provide and improve the repeatability of tests. It should be able to approximate the current for various test levels, test set-ups and procedures, and also for various ESD conditions such as approach speeds, types of electrodes, relative arc length, humidity, etc. A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition. |

Power series expansion of functions involving generalized Vandermonde matrices | Österberg | Approved | Explicit expressions for power series expansions of functions involving generalized Vandermonde matrices are presented. Many generalizations of Vandermonde matrices exist. Some considered generalizati . . . Read More ## Power series expansion of functions involving generalized Vandermonde matrices
Explicit expressions for power series expansions of functions involving generalized Vandermonde matrices are presented. |

Identification and functional characterization of a glioma specific retroviral integration landscape | Weishaupt | Approved | A variety of different methods, including the Sleeping Beauty and PiggyBac transposon systems as well as retroviruses, are currently used for the tagging of cancer genes in forward genetic screens. Co . . . Read More
## Identification and functional characterization of a glioma specific retroviral integration landscape
A variety of different methods, including the Sleeping Beauty and PiggyBac transposon systems as well as retroviruses, are currently used for the tagging of cancer genes in forward genetic screens. Comparisons of the insertional landscapes between some of these techniques have previously suggested that there might exist a certain degree of bias in how they integrate into the genome. Specifically, rather than integrating randomly, some retroviruses are now considered to integrate preferentially in regions involved in active transcription. As a consequence, using this system for the tagging of cancer genes one would expect different functional outcomes depending on the model cell and target cancer type. In this project we aim to characterize these functional differences in more detail on a set of glioma integration sites, which we previously derived using a PDGFB-MMLV retrovirus system. We propose here to compare the functional properties of this glioma integration landscape against a variety of other virus and tumor models available through the Retrovirus and Transposon tagged Cancer Gene Database (RTCGD). Specifically, we propose first to identify clusters of integration site, referred to as common insertion sites (CIS), which are either unique for distinct normal brain cells or glioma or shared with other tumors. Next we will determine dependencies between CIS in terms of co-occurrence or mutual exclusivity. Subsequently, for each of these sets of signature CIS, we will finally determine functional annotations and overrepresentation of certain biological pathways or genes sets. |

Test Application for Support Vector Machines: The Estimation of Adults’ Cognitive Skills through Certain Kernel Types based on WAIS-R | Karaca | Approved | Test Application for Support Vector Machines: The Estimation of Adults’ Cognitive Skills through Certain Kernel Types based on WAIS-R Abstract Wechsler Adult Intelligence Scale—Revised (WAIS-R) is a . . . Read More ## Test Application for Support Vector Machines: The Estimation of Adults’ Cognitive Skills through Certain Kernel Types based on WAIS-R
Test Application for Support Vector Machines: The Estimation of Adults’ Cognitive Skills through Certain Kernel Types based on WAIS-R Abstract |

Iterated function systems, wavelets, fixed points, fractal attractors and commutative and non-commutative families of operators | Silvestrov | Approved | In this talk I will present some results and constructions connecting iterated function systems, wavelets, fixed points, fractal attractors and commutative and non-commutative families of operators Read More ## Iterated function systems, wavelets, fixed points, fractal attractors and commutative and non-commutative families of operators
In this talk I will present some results and constructions connecting iterated function systems, wavelets, fixed points, fractal attractors and commutative and non-commutative families of operators |

Total Abstracts: 19

#### M3: Mathematical modeling, numerical algorithms and aerospace techniques

Abstract: The session is dedicated to contributions on fluid mechanics, optimization and control from aerospace with application to various problems such as renewable energy problems.

Our session incl . . .Read More

##### M3: Mathematical modeling, numerical algorithms and aerospace techniques

*Abstract:*

**Abstract:** The session is dedicated to contributions on fluid mechanics, optimization and control from aerospace with application to various problems such as renewable energy problems.

Our session includes but is not limited to the following topics:

Numerical algorithms and computing methods in aerodynamics;

CFD analysis on the rotor or on the rotor blades;

Aerodynamic design optimization (rotor, blades, airfoils);

Active or passive flow control methods;

Structural-response / Aeroelastic analysis;

Hybrid photovoltaic/wind energy systems;

Noise of wind turbines (prediction and reduction methods);

Computation of classes of models based on the experimental data;

Wind engineering.

** Organizers:** Alexandru DUMITRACHE , “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, ROMANIA Florin FRUNZULICA, Faculty of Aerospace Engineering, POLITEHNICA University of Bucharest, ROMANIA.

Title | Author | Status | Abstract |
---|---|---|---|

Bifurcation of transonic flows admitting a shock wave/ sonic surface interaction | Kuzmin | Approved | In the 1990s and 2000s, numerical simulations revealed an instability of the 2D transonic flow over airfoils comprising a flat or nearly flat arc [1]. The instability is caused by an interaction of do . . . Read More
## Bifurcation of transonic flows admitting a shock wave/ sonic surface interaction
In the 1990s and 2000s, numerical simulations revealed an instability of the 2D transonic flow over airfoils comprising a flat or nearly flat arc [1]. The instability is caused by an interaction of double supersonic regions that arise and expand on the arc when the free-stream Mach number increases. The expansion is followed by an abrupt coalescence of the supersonic regions, crucial changes of the flow field, and non-unique steady states. In the 3D flow over wings, the supersonic regions may coalesce either gradually or abruptly, depending on the wing twist and sweep angle [2]. The non-uniqueness of transonic flow also arises in channels where a sonic surface forms over an expansion corner of the lower wall, while the shock wave appears due to a bend of the upper wall [3]. In practice such a problem may occur, e.g., when an intake encounters variations of the incoming flow because of a maneuvering flight of supersonic aircraft. This work addresses 3D flow bifurcation in both divergent and convergent-divergent channels of rectangular cross section. A computational domain expands upstream of the channels in order to capture a detached shock wave. Numerical solutions of the unsteady Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver of the second order accuracy using several turbulence models. We study bifurcations arisen due to the interaction of the expansion flow at the channel throat with the shock wave formed in front of the cowl. Computations show that the bifurcation band widens as the cowl slope angle or the distance between the cowl tip and throat increases. Inversely, when the distance decreases, the hysteresis shrinks and the flow becomes very sensitive to unsteady perturbations at adverse values of the free-stream Mach number. In addition we examine the instability of transonic flow over a cylinder located above an expansion corner for several values of the expansion angle. References [1] A. Kuzmin. Non-unique transonic flows over airfoils. Computers and Fluids, Vol. 63, p. 1-8, 2012. [2] A.N. Ryabinin, Transonic flow past symmetrical unswept and swept wings with elliptic nose. ARPN Journal of Engineering and Applied Sciences, Vol. 10, no. 20, p. 9359-9363, 2015. [3] A. Kuzmin. Shock wave bifurcation in channels with a bend. Archive of Applied Mechanics, doi: 10.1007/s00419-015-1062-z, p. 1-9, 2015. |

Using Potential Flow Theory and Conformal Mapping Technique to Measure Pressure Differential on Airfoil | Mughal | Approved | Flow around an airfoil to calculate pressure co-efficient variations at different relative velocities have always been an important/basic part of Aerodynamic Study. Potential flow theory is used to st . . . Read More
## Using Potential Flow Theory and Conformal Mapping Technique to Measure Pressure Differential on Airfoil
Flow around an airfoil to calculate pressure co-efficient variations at different relative velocities have always been an important/basic part of Aerodynamic Study. Potential flow theory is used to study flow behavior on rankine half body, non rotating cylinder and rotating cylinder as it is more trackable. Falkan Skan Similarity Solution is taken to simulate the flow behavior on wedge. However, to use potential flow theory on usable airfoils the author have used conformal mapping to show a relation between realistic airfoil shapes and the knowledge gained from flow about cylinders. This method can further be used in the designing of an airfoil section. The author has used Joukowski Tranform to generate the flow around airfoils of various geometries and then utilized Kutta condition to force the stagnation point at the trailing edge. Co-efficient of pressure over the entire airfoil surface were calculated and corrected using Karman-Tsien compressibility correction equations. On the basis of this, the location of the ports to install the flush measurement system is suggested. |

Stability of shallow flows: a weakly nonlinear approach | Kolyshkin | Approved | We analyze stability of shallow flows with free surface using weakly nonlinear theory. Resistance forces in the system of equations are modeled using the Chezy formula. Previous studies in a weakly n . . . Read More ## Stability of shallow flows: a weakly nonlinear approach
We analyze stability of shallow flows with free surface using weakly nonlinear theory. |

Modelling of delamination growth in laminated plates using cohesive zone model techniques | Chernyakin | Approved | The damage growth of delamination in composite structure was investigated numerically. An effective approach based on a cohesive zone model is proposed to simulate the delamination propagation in the . . . Read More
## Modelling of delamination growth in laminated plates using cohesive zone model techniques
The damage growth of delamination in composite structure was investigated numerically. An effective approach based on a cohesive zone model is proposed to simulate the delamination propagation in the laminated composite materials subjected to the quasistatic loading. This technique is based on interaction of two coinciding surfaces which will represent reference surfaces of two connected shells. The cohesive zone model is used to define the cohesion area for potential delamination propagation. This approach was implemented in the ANSYS® software package and was validated on testing models that are commonly used for experimental research of fracture processes. |

Finite element analysis of panels with surface cracks | Chernyakin | Approved | Dangerous conditions to the aerospace structures can often be caused by different defects which occur in the panels. Non-through surface cracks attract particular interest. Generally these cracks have . . . Read More
## Finite element analysis of panels with surface cracks
Dangerous conditions to the aerospace structures can often be caused by different defects which occur in the panels. Non-through surface cracks attract particular interest. Generally these cracks have compound front form. In global practice defects are approximated with the semielliptical cracks to simplify calculation methods. In this case the defect is considered two-parameter and it is only defined by maximum depth and length. |

Fatigue life prediction for expansion bellows | Chernyakin | Approved | In this paper the expansion bellows which was designed to make compensation for the mutual axial displacement of the fuel line flanges is considered. The aim of this study to evaluate the performance . . . Read More ## Fatigue life prediction for expansion bellows
In this paper the expansion bellows which was designed to make compensation for the mutual axial displacement of the fuel line flanges is considered. |

Numerical Analysis of NREL VI Wind Turbine Rotor Performance | Cernat | Approved | In the present study, a number of RANS simulations were performed on the well-known NREL VI wind turbine rotor. The simulations are based on finite volume method performed to characterize in detail th . . . Read More
## Numerical Analysis of NREL VI Wind Turbine Rotor Performance
In the present study, a number of RANS simulations were performed on the well-known NREL VI wind turbine rotor. The simulations are based on finite volume method performed to characterize in detail the three-dimensional behavior of the flow in order to identify the re-circulation zones, which the classical methods of design, like blade element momentum theory cannot predict. This information is very useful in the rotor’s geometry optimization and the active flow control applied to increase the wind turbine performance. |

Numerical Study of Aerodynamic Effects on Road Vehicles Lifting Surfaces | Cernat | Approved | Road vehicles aerodynamic performance analysis depends on the study of engine intake and cooling flow, internal ventilation, tire cooling, and overall external flow as the motion of air around a movin . . . Read More
## Numerical Study of Aerodynamic Effects on Road Vehicles Lifting Surfaces
Road vehicles aerodynamic performance analysis depends on the study of engine intake and cooling flow, internal ventilation, tire cooling, and overall external flow as the motion of air around a moving vehicle affects all of its components in one form or another. Due to the complex geometry of these, the aerodynamic interaction between the various body components is significant, resulting in vortex flow and lifting surface shapes. The present study, however focuses on the effects of external aerodynamics only, and in particular on the flow over the lifting surfaces. |

THE EFFECT OF WIND DIRECTION AND BUILDING SURROUNDINGS ON A MARINA BAY IN THE BLACK SEA | Katona | Approved | The wind effect has usually a major importance in the marina bay. These environmental sites are an interplay between tourist and commercial activities, requiring a high-detailed and definition studies . . . Read More
## THE EFFECT OF WIND DIRECTION AND BUILDING SURROUNDINGS ON A MARINA BAY IN THE BLACK SEA
The wind effect has usually a major importance in the marina bay. These environmental sites are an interplay between tourist and commercial activities, requiring a high-detailed and definition studies of the dynamic fluid in the harbor. Computational Fluid Dynamics (CFD) has been used elaborately in urban surroundings research. However, most CFD studies were performed for harbors for only a confined number of wind directions and/or without considering the building surroundings effects. This paper presents the results of different simulations based on various wind flows and the CFD simulations of coupled urban wind flow and general wind directions upon a coastal semi-closed area. Thus the importance of wind effects on the evaluation of the marina bay will be pointed out to achieve a safe and secure mooring at the berth and eventually a good potential of renewable energy for an impending green harbor. |

Non Lyapunov stability of a constant spatially developing 2-D gas flow | Tanasie | Approved | Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in the phase space of continuousl . . . Read More
## Non Lyapunov stability of a constant spatially developing 2-D gas flow
Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1]. |

Lyapunov stability of a spatially developing constant 2D gas flow | Szabo | Approved | The Lyapunov stability of a spatially developing constant 2D gas flow is analyzed in a particular infinite dimensional phase space. The elements of the phase space are continuously differentiable func . . . Read More
## Lyapunov stability of a spatially developing constant 2D gas flow
The Lyapunov stability of a spatially developing constant 2D gas flow is analyzed in a particular infinite dimensional phase space. The elements of the phase space are continuously differentiable functions, the algebraic operations are usual and the topology is that generated by the uniform convergence. The Lyapunov stability with respect to instantaneous, as well with respect to source produced permanent time harmonic perturbations are investigated. Some of the obtained results are completely different from those reported in the literature. |

Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate | Balint | Approved | Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow is analyzed in the phase space of continuously . . . Read More
## Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate
Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow is analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1]. |

Rationality of Large Mass Method for Frequency Response Analysis | Mehmood | Approved | Most of previous work on Large Mass (LM) Method by Kim Y.-W. and Jhung, M. J.for dynamic problems is related to the study of transient responses. This paper discusses the numerical effectiveness of La . . . Read More
## Rationality of Large Mass Method for Frequency Response Analysis
Most of previous work on Large Mass (LM) Method by Kim Y.-W. and Jhung, M. J.for dynamic problems is related to the study of transient responses. This paper discusses the numerical effectiveness of Large Mass Method for frequency response problems in truss structures. The results achieved are of great importance for design of launch vehicle structures which must be capable of withstanding a wide range of frequencies for smooth operation of sensors. The paper also presents a very simple technique for developing an LM analysis model through programming language e.g. MATLAB. |

Numerical study of a finite volume scheme for incompressible Navier-Stokes equations based on SIMPLE-family algorithms. | Alahyane | Approved | In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large categor . . . Read More
## Numerical study of a finite volume scheme for incompressible Navier-Stokes equations based on SIMPLE-family algorithms.
In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large category of problems this could be understood from its stability and convergence, which depends strongly on the parameter of relaxation, in some cases this algorithm could have an unexpected behavior. Therefore, in our work we focus on this particular point to overcome this respected choice of relaxation parameter. This will be followed by numerical applications in image processing variety of fluid flow problems described by incompressible Navier-Stokes equations. |

Twin Flapping wings as an alternative method of harvesting energy from wind | Alexandru | Approved | F. Frunzulica*,**, Al. Dumitrache**, M. Stoia-Djeska* *POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering, Polizu 1-6, RO-011061, Bucharest, Romania Institute of Mathematical Statis . . . Read More ## Twin Flapping wings as an alternative method of harvesting energy from wind
F. Frunzulica*,**, Al. Dumitrache**, M. Stoia-Djeska* *POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering, Polizu 1-6, RO-011061, Bucharest, Romania In the last decades, the wind energy became more attractive to Romania, and thus many resources are allocated to develop the energetic systems based on wind energy. In this work we have investigated the possibility to harvest the wind energy with an controlled pitch-plunge aeroelastic system composed by two wings in side-by-side configuration. Compared to the conventional systems using wind turbines which are based on transforming the wind energy into mechanical energy of a rotational horizontal or vertical axle rotor, the new proposed systems under consideration convert the wind energy into mechanical energy too, but of a coupled translation-rotation (plunge-pitch) motion, the wings oscillates in opposite directions. The pitch-plunge motion may be passively or actively controlled by the driving elastic system and by flap and/or slat controls for each wing. In the present study, aerodynamic analysis of twin-wing, in side-by-side position, is numerically investigated using an imposed motions for wings. Two-dimensional unsteady flow over system is performed with Ansys Fluent program, using Reynolds-Averaged Navier-Stokes model, completed by k – \omega Shear Stress Transport Turbulence model. Main parameters like individually coefficient of torque, and power coefficient of moving wings system are investigated. The results from our dual-wing found that a twin-wing device can produce more power compared to a single wing due to the strong unsteady flow interaction between the wings. |

ANALYSIS OF CONTROL SYSTEM RESPONSES FOR AIRCRAFT STABILITY AND EFFICIENT NUMERICAL TECHNIQUES FOR REAL-TIME SIMULATIONS | ANDREI | Approved | The objectives of this paper are the study and the implementation of both aerodynamic and propulsion models, as linear interpolations using look-up tables in a database. The aerodynamic and propulsion . . . Read More
## ANALYSIS OF CONTROL SYSTEM RESPONSES FOR AIRCRAFT STABILITY AND EFFICIENT NUMERICAL TECHNIQUES FOR REAL-TIME SIMULATIONS
The objectives of this paper are the study and the implementation of both aerodynamic and propulsion models, as linear interpolations using look-up tables in a database. The aerodynamic and propulsion dependencies on state and control variable have been described by analytic polynomial models. Some simplifying hypotheses were made in the development of the nonlinear aircraft simulations. The choice of a certain technique to use depends on the desired accuracy of the solution and the computational effort to be expended. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. The engine power dynamic response was modeled with an additional state equation as first order lag in the actual power level response to commanded power level was computed as a function of throttle position. The number of control inputs and engine power states varied depending on the number of control surfaces and aircraft engines. The set of coupled, nonlinear, first-order ordinary differential equations that comprise the simulation model can be represented by the vector differential equation. A linear time-invariant (LTI) system representing aircraft dynamics for small perturbations about a reference trim condition is given by the state and output equations present. The gradients are obtained numerically by perturbing each state and control input independently and recording the changes in the trimmed state and output equations. This is done using the numerical technique of central finite differences, including the perturbations of the state and control variables. For a reference trim condition of straight and level flight, linearization results in two decoupled sets of linear, constant-coefficient differential equations for longitudinal and lateral / directional motion. The linearization is valid for small perturbations about the reference trim condition. Experimental aerodynamic and thrust data are used to model the applied aerodynamic and propulsion forces and moments for arbitrary states and controls. There is no closed form solution to such problems, so the equations must be solved using numerical integration. Techniques for solving this initial value problem for ordinary differential equations are employed to obtain approximate solutions at discrete points along the aircraft state trajectory. |

PERFORMANCE ANALYSIS AND DYNAMIC MODELING OF A SINGLE-SPOOL TURBOJET ENGINE | ANDREI | Approved | The research performed in this paper is focused on two main directions. The first objective is represented by the modeling a single-spool turbojet engine such that to calculate its performances for a . . . Read More
## PERFORMANCE ANALYSIS AND DYNAMIC MODELING OF A SINGLE-SPOOL TURBOJET ENGINE
The research performed in this paper is focused on two main directions. The first objective is represented by the modeling a single-spool turbojet engine such that to calculate its performances for a specified range of flight altitude and Mach number, as well as various engine operational regimes. From the numerical simulations which are based on thermo-dynamical analysis of the engine, have been determined parameter correlations, e.g. thrust -fuel flow, which enables the deduction of a control law for the fuel flow. From the thermo-dynamical analysis are obtained the values for significant engine parameters which are required by the engine’s dynamic study. The second objective refers to the study of the dynamic behavior of the turbojet engine, with appropriate dynamic modeling. The universal maps of both compressor and turbine are required for the dynamic analysis, and the thrust (as the engine’s main performance) is controlled in case of a single spool turbojet by a single parameter, i.e. the fuel flow; the determination of the necessary amount of fuel is done iteratively, with slight corrections, as perturbations of input fuel flow from the calculation of flow balance at turbine inlet and turbine exit. |

The Buckling Analysis of Elements of Stiffened Aircraft Structure | Borisova | Approved | Investigation of stability of stiffened cylindrical thin shells involves great mathematical difficulties, connected with sufficiently high order of equations. These difficulties in most cases eliminat . . . Read More
## The Buckling Analysis of Elements of Stiffened Aircraft Structure
Investigation of stability of stiffened cylindrical thin shells involves great mathematical difficulties, connected with sufficiently high order of equations. These difficulties in most cases eliminate the possibility of analytical approach of such structures. In this cases numerical methods are used. Thin-walled profiles are commonly used as the reinforcing ribs. In many cases these structures under the acting external loads are compressed. Therefore, the problem of determination of the critical stress of compressed cylindrical shells stiffened by longitudinal ribs has great practical interest. In this paper we consider plate, as a limiting case of curved panels. A new approach, based on Ritz method, for buckling analysis of stiffened plates under axial compression with the discrete and eccentric location of the longitudinal elastic ribs, is developed. Suggested approximations of displacements allow to take into account the features of system wave formation. It takes into account the effect of warping of the cross section of the rod. Contact interaction of the plate and the rod is taken into account approximately by using the concept of reduced plate width. This method provides sufficient accuracy in determining critical loads. The results are compared with data, received by finite element method. |

Considering factorial series as time integration method | Razafindralandy | Approved | Recently, a time integration method of ODE’s and PDE’s, based on a Taylor series decomposition of the solution, has been proposed. In this method, the series decomposition is followed by a Borel summa . . . Read More
## Considering factorial series as time integration method
Recently, a time integration method of ODE’s and PDE’s, based on a Taylor series decomposition of the solution, has been proposed. In this method, the series decomposition is followed by a Borel summation procedure. This procedure, which consists in finding an (sectorial-wise) analytic solution from the Taylor series, is indeed necessary if the radius of convergence is zero. And if the Taylor series is convergent, the Borel summation acts like an extrapolation method outside the convergence disc, and speeds up the numerical resolution. The most natural algorithm to realize the Borel summation is the Borel-Padé algorithm. It consists in computing the Borel transform of the series, replacing it by an analytic solution via a Padé approximant, and going back to the physical space thanks to a Laplace transformation. This algorithm has proven to be efficient in solving mechanics problems (explicit scheme, natural handling of some non-linearities, faster than some other explicit methods, good conservation properties for Hamilton systems, resolution of the Navier-Stokes equations, …). The force, but also the weakness of the proposed algorithm is the use of Padé approximants. Indeed, on one hand, the latter are known to be an efficient tool in prolonging a convergent series outside its validity disk. They may also be usefull in finding poles and then in choosing the direction of the Laplace transform. On the other hand, the standard algorithm of Padé approximation requires the resolution of a linear problem which may be ill-conditioned and, sometimes, not inversible. Solutions to circumvent these problems exist but at extra costs. The aim of this communication is to present an alternative to the Borel-Padé algorithm in the computation of the Borel sum of the series. It consists in representing directly the Borel sum as an inverse or generalised factorial series. We then explore the advantages and limits of this algorithm in the perspective of a time integration method. |

Nonlinear analysis and control of an aircraft in the neighbourhood of deep stall | KOLB | Approved | When an aircraft is locked in a stable equilibrium at high angle-of-attack, we have to do with the so-called deep stall which is a very dangerous situation. Airplanes with T-tail are mainly concerned . . . Read More
## Nonlinear analysis and control of an aircraft in the neighbourhood of deep stall
When an aircraft is locked in a stable equilibrium at high angle-of-attack, we have to do with the so-called deep stall which is a very dangerous situation. Airplanes with T-tail are mainly concerned with this phenomenon since the wake of the main wing flows over the horizontal tail and renders it ineffective but other aircrafts such as fighters can also be affected. |

Nasedkin A.V., Nasedkina A.A., Kornievsky A.S. Modeling of nanostructured porous thermoelastic composites with surface effects | Nasedkin | Approved | The paper considers an integrated approach to the determination of the material properties of nanoscale thermoelastic bulk (mixture) stochastically distributed composites of an arbitrary anisotropy cl . . . Read More
## Nasedkin A.V., Nasedkina A.A., Kornievsky A.S. Modeling of nanostructured porous thermoelastic composites with surface effects
The paper considers an integrated approach to the determination of the material properties of nanoscale thermoelastic bulk (mixture) stochastically distributed composites of an arbitrary anisotropy class with account for their internal microstructure. ANSYS finite element package was used to simulate representative volumes and to calculate the effective moduli. This approach is based on the theory of effective moduli of composite mechanics, modeling of representative volumes and the finite element method. Here, the contact boundaries between material and pores were covered by the surface membrane elastic elements in order to take the surface effects into account. For automated coating of internal boundaries of pores in the cubic representative volume the following algorithm was used. At the beginning, as a result of the formation of the porous structure, the finite element mesh from octanodal cubic elements was created, some of which had the material properties of thermoelastic material, and the other part of the elements had the material properties of the pores (with negligible elastic stiffness moduli). Further, only the finite elements with thermoelastic material properties were selected. The resulting elements on the outer boundaries were covered by four nodal target contact elements. Then, the contact elements, which were located on the external surfaces of the full representative volume, were removed, and the remaining contact elements were replaced by the four nodal membrane elastic elements. As a result, all the facets of the contact of thermoelastic structural elements with pores were coated by membrane finite elements. The next step consisted in solving the static problems for obtained representative volume with the main boundary conditions which were conventional for effective moduli method. Further, in the ANSYS postprocessor the averaged stresses were calculated, both on the volume finite elements and on the surface finite elements. Finally, the effective moduli of porous composite with surface effects were calculated from the corresponding formulas of the effective moduli method by using the estimated average characteristics. In the results of computational experiments, the following features were observed. If we compare two similar bodies, one of which has usual dimensions and the other is a nanoscale body, then for the nanosized body due to the surface stresses the effective stiffness will be greater than for the body with usual sizes. Furthermore, for the porous body of the usual size the effective elastic stiffness decreases with increasing porosity. Meanwhile, the effective stiffness of nanocomposite porous body with the same porosity may either decrease or increase depending on the values of surface moduli, dimensions and number of pores. This effect is explained by the fact that the sizes of the surface pore with surface stresses depend not only on the overall porosity, but also on the configuration, size and number of pores. This work was supported by the Russian Science Foundation (grant number 15-19-10008). |

Aerodynamics investigations of a disc-wing UAV | Florin | Approved | Alexandru DUMITRACHE**, Florin FRUNZULICA*,**, Sorin GRIGORESCU*, Bogdan SUATEAN (PhD)* *POLITEHNICA University of Bucharest, Romania **Institute of Mathematical Statistics and Applied Mathematics, . . . Read More ## Aerodynamics investigations of a disc-wing UAV
Alexandru DUMITRACHE**, Florin FRUNZULICA*,**, Sorin GRIGORESCU*, An axi-symmetric disc-wing with hollowed out underside cavity and an elliptic cross-section is considered in a flow speed range up to 20 m/s. This type of wing can be used in the construction of a unmanned air vehicle (UAV) to achieve a high maneuverability. The purpose of this study is to understand the physics of flow around this type of wing in flight in order to determine appropriate methods of control. Passive flow control methods by which aerodynamic control moments can be generated are considered instead of those which use moving surfaces. |

Total Abstracts: 22

#### M5: Nonlinear Problems of Guidance, Navigation and Control

Abstract: The session topic is focused on modeling, nonlinear mathematical and computational research of the guidance, navigation and control systems for both information satellites, space astronomica . . .Read More

##### M5: Nonlinear Problems of Guidance, Navigation and Control

*Abstract:*

**Abstract:** The session topic is focused on modeling, nonlinear mathematical and computational research of the guidance, navigation and control systems for both information satellites, space astronomical observatories, space free-flying robots and all kinds of aeronautical vehicles. New methods and results will be presented from Russia (Moscow, Saint Petersburg, Samara, Kazan, Irkutsk), France (Paris, Toulouse), Germany, Italy, Spain and Turkey. Speakers from other countries are welcome for participation in the session, which also will contain papers submitted by members of the IFAC http://www.ifac-control.org/ Technical committee on Aerospace.

**Organizers**: Prof. Yevgeny Somov, *Russia **, *Prof. Houria Siguerdidjane, France

Title | Author | Status | Abstract |
---|---|---|---|

Attitude guidance and control of the GLONASS navigation satellites at passage of singular orbit sites | Somov | Approved | We have considered a logic of the GLONASS spacecraft (SC) attitude guidance laws during their passage of the singular orbit sites, namely large and small angles between the Sun and Earth directions ap . . . Read More
## Attitude guidance and control of the GLONASS navigation satellites at passage of singular orbit sites
We have considered a logic of the GLONASS spacecraft (SC) attitude guidance laws during their passage of the singular orbit sites, namely large and small angles between the Sun and Earth directions applied for definition of the solar-terrestrial reference frame (STRF). Moreover, we have studied problems on minimization of influence the solar pressure forces upon the SC mass centre and on calculation of the position errors by an onboard antenna phase centre with respect to the STRF. We developed algorithms for the SC anticipatory turn which are put both in the satellite onboard computer and in the consumer equipment. The algorithms allow to calculate both the SC guidance law on the SC yaw channel and corrections on position of its antenna phase centre applied in the consumer devices. |

Guidance and adaptive-robust attitude & orbit control of a small information satellite | Somov | Approved | We have considered a small information satellite (for communication, radio-electronic and optoelectronic land-survey, etc.) which may be placed into an orbit with altitude from 600 to 1000 km. Diffe . . . Read More
## Guidance and adaptive-robust attitude & orbit control of a small information satellite
We have considered a small information satellite (for communication, radio-electronic and optoelectronic land-survey, etc.) which may be placed into an orbit with altitude from 600 to 1000 km. Different disturbance factors necessitate correction of such satellite orbit motion intended for long-term (up to 15 years) operation. When a spacecraft (SC) is moving on orbit, its solar array panels are directed to the Sun, therefore, both the satellite inertia tensor and the satellite mass change because of fuel expenditure for the orbit station-keeping. The SC attitude and orbit control system (AOCS) contains a strap-down inertial navigation system with astronomic correction and a cluster of four reaction wheels, which is unloaded from an accumulated angular momentum due to the magnetic driver and also a correcting engine unit with the electro-reaction engines. We present the solution for the following problems: |

Estimation of Land Remote Sensing Satellites Productivity Based on the Simulation Technique | Kucherov | Approved | While designing land remote sensing satellites (LRSS), it is essential to satisfy the requirements to their efficiency indices. One of the most important efficiency indices is the satellite productivi . . . Read More
## Estimation of Land Remote Sensing Satellites Productivity Based on the Simulation Technique
While designing land remote sensing satellites (LRSS), it is essential to satisfy the requirements to their efficiency indices. One of the most important efficiency indices is the satellite productivity. Here, productivity is treated as a number of separate survey objects taken in a definite time. |

Attitude guidance and simulation with animation of a land-survey satellite motion | Somova | Approved | Nonlinear guidance problem has been solved for a land-survey satellte with analytical representation of the optimal angular guidance laws at scanning observation with given accuracy. A solving o . . . Read More
## Attitude guidance and simulation with animation of a land-survey satellite motion
Nonlinear guidance problem has been solved for a land-survey satellte with analytical representation of the optimal angular guidance laws at scanning observation with given accuracy. A solving of the problem is based on polynomial interpolation for a vector function of the modified Rodrigues parameters. We also consider problem for optimization of spatial rotational maneuver by a land-survey satellite at its passage from any scanning route to other route with general kinematic boundary conditions – on an orientation quaternion, on vectors of angular rate and acceleration. For the nonlinear optimization problem we present an approximate analytic solution in the form of the smooth conjugated vector splines with different degrees. In result for a land-survey satellite we have obtained the vector polynomial guidance laws for all its operational modes. These guidance laws are applied for animation of the land-survey satellite spatial motion. In-flight support has provided for the attitude determination and control system (ADCS) of a land-survey satellite. The support is implemented in terrestrial control flight centre (CFC) in order to ensure the ADCS reliability and survivability at faults of onboard devices. Moreover a telemetric information of operative diagnosis is applied where the measured data have been contained on the satellite kinematic parameters both motion of mass center and angular motion. For the ADCS in-flight supporting the CFC operators have been applied a computer supporting system. In this system the localization is carried out on faults of onboard devices and by dialog with operators the recommendations are forming on needed operations by the solving rules in the knowledge base data. |

Time-Optimal Control of the Spacecraft Trajectories in the Earth-Moon System | Fain | Approved | This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko succe . . . Read More
## Time-Optimal Control of the Spacecraft Trajectories in the Earth-Moon System
This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times. |

Methods for Predicting Unsteady Takeoff and Landing Trajectories of the Aircraft | Shevchenko | Approved | Processes takeoff roll and ground braking on the runway are essentially nonlinear and nonstationary. These phases of the flight mission are performed with the participation of the pilot. Being under t . . . Read More
## Methods for Predicting Unsteady Takeoff and Landing Trajectories of the Aircraft
Processes takeoff roll and ground braking on the runway are essentially nonlinear and nonstationary. These phases of the flight mission are performed with the participation of the pilot. Being under time pressure and in the absence of information support, the pilot is experiencing high psychological stress. Therefore, there are prerequisites for taking improper or wrong decisions |

Nonlinear Modeling and Study for Control of the Research Spacecraft with Solar Sail | Khabibullin | Approved | This paper outlines the mathematical motion model of the research spacecraft that uses solar sail instead of an engine and a propellant. The mathematical motion model for solar sail spacecraft is form . . . Read More
## Nonlinear Modeling and Study for Control of the Research Spacecraft with Solar Sail
This paper outlines the mathematical motion model of the research spacecraft that uses solar sail instead of an engine and a propellant. The mathematical motion model for solar sail spacecraft is formulated and described. The work considers the mathematical motion model within the heliocentric system of coordinates. The best way to assess the reasonableness of the mathematical model is the using model in motion simulation process. On the basis of the formulated mathematical model the special software complex for interplanetary transfer simulation is developed. Especially, the mission of the transfer of the spacecraft from the Earth’s orbit to the potentially hazardous asteroid is simulated. The obtained results during simulation demonstrate correctness and feasibility of the considered mathematical motion model. |

Nonlinear Algorithm for Navigation of a Moving Object in Magnetic Field | Shevchenko | Approved | Consideration was given to the problem of relative positioning with the use of alternating magnetic ﬁeld. The problem was shown to be solvable using a system of three magnetic dipoles emitting magneti . . . Read More
## Nonlinear Algorithm for Navigation of a Moving Object in Magnetic Field
Consideration was given to the problem of relative positioning with the use of alternating magnetic ﬁeld. The problem was shown to be solvable using a system of three magnetic dipoles emitting magnetic ﬁeld at different frequencies. Ambiguity of its solution was discussed, and ways to resolve it were proposed. An algorithm for relative positioning based on the solution of this problem was proposed. Error equations of the positioning algorithm and the results of their analysis were presented. Calibration procedures, improving accuracy of relative positioning, are also considered. One of these procedures, based on nonlinear optimization techniques, was presented in greater details. Particularly,the problem of avoiding local minima during minimization of non-convex cost function was considered carefully. The paper was supplied with several numerical examples demonstrating effectiveness of proposed algorithms in relative positioning. |

An analytic approach to the relation between GPS attitude determination accuracy and antenna configuration geometry | Kozlov | Approved | The reliability and accuracy of GPS attitude determination are still the main relevant theoretical questions. While the first one derives from the probabilistic nature of phase ambiguity resolution al . . . Read More
## An analytic approach to the relation between GPS attitude determination accuracy and antenna configuration geometry
The reliability and accuracy of GPS attitude determination are still the main relevant theoretical questions. While the first one derives from the probabilistic nature of phase ambiguity resolution algorithms and effectiveness of multipath reduction, the second is additionally affected by geometric properties of GNSS antenna configuration. Being trivial in two-antenna system, the relation between GPS attitude determination accuracy and antenna spatial layout becomes much less intuitive for multi-antenna configurations, and seems to have been examined analytically in some specific cases only. For example, most of research papers in the field use Euler angles as attitude representation, which have singularity in some cases, and consider the number of antennas of not more than four. We present some further investigation in this area. In our study we obtain a polynomial representation for the relation between attitude determination accuracy factors, i.e. the singular values of some certain measurement matrix, and antenna baseline vector coordinates. An examination of several specific cases show that our representation can be used to determine the optimal antenna configuration under conventional geometry limitations. |

Block Design of Tracking Systems under Unmatched Disturbances via Sigmoidal Feedbacks | Kochetkov | Approved | The paper deals with the tracking output variables of quasi-canonical system for given signals under unmatched external disturbances and functional uncertainties within the restrictions on state varia . . . Read More
## Block Design of Tracking Systems under Unmatched Disturbances via Sigmoidal Feedbacks
The paper deals with the tracking output variables of quasi-canonical system for given signals under unmatched external disturbances and functional uncertainties within the restrictions on state variables. A new approach, based on the block control principle via sigmuidal local feedbacks is designed. In contrast to the commonly used linear local feedbacks with high gains required for the suppression of disturbances, S-shaped sigma-function is nonlinear, smooth and bounded everywhere, which allows us to take into account the restrictions on the phase variables at the synthesis stage. It is shown that properties similar to the properties of systems with discontinuous controls operating in the sliding mode, are provided in the closed-loop system via smooth and bounded signals in the prelimit case. Namely, the decomposition of the total motion on multirate components and invariance with respect to disturbances with a given accuracy are provided. Decomposition procedure for selecting the parameters of sigmoidal local feedbacks based inequalities is developed. This approach extends the class of admissible systems by nonlinear systems with non-smooth disturbances, where special requirements for the arguments composition of functional uncertainties not needed. Also systems with uncertain input channels of controls are studied. We consider the general case, when matrix front of controls is non-singular, does not have a dominant diagonal, analytical view of its elements is known, their current values are unknown, and limited. For this case, the decomposing synthesis procedure of sigmoidal control actions, based on the method of the hierarchy of controls, is developed. The developed approach is promising and expanding class of robust systems, since in contrast to the known algorithms does not require of constancy (low drift) of unknown parameters. As an example, block procedure of feedback synthesis for controlling the position of the endpoint of a manipulator with electric actuators is designed. Local feedbacks and corrective actions of the states observer in the form of smooth sigma-functions provide tracking of trajectories defined in the coordinate system of the manipulator endpoint. Tracking system is provided the invariance with a given accuracy with respect to the existing uncertainties subject to the restrictions on the variables of the mechanical subsystem. The simulation results of a three-link manipulator in a cylindrical coordinate system show the effectiveness of the developed method. |

Application of GNSS-INS simulator for testing algorithms of the airborne vector gravimetry problem. | Bogdanov | Approved | Laboratory of Control and Navigation of Lomonosov Moscow State University in cooperation with several Russian companies is involved into the project of GNSS-INS simulator elaboration. The first versio . . . Read More
## Application of GNSS-INS simulator for testing algorithms of the airborne vector gravimetry problem.
Laboratory of Control and Navigation of Lomonosov Moscow State University in cooperation with several Russian companies is involved into the project of GNSS-INS simulator elaboration. The first version of the above-mentioned simulator deals with simulation of GNSS (GPS, Galileo, GLONASS) radio signals and was used for testing GNSS users navigation equipment (UNE). The idea of synchronous computer modeling of algorithms of strapdown inertial navigation system (INS) and GNSS radio signals simulation represents an evident development of simulator functional capabilities. GNSS-INS simulator represents a universal tool for testing and investigation of a wide range of navigation applications for land, marine, airborne and space vehicles in case when INS inertial sensors – angular rate sensors, accelerometers – can have different accuracy: from precise laser or FOG gyros to MEMS sensors. |

Tracking problem for electromechanical system under influence of unknown unmatched perturbation | Kochetkov | Approved | The theory of relay systems is widely used for design of electromechanical systems. In particular, modern electric drives are supplied by power electronic converters that have switching nature, and us . . . Read More
## Tracking problem for electromechanical system under influence of unknown unmatched perturbation
The theory of relay systems is widely used for design of electromechanical systems. In particular, modern electric drives are supplied by power electronic converters that have switching nature, and using bang-bang control actions is most convenient from practical point of view. Also, the relay control algorithms can be used for synthesis of closed loop systems on the base of sliding mode. The main advantages of closed loop systems with sliding mode are: |

Estimation of Land Remote Sensing Satellites Operational Efficiency | Kucherov | Approved | One of the most advanced approaches in spacecraft designing is based on regard for required efficiency indices. As to land remote sensing satellites (LRSS), these indices are surveillance frequency, g . . . Read More ## Estimation of Land Remote Sensing Satellites Operational Efficiency
One of the most advanced approaches in spacecraft designing is based on regard for required efficiency indices. |

Arrangement of spacecraft onboard equipment with minimizing the influence of external factors | Shulepov | Approved | We consider actual problems on protection of the spacecraft onboard equipment for decreasing influence of external environment. The problems are studied at design of spacecraft and a flight support of . . . Read More
## Arrangement of spacecraft onboard equipment with minimizing the influence of external factors
We consider actual problems on protection of the spacecraft onboard equipment for decreasing influence of external environment. The problems are studied at design of spacecraft and a flight support of its control system with respect to meteoric particles, electromagnetic radiation and other external factors. We have suggested constructive mathematical methods for increasing the spacecraft survivability during its long-term operation and present some results on the efficiency of the developed methods. |

Nonlinear research of an image motion stabilization system embedded in a space land-survey telescope | Somov | Approved | Unique requirements are presented to an attitude control system of a large-scale maneuvering land-survey satellite on accuracy of its attitude motion stabilization at a scanning optoelectronic observa . . . Read More
## Nonlinear research of an image motion stabilization system embedded in a space land-survey telescope
Unique requirements are presented to an attitude control system of a large-scale maneuvering land-survey satellite on accuracy of its attitude motion stabilization at a scanning optoelectronic observation. For solving of this problem we usually apply an astro-inertial satellite attitude determination system and a gyro moment cluster based on a redundant number of gyrodines. A radically different method is known for an image motion stabilization in space engineering for optoelectronic observation. This method is based on the use of an image motion compensator (IMC) embedded into the telescope optical scheme, moreover, variation of the IMC position causes a displacement of rays at the image formation. |

NONLINEAR MODELING OF AN AEROSPACE OBJECT DYNAMICS | Davydov | Approved | We present the results on modeling of a complicated aerospace object system motion with consideration of nonlinearities. We have developed a computerized panel that allows to measure mutual influence . . . Read More
## NONLINEAR MODELING OF AN AEROSPACE OBJECT DYNAMICS
We present the results on modeling of a complicated aerospace object system motion with consideration of nonlinearities. We have developed a computerized panel that allows to measure mutual influence of the object motion and stabilization device with consideration of its real characteristics. Analysis of the system stability in general was carried out and the time relationships are presented for the system taking into account nonlinearities. |

Liquid oscillations in the tanks’ level sensors of aerospace objects | Davydov | Approved | We have considered reasons on appearance of longitudinal oscillations in the system of fuel consumption control and the methods for reducing of these oscillations. Valuation of the most significant f . . . Read More
## Liquid oscillations in the tanks’ level sensors of aerospace objects
We have considered reasons on appearance of longitudinal oscillations in the system of fuel consumption control and the methods for reducing of these oscillations. Valuation of the most significant factors and them influence on accuracy of the system’s operation in general has been carried out. We have presented recommendations for installation of the system’s sensitive elements. |

A VLF-based technique for analysis and synthesis of nonlinear digital control systems and its applications | Ul’yanov | Approved | In this paper, the development of a computational technology for rigorous analysis and design of nonlinear digital control systems on the basis of the reduction method and sublinear vector Lyapunov fu . . . Read More
## A VLF-based technique for analysis and synthesis of nonlinear digital control systems and its applications
In this paper, the development of a computational technology for rigorous analysis and design of nonlinear digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is given. The digital control system under consideration incorporates the continuous-time dynamics of the plant and the discrete-time dynamics of the controller, i.e. it is hybrid in nature. Unlike most known approaches to analysis of such systems, the proposed technique does not consider the preliminary reduction of the system to the discrete one, which allows us to eliminate the errors associated with discretization and improve the accuracy of the analysis. The technology is applied to the attitude control of a flexible spacecraft in the fine stabilization mode and to the formation control problem for a fleet of autonomous underwater vehicles. Simulation results are provided to demonstrate the performance of the designed control systems. |

Automation of Multi-Agent Control for Complex Dynamic Systems in Heterogeneous Computational Network | Oparin | Approved | Currently, the organization of multi-agent control is one of the most actually problems in the field for research of complex dynamic systems. Within the framework of such control, system objects are p . . . Read More
## Automation of Multi-Agent Control for Complex Dynamic Systems in Heterogeneous Computational Network
Currently, the organization of multi-agent control is one of the most actually problems in the field for research of complex dynamic systems. Within the framework of such control, system objects are presented by the specialized applications (agents), which interact with other objects based on their self-organization in the system control process. This problem becomes much more complicated when agents interact in a heterogeneous computational network and distributed computing is needed for forming control actions by these agents. Analysis of researches in this field shows that nowadays there are no all necessary methods and tools to solve this problem completely. In this regard there is a need to develop new models, methods, algorithms and tools for organizing multi-agent control in a heterogeneous computational network. These developments will provide the fundamentals and high-level tools for creating control systems in various subject areas. In this report the most important aspects for the automation technology of creating self-organizing multi-agent control system are considered. The special attention is paid to the information-logical scheme of a multi-agent control system, the simulation modeling system for analysis of a heterogeneous computational network, the network monitoring system and the algorithms that provide the reliability and effectiveness of control processes. Some features of the technology use are illustrated by the example of solving problems of an automated analysis and parametric synthesis of control systems for variety complex dynamic objects. |

On the problem of discrete-event systems properties preservation | Nadezhda | Approved | We present a novel approach to solving a problem generally arising in studying dynamical systems, namely the problem of a system’s properties preservation under some transformation. For example, since . . . Read More
## On the problem of discrete-event systems properties preservation
We present a novel approach to solving a problem generally arising in studying dynamical systems, namely the problem of a system’s properties preservation under some transformation. For example, since XIX century the problem of stability property preservation during coordinate transformations of differential equations systems is known: stability of the solution in one variables does not imply stability in other variables (A.M. Lyapunov, 1892). On the other hand, properties preservation is the important problem in studying algebraic systems. A number of statements of classical model theory, so called stability theorems, or characteristic theorems, determine a connection between semantic and syntactic properties of the formulas of the first order logic language. Combining algebra, logic and dynamics, the method of logical-algebraic equations (LAE-method) is developed, serving to synthesize criteria for preservation properties of systems connected by special type of morphisms. |

Total Abstracts: 20

#### M1: Functional Analysis and Related Topics with Applications

Abstract:

Functional Analysis and its interaction with PDE are increasingly important areas for mathematical modelling in various kinds of applications both to other fields of Mathematics and to other . . .Read More

##### M1: Functional Analysis and Related Topics with Applications

*Abstract:*

Abstract:

Functional Analysis and its interaction with PDE are increasingly important areas for mathematical modelling in various kinds of applications both to other fields of Mathematics and to other sciences, e.g. physics, material science, numerical analysis, geophysics etc. The main aim of the symposium is to bring together researchers involved to share ideas, recognising the common thread in the recent developments in all aspects of these areas of mathematics and plan for future cooperation and new directions of joint research. As background the participants will present the “state of art” of their research fields. The topics of interest include (but are not limited to): Harmonic Analysis, Operators Theory, Function spaces, Inequalities, Real Analysis, Interpolation Theory, Homogenization Theory, PDE. Summing up, we invite all interested researchers in the areas described above to participate.

Organizers:

Lars-Erik Persson , LTU, Sweden, E-mail: Lars-Erik.Persson@ltu.se

Natasha Samko, LTU, Sweden, E-mail: nsamko@gmail.com

Alessandra Ragusa, UniCt, Italy. E-mail: maragusa@dmi.unict.it

Title | Author | Status | Abstract |
---|---|---|---|

The dual spaces of new lambda^m-sequence spaces and their matrix maps | ERCAN | Approved | In this paper, we compute alpha-, beta- and gamma- duals of the new BK-spaces. We also give some classes of matrix transformations from these spaces to the spaces of convergent, null-convergent, bound . . . Read More
## The dual spaces of new lambda^m-sequence spaces and their matrix maps
In this paper, we compute alpha-, beta- and gamma- duals of the new BK-spaces. We also give some classes of matrix transformations from these spaces to the spaces of convergent, null-convergent, bounded, almost convergent and almost null convergent. |

On spectral properties and invertibility of some operators of Mathematical Physics | Rabinovich | Approved | The main aim of the talk is the Fredholm property, essential spectrum, and invertibility of some operators of the Mathematical Physics, such that the Schrödinger and Dirac operators with complex ele . . . Read More ## On spectral properties and invertibility of some operators of Mathematical Physics
The main aim of the talk is the Fredholm property, |

On Weighted Sub-linear Operators in Generalized Morrey Spaces and their applications | Samko | Approved | We prove point-wise estimates of Weighted Sub-linear Operators of a certain class via the sum of the non-weighted such operator, and a combination of Hardy and potential operators. By use of known res . . . Read More
## On Weighted Sub-linear Operators in Generalized Morrey Spaces and their applications
We prove point-wise estimates of Weighted Sub-linear Operators of a certain class via the sum of the non-weighted such operator, and a combination of Hardy and potential operators. By use of known results for the operators in this sum, we obtain conditions on the boundedness of sub-linear operators in weighted generalized Morrey spaces for a class of radial weights. |

Homogenization and thin film flow | Wall | Approved | Homogenization is the branch of mathematics where partial differential equations with rapidly oscillating coefficients are studied. We will discuss how homogenization can be used to model and analyze . . . Read More
## Homogenization and thin film flow
Homogenization is the branch of mathematics where partial differential equations with rapidly oscillating coefficients are studied. We will discuss how homogenization can be used to model and analyze the effects of surface roughness in lubrication between surfaces in sliding and/or rolling contact (as in bearings, gears or hip joints). |

A convexity approach to consider and prove Hardy type inequalities with sharp constants | Persson | Approved | As background I fist give some remarkable details concerning the prehistory before Hardy discovered his famous inequality. After that I will present a fairly new convexity approach to prove Hardy typ . . . Read More ## A convexity approach to consider and prove Hardy type inequalities with sharp constants
As background I fist give some remarkable details concerning the prehistory before Hardy discovered his famous inequality. [1] S. Barza, L.E. Persson and N. Samko, Some new Hardy-type inequalities via convexity, J. Inequal. Appl. 2014:6, 10 pp. |

On the boundedness of Hardy-type operators in Hölder-type spaces | Lundberg | Approved | We present theorems on boundedness of Hardy type operator in Hölder type spaces in multidimensional case. We also discuss the Hölder spaces with compactification and present the corresponding theorems . . . Read More
## On the boundedness of Hardy-type operators in Hölder-type spaces
We present theorems on boundedness of Hardy type operator in Hölder type spaces in multidimensional case. We also discuss the Hölder spaces with compactification and present the corresponding theorems on the boundedness of Hardy operators in such spaces. |

SIO in non-standard spaces | Burtseva | Approved | We discuss Singular Integral Operators on closed contours in different function spaces. Read More ## SIO in non-standard spaces
We discuss Singular Integral Operators on closed contours in different function spaces. |

The concept of very weak multiscale convergence and some applications to homogenization of evolution problems | Holmbom | Approved | We give a brief introduction to two-scale convergence and multiscale convergence. Then we define the notion of very weak multiscale convergence [1], [2] and demonstrate its applicability to various ev . . . Read More
## The concept of very weak multiscale convergence and some applications to homogenization of evolution problems
We give a brief introduction to two-scale convergence and multiscale convergence. Then we define the notion of very weak multiscale convergence [1], [2] and demonstrate its applicability to various evolution problems of parabolic and hyperbolic type. Very weak multiscale convergence is particularly well suited to treat evolution problems with different combinations of rapid spatial and temporal scales. |

Several estimates for generalized fractional integrals on $\lambda$-$\mathrm{CMO}$ spaces | Matsuoka | Approved | Rencetly, we generalized the modified fractional integrals ${\tilde{I}}_{\alpha}$, whicn modify the fractional integrals $I_{\alpha}$, and showed the boundedness results of generalized fractional inte . . . Read More ## Several estimates for generalized fractional integrals on $\lambda$-$\mathrm{CMO}$ spaces
Rencetly, we generalized the modified fractional integrals |

Homogenization of a mathematical model of thin film flow | Tsandzana | Approved | We derive a mathematical model of thin film flow between two close rough surfaces which are in relative motion. In particular, the model takes cavitation, surface roughness and pressure dependent dens . . . Read More ## Homogenization of a mathematical model of thin film flow
We derive a mathematical model of thin film flow between two close rough |

Elliptic PDE, and SIO in non-standard spaces | Burtseva | Approved | We discuss Singular Integral Operators and their commutators in some non-standard function spaces, and their applications to partial differential equations. We also discuss Singular Integral Operator . . . Read More ## Elliptic PDE, and SIO in non-standard spaces
We discuss Singular Integral Operators and their commutators in some non-standard function spaces, and their applications to partial differential equations. We also discuss Singular Integral Operators on closed contours in different function spaces. |

On a new space of defined by using Orlicz functions | A. BEKTAŞ | Approved | In this paper, we introduce a new paranormed sequence space defined by a sequence of Orlicz functions over a seminormed sequence space. We investigated some properties of this space. Read More ## On a new space of defined by using Orlicz functions
In this paper, we introduce a new paranormed sequence space defined by a sequence of Orlicz functions over a seminormed sequence space. We investigated some properties of this space. |

Regularity of solutions to linear elliptic equations in Generalized Morrey Spaces | Scapellato | Approved | The author shows some results obtained in cooperation with Maria Alessandra Ragusa. We prove regularity results, in some Generalized Morrey Spaces, for highest order derivatives of solutions of second . . . Read More
## Regularity of solutions to linear elliptic equations in Generalized Morrey Spaces
The author shows some results obtained in cooperation with Maria Alessandra Ragusa. We prove regularity results, in some Generalized Morrey Spaces, for highest order derivatives of solutions of second-order elliptic equations. We would like to extend some known local regularity results in the case that the coefficients of the principal part of the differential operator under consideration are discontinuous and the source term belongs to certain Generalized Morrey Spaces. |

Layer potentials on rough boundaries and fractals | Guseynov | Approved | Oqtay Q. Azizov Azerbaycan Technical Universitu Riyaziyyat kafedrası, Baku, Azerbaijan Yevgeniy Guseynov Policy Research and Analysis Department, PBGC, Washington, DC, USA Layer potentials on rough bo . . . Read More ## Layer potentials on rough boundaries and fractals
Oqtay Q. Azizov Yevgeniy Guseynov Layer potentials on rough boundaries and fractals In layer potentials theory, the new surface integral introduced by the second author allows extend layer potentials properties to highly irregular boundaries. This surface integral was defined over boundary of open bounded sets in d-dimensional Euclidean space, d > 1 and a criterion based on geometry of boundary was provided that completely describes all boundaries where this integral exists for (d – 1)-differential forms from Holder classes. This integration process substantially extends class boundaries where surface integrals were previously defined for Holder classes and includes highly irregular surfaces like non-rectifiable Jordan curves, fractals, sets of finite perimeter boundaries and flat chains. Such surfaces could have the normal to boundary nowhere, and in the current presentation we define single and double layer potentials for continuous differential forms over a boundary of open bounded set that does not require a notion of boundary smoothness. Meanwhile, we show that for piecewise smooth boundaries the introduced layer potentials equal classical single and double layer potentials. |

Perturbation methods for nonlinear elliptic problems | Ragusa | Approved | – Read More ## Perturbation methods for nonlinear elliptic problems
– |

Total Abstracts: 15

#### M6: Studies on Mathematical Methods and Models in Engineering, Sciences and Technology

Abstract: This special session is focused on the mathematical methods and models which need to be constructed by using the tools of mathematics. Generally, it is the most attraction to obtain the rea . . .Read More

##### M6: Studies on Mathematical Methods and Models in Engineering, Sciences and Technology

*Abstract:*

Abstract: This special session is focused on the mathematical methods and models which need to be constructed by using the tools of mathematics. Generally, it is the most attraction to obtain the reasonable results by solving the unsolved problems placed in the different fields of engineering, sciences and technology. This special session is to give an opportunity for getting together with the colleagues, graduate and undergraduate students who are working on these special topics.

The proposed special session will seek to assemble the leading experts in the field to present the latest methods, compare them and discuss new avenues of research. The main goal of the special session would be to stimulate interesting new ideas for future research.

Authors are invited to submit original unpublished results which are not under review in any other conference or journal, to the peer review for publication and presentation. The special session covers the following topics areas but is not limited to:

• Improvement of analytical approaches and their applications in science and engineering problems

• Analytical or semi-analytical techniques for solving ordinary or partial differential equations

• Fractional ordinary and partial differential equations with applications

• Stability and convergence of numerical methods

• Numerical methods in engineering

• Mathematical modelling and analysis for lasers in nanoscience

• Analysis of models in sciences and engineering

• Computational techniques for applications in engineering, science, and other disciplines

• Computational Geometry and Topology

Organizers:

Prof. Dr. Necdet Bildik, Celal Bayar University, Faculty of Art & Sciences, Department of Mathematics, 45047, Manisa, Turkey, necdet.bildik@cbu.edu.tr

Ass. Prof. Dr. Duygu Dönmez Demir, Celal Bayar University, Faculty of Art & Sciences, Department of Mathematics, 45047, Manisa, Turkey, duygu.donmez@cbu.edu.tr

Ass. Prof. Dr. Yusuf Pandir, Bozok University, Faculty of Art & Sciences, Department of Mathematics, 66100, Yozgat, Turkey, yusufpandir@gmail.com

Title | Author | Status | Abstract |
---|---|---|---|

Applicability Extent of 2-D Heat Equation for Numerical Analysis of Multiphysics Problems | Khawaja | Approved | This work focuses on thermal problems solvable using the Heat Equation. The fundamental question being answered here is what are the limits of the dimensions that will allow a 3-D thermal problem to b . . . Read More
## Applicability Extent of 2-D Heat Equation for Numerical Analysis of Multiphysics Problems
This work focuses on thermal problems solvable using the Heat Equation. The fundamental question being answered here is what are the limits of the dimensions that will allow a 3-D thermal problem to be accurately modelled using a 2-D Heat Equation. The presented work solves 2-D and 3-D Heat Equations using Finite Difference Method also known as ‘Forward Time Central Space (FTCS)’ method in MATLAB®. For this study, a cuboidal shape domain with a square cross-section is assumed. The boundary conditions are set such that there is a constant temperature in its centre and outside its boundaries. The 2-D and 3-D Heat Equations are solved in time dimension to develop a steady state temperature profile. The method is tested for its stability using Courant Friedrichs Lewy (CFL) criteria. The results are compared in the space dimension not taken into consideration in 2-D solution. The maximum error is calculated and recommendations are given on the applicability of 2-D Heat Equation. |

New Complex and Hyperbolic Function Solutions to the Generalized Double Combined Sinh-Cosh-Gordon Equation | Baskonus | Approved | In this study, we have applied the improved Bernoulli sub-equation function method to the generalized double combined Sinh-Cosh-Gordon equation. This method gives new analytical solutions such as comp . . . Read More ## New Complex and Hyperbolic Function Solutions to the Generalized Double Combined Sinh-Cosh-Gordon Equation
In this study, we have applied the improved Bernoulli sub-equation function method to the generalized double |

Application of the Modified Exponential Function Method to the Cahn-Allen Equation | Bulut | Approved | In this study, we have applied the modified exp (-Ω(ξ))-expansion function method to the Cahn-Allen equation. We have obtained some new analytical solutions such hyperbolic function solutions. Then, w . . . Read More
## Application of the Modified Exponential Function Method to the Cahn-Allen Equation
In this study, we have applied the modified exp (-Ω(ξ))-expansion function method to the Cahn-Allen equation. We have obtained some new analytical solutions such hyperbolic function solutions. Then, we have constructed the two and three dimensional surfaces for all analytical solutions obtained in this paper by using Wolfram Mathematica 9. |

Analytical Study of Sandwich Structures using Euler-Bernoulli Beam Equation | Khawaja | Approved | This paper presents an analytical study of sandwich structures. In this study, Euler–Bernoulli beam equation is solved analytically for a four-point bending problem. Appropriate initial and boundary c . . . Read More
## Analytical Study of Sandwich Structures using Euler-Bernoulli Beam Equation
This paper presents an analytical study of sandwich structures. In this study, Euler–Bernoulli beam equation is solved analytically for a four-point bending problem. Appropriate initial and boundary conditions are specified to enclose the problem. In addition, the balance coefficients are calculated and the rule of mixture is applied. The focus of this study to determine the effective material properties and geometric features such as the moment of inertia of a sandwich beam. The effective parameters help in the development of a generic analytical correlation for complex sandwich structures for the perspective of four-point bending calculations. The main outcomes of these analytical calculations are the lateral displacements and longitudinal stresses for each particular material in the sandwich structure. |

Dark Soliton Solutions of Klein-Gordon-Zakharov Equation in (1+2) Dimensions | Bulut | Approved | This study base on dark soliton solutions of Klein-Gordon-Zakharov (KGZ) equation in (1+2) dimensions. The generalized Kudryashov method (GKM) which is one of the analytical methods has been handled f . . . Read More
## Dark Soliton Solutions of Klein-Gordon-Zakharov Equation in (1+2) Dimensions
This study base on dark soliton solutions of Klein-Gordon-Zakharov (KGZ) equation in (1+2) dimensions. The generalized Kudryashov method (GKM) which is one of the analytical methods has been handled for finding exact solutions of KGZ equation in (1+2) dimensions. By using this method, dark soliton solutions of this equation have been obtained. Also, by using Mathematica Release 9, some graphical simulations were done to see the behavior of these solutions. |

Modification of perturbation-iteration method to solve different types of nonlinear differential equations | Bildik | Approved | Perturbation iteration method has been recently constructed by Pakdemirli and co-workers. It has been also proven that this technique is very effective and applicable for solving some nonlinear differ . . . Read More
## Modification of perturbation-iteration method to solve different types of nonlinear differential equations
Perturbation iteration method has been recently constructed by Pakdemirli and co-workers. It has been also proven that this technique is very effective and applicable for solving some nonlinear differential equations. In this study we suggest a modification to expedite the solution process of perturbation-iteration algorithms. This work might greatly improve the computational efficiency of the perturbation iteration method and also its Mathematica package to solve nonlinear equations. Numerical illustrations are also given to show how modified method eliminates cumbersome computational work needed by perturbation iteration method. |

Determining Critical Load in the Multispan Beams with the Nonlinear Model | Dönmez Demir | Approved | In this study, the buckling behaviors of beams are investigated. The general nonlineer mathematical of the beams are derived for multi support case. For some span numbers such as one, two and three, t . . . Read More
## Determining Critical Load in the Multispan Beams with the Nonlinear Model
In this study, the buckling behaviors of beams are investigated. The general nonlineer mathematical of the beams are derived for multi support case. For some span numbers such as one, two and three, the nonlinear mathematical model is presented. To be able to obtain the independent of the material and the geometry, the presented model are became dimensionless. The analytical solution for fixed–fixed supported beam gives the critical axial load and bifurcation diagrams. Effect of the multisupport on the critical axial load is found. For this pusposes, the nonlinear models are analytically solved. It is found that the support number and support location have an effect on the critical axial load. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. |

Rationality of Large Mass Method for Frequency Response Analysis | Mehmood | Approved | Most of previous work on Large Mass (LM) Method by Kim Y.-W. and Jhung, M. J.for dynamic problems is related to the study of transient responses. This paper discusses the numerical effectiveness of La . . . Read More
## Rationality of Large Mass Method for Frequency Response Analysis
Most of previous work on Large Mass (LM) Method by Kim Y.-W. and Jhung, M. J.for dynamic problems is related to the study of transient responses. This paper discusses the numerical effectiveness of Large Mass Method for frequency response problems in truss structures. The results achieved are of great importance for design of launch vehicle structures which must be capable of withstanding a wide range of frequencies for smooth operation of sensors. The paper also presents a very simple technique for developing an LM analysis model through programming language e.g. MATLAB. |

Properties of Soft Homotopy in Digital Images | Öztunç | Approved | In this paper first of all it is aimed to define the soft continuity in digital images. Also soft homeomorphism and soft homotopy in digital images is defined by determining soft continuity in digital . . . Read More
## Properties of Soft Homotopy in Digital Images
In this paper first of all it is aimed to define the soft continuity in digital images. Also soft homeomorphism and soft homotopy in digital images is defined by determining soft continuity in digital images. Then some results of soft set theory dealing with soft continuity and soft homotopy in digital images is obtained. In addition to this, we give new examples of soft continuity in digital images and soft homotopy in digital images. Since this paper contains important examples and results, it becomes a usuful tool for mathematicians especially working in digital topology. |

Numerical simulations to the nonlinear model of interpersonal Relationships with time fractional derivative | Gencoglu | Approved | The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretical . . . Read More
## Numerical simulations to the nonlinear model of interpersonal Relationships with time fractional derivative
The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. |

Applications of Optimal Perturbation Iteration Method for solving Nonlinear Differential Equations | Deniz | Approved | Perturbation iteration method has been recently constructed and it has been also proven that this technique is very effective and applicable for solving some nonlinear differential equations. In this . . . Read More
## Applications of Optimal Perturbation Iteration Method for solving Nonlinear Differential Equations
Perturbation iteration method has been recently constructed and it has been also proven that this technique is very effective and applicable for solving some nonlinear differential equations. In this study, we develop the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. This work might greatly improve the computational efficiency of the perturbation iteration method. Applications also show that only a few terms are required to get an approximate solution which is more accurate and efficient than many other methods in literature. |

Nonlinear Stability and Optimization Techniques: Modeling, Analysis and Computational Methods | Cave | Approved | Nonlinear stability and optimization techniques are modified and briefly outlined in terms of their inherent relationships with one another. This is done by making use of the interrelationships among . . . Read More
## Nonlinear Stability and Optimization Techniques: Modeling, Analysis and Computational Methods
Nonlinear stability and optimization techniques are modified and briefly outlined in terms of their inherent relationships with one another. This is done by making use of the interrelationships among modeling, analysis and computational methodologies. Then modification of existing methods in aerospace, land and marine vehicles,engineering, physical sciences and biotechnology are used to illustrate the techniques.The specific areas considered are Variational Principle Modeling, Control, Estimation, Energy and Power Requirements,Computational Methods directly derivable from formal solutions, Langevin Enhancements in molecular modeling, Variational Principles in Error Analysis, and Standard Error Analysis Approach of previously enhanced endo and exoatmospheric techniques. |

A general method for the study of systems of rigid bodies interconnected with the aid of elastic links and the rod | Mizhidon | Approved | As far as investigations of mechanical vibrations of elements of different constructions, parts and mechanisms are concerned, the computational schemes to be investigated are in many cases represented . . . Read More
## A general method for the study of systems of rigid bodies interconnected with the aid of elastic links and the rod
As far as investigations of mechanical vibrations of elements of different constructions, parts and mechanisms are concerned, the computational schemes to be investigated are in many cases represented by rigid bodies (or systems of rigid bodies) interconnected with the aid of elastic links and the rod. Application of the Hamilton variation principle for constructing such systems necessitates consideration of hybrid systems of differential equations. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. The report discusses a generalized mathematical model of a system of rigid bodies mounted on the Euler-Bernoulli beam in the form of a hybrid system of differential equations of a given structure, on whose basis a universal method of investigation of the natural oscillations for a given class of mechanical systems is developed. Note the issues of investigation of the natural oscillations for a given class of mechanical systems under certain specific types of typical computational schemes can be found in a sufficient number of publications, for example in the journal “Sound and Vibration”. In all these publications special analytical and numerical-analytical methods are developed or method of finite elements is used. Unfortunately, the majority of the mathematical models of the typical computational schemes are the case models elaborated for particular case studies. Meanwhile, the natural vibrations of mechanical systems considered in these papers, you can explore on the basis of a generalized mathematical model with universal analytical-numerical method proposed in the report. |

Solutions of Young-Laplace equation for capillary bridges and stability analysis | Millet | Approved | We revisit from an inverse problem method the exact resolution of the Young-Laplace equation for capillary doublets. The missing information on the pressure deficiency (which is often an unknown of th . . . Read More ## Solutions of Young-Laplace equation for capillary bridges and stability analysis
We revisit from an inverse problem method the exact resolution of the Young-Laplace equation We establish a simple criterion based on the observation of the contact point, of the wetting angle The pertinence of the addressed approach will be put in a prominent position on several experimental |

THE PREDICTION OF BRICK WALL STRENGTHS WITH ARTIFICIAL NEURAL NETWORKS MODEL | Demir | Approved | The aim of this study is to predict with Artificial Neural Networks (ANN) compressive and shear strengths of brick walls plastered with specific stuccos. It is very difficult to determine strengths of . . . Read More
## THE PREDICTION OF BRICK WALL STRENGTHS WITH ARTIFICIAL NEURAL NETWORKS MODEL
The aim of this study is to predict with Artificial Neural Networks (ANN) compressive and shear strengths of brick walls plastered with specific stuccos. It is very difficult to determine strengths of brick walls with experimental procedures. Therefore, an Artificial Neural Networks model was developed with data obtained by investigating many papers from literature and experiments carried out by authors. Finally, a good degree of coherency was obtained between the experimental and predicted data. The model that was developed makes it possible to easily predict the compressive and shear strengths of the brick walls. Additionally, this model can be continuously trained with new data and its practicability range can easily be extended. |

A new version of the generalized F-expansion method and its applications | Pandir | Approved | In this study, a new version of the generalized F-expansion method is suggested to search exact solutions of nonlinear partial differential equations. We find many new and interesting results for Kort . . . Read More
## A new version of the generalized F-expansion method and its applications
In this study, a new version of the generalized F-expansion method is suggested to search exact solutions of nonlinear partial differential equations. We find many new and interesting results for Korteweg-de Vries(KdV) equation by use of the proposed method. The solutions acquired from the proposed method are single and combined non-degenerate Jacobi elliptic function solutions. The new method allows a more systematic, easiness use of the solution process of nonlinear equations. |

Extended (G’/G)-Expansion Method for non lineer partial equations | Tuz | Approved | In this study, we present a new version of (G’/G)- expansion method by using extended (G’/G)-expansion method which is suggested in [1]. By this method, we find traveling wave solutions of Burgers, . . . Read More
## Extended (G’/G)-Expansion Method for non lineer partial equations
In this study, we present a new version of (G’/G)- expansion method by using extended (G’/G)-expansion method which is suggested in [1]. By this method, we find traveling wave solutions of Burgers, KdV and Hirota-Satsuma equations. |

Numerical modelling and experimentation of curtain containing floating oil pollution in harbor | MUTTIN | Approved | Numerical modelling and experimentation of curtain containing floating oil pollution in harbor Frédéric MUTTIN*, Abdellatif OUANSAFI**, Youssef BENELMOSTAFA** *EIGSI La Rochelle and ** EIGSICA Casabla . . . Read More ## Numerical modelling and experimentation of curtain containing floating oil pollution in harbor
Numerical modelling and experimentation of curtain containing floating oil pollution in harbor Marine water pollution is a most challenging problem for coastal environment. The main challenges faced by port authorities are the optimization of the deployment of resources, both in men power and technical barriers to limit the pollution extent, Our research works aim to provide those managers decision aid tools to accelerate the implementation of the best adequate technical and preorganization solutions. These models have been implemented in simulation software and experimented in real life situation in the fishing port of La Rochelle located in the Chef de Baie district. A comparison is given between the experiment results (in the port with real barrier) and the numerical computations showing major issues in term of mathematical modelling and pollution containment. |

Total Abstracts: 18

**Keynote talks of ICNPAA 2016:**

**Prof. Jan AWREJCEWICZ, Technical University of Lódz, Poland**

Title: Novel non-linear phenomena exhibited by interacting structural members

**Prof. Stefan BALINT, West University of Timisoara, Romania**

**Title: Space-Time Evolution of the Perturbations of a Spatially Developing Constant Gas Flow**

**Title:A tour of nonlinear dynamic analysis of a flexible slewing structures, excited by non-ideal sources (nis),using sma actuators and including parameter sensibility analysis**

**Prof. José Manoel BALTHAZAR, ITA-Aeronautics Technological Institute, Mechanical-Aeronautics Division, Brazil****Title: Can Stability Analysis be really simplified? (Revisiting Lyapunov, Barbalat, LaSalle and all that)**

**Dr. Itzhak BARKANA, Barkana Consulting, 11 Hashomer St., Ramat Hasharon, Israel****Title: “TBA”**

**Prof Francesco Dell'isola, University of Rome, Italy****Title: Enhanced multivariance products representation (empr) from scratch to its most recent status**

**Prof. Metin DEMIRALP, Istanbul Technical University, Turkey****Title: “TBA”**

**Prof Marc Garbey, University of Houston, USA****Title: ""Experimental implications of Bochner-Levy-Riesz diffusion""**

**Prof. Rudolf HILFER, Institut für Computerphysik, Universität Stuttgart, Germany****Title: The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives**

**Prof. Harry H. HILTON, University of Illinois at Urbana-Champaign, USA****Title: “Cooperative Control of UAVs”**

**Prof Naira Hovakimyan, University of Illinois at Urbana-Champaign, USA****Title: "TBA"**

**Prof. Gangaram S. LADDE, University of South Florida, USA****Title: “How to control flutter arising in flow structure interactions”**

**Prof Irena Lasiecka, The University of Memphis, USA****Title: Some Considerations on Prandtl Lifting-Line Theory**

**Dr. Jiro NAKAMICHI, Japan Aerospace Exploration Agency (JAXA), Japan****Title: outline of the new era in mathematics and its applications**

**Prof. Ruggero Maria Santilli, Thunder Energies Corporation , USA****Title: "Engineering Mathematics for big data networks and computational electromagnetics. ”**

**Prof Sergei Silvestrov, Mälardalen University, Sweden****Title: Operational Loads Identification for Aerospace Structures**

**Dr. Toshiya Nakamura, Japan Aerospace Exploration Agency (JAXA), Japan****Title: Research on Advanced Flight Control System Using UAV**

**Prof.Takeshi Tsuchiya, University of Tokyo, Japan****Title: Riemann Liouville Dynamic systems versus sequential Caputo dynamic systems with applications**

**Prof..Aghalaya Vatsala, Lousiana State University, USA****Title: Differential equations, Invariants and Qualitative Properties of Solutions**

**Prof. S.N. VASSILYEV, Trapeznikov Insitute of Control Sciences of RAS, Moscow, Russia**#### General Sessions

General Sessions

Read More

##### General Sessions

*Abstract:*

General Sessions

Title | Author | Status | Abstract |
---|---|---|---|

Optimization of Wall Thickness and Lay-Up for the Shell-Like Composite Structure Loaded by Non-Uniform Pressure Field | Shevtsov | Approved | S. Shevtsov1,2,a), I. Zhilyaev1,2,b), P. Oganesyan2,c), I, Tarasov3,d, V. Axenov4,5,e) 1 South Center of Russian Academy, 344006, Tchekhov str., 41, Rostov on Don, Russia 2 Southern Federal University . . . Read More ## Optimization of Wall Thickness and Lay-Up for the Shell-Like Composite Structure Loaded by Non-Uniform Pressure Field
S. Shevtsov1,2,a), I. Zhilyaev1,2,b), P. Oganesyan2,c), I, Tarasov3,d, V. Axenov4,5,e) a) Corresponding author: sergnshevtsov@gmail.com Abstract. The glass/carbon fiber composites are widely used in the design of such aircraft and rotorcraft components such as wing-body fairings, engine pylon fairings, engine and radar cowlings due to increased specific and fatigue strength or stiffness, better weight saving of composite materials that are sufficiently exceed the same properties of metallic light weight alloys. All these components made of quasi-isotropic laminates have predominantly a shell-like geometry. The term quasi-isotropic means that such laminates have different properties in the out-of-plane direction. In order to achieve these quasi-isotropic properties of laminates need to adopt a lay-up having an equal number of plies oriented parallel to the sides of an equilateral triangle. For example, a quasi-isotropic 24-ply laminate could be made with 8 plies oriented at each of 0 °, + 60 °, and – 60 °, or by use equal numbers of plies oriented at 0 °, +45 °, -45 °, and 90 ° [1]. [1] A. Baker, S. Dutton, D. Kelly, Composite Materials for Aircraft Structures. Reston, Virginia: AIAA ltd., 2004, pp. 597. |

Nasedkin A.V. Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium | Nasedkin | Approved | This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mec . . . Read More
## Nasedkin A.V. Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium
This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. We have paid special attention to the boundary conditions for the piezoelectric bodies with surface effects, interacting with the acoustic medium. For all the problems we have implemented the finite element technologies based on the generalized statements. Here we have used various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point) for modal, harmonic and transient problems, as well as the algorithms of the mode superposition methods. To increase the accuracy of calculations, especially for nanoscale and nonlinear problems, we have provided the ability of automatic transfer to the dimensionless problem statements. Analysis of the well-known finite element software shows that the proposed models and technologies significantly increase the facilities for analyzing complex active materials and provide the methods of solving new problems with coupled physico-mechanical fields, including the problems for nanoscale and composite bodies. This work was supported by the Russian Science Foundation (grant number 15-19-10008). |

Second Law considerations for Fourier Heat Conduction in relation to intermolecular potentials | Jesudason | Approved | %the form I am submitting a latex document \documentclass[a4paper]{article} % \usepackage{graphicx,amssymb} % \textwidth=15cm \hoffset=-1.2cm % \textheight=25cm \voffset=-2cm % \pagestyle{empty} % \d . . . Read More ## Second Law considerations for Fourier Heat Conduction in relation to intermolecular potentials
%the form I am submitting a latex document \textwidth=15cm \hoffset=-1.2cm % \pagestyle{empty} % \date{} % \def\keywords#1{\begin{center}{\bf Keywords}\\{#1}\end{center}} % \begin{document} % Type down your paper title % Authors \maketitle \thispagestyle{empty} % The abstract \begin{abstract} \end{abstract} % Write down at least 3 Keywords % \section{Introduction} %%\bibliographystyle{model1a-num-names} \begin{thebibliography}{100} \bibitem{bq} \bibitem{cgj1} \bibitem{lebo1} \end{thebibliography} %%%%%%%%%%%%% end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |

Atmospheric Icinig Intensity on Slowly Rotating Hexagonal Prism and Cylinder with Fins | Mughal | Approved | Atmospheric ice accretion intensities on constantly slowly rotating hexagonal prism with six fins and constantly slowly rotating cylinder with four fins were studied using experimental and mathematica . . . Read More
## Atmospheric Icinig Intensity on Slowly Rotating Hexagonal Prism and Cylinder with Fins
Atmospheric ice accretion intensities on constantly slowly rotating hexagonal prism with six fins and constantly slowly rotating cylinder with four fins were studied using experimental and mathematical analysis. The experimental intensities were compared with the existing ice accretion intensity models of Makkonen. Based upon this study a forced rotation constant and generalized windward area ratio is proposed to be added in the existing intensity models, in order to validate the experimental observations. |

Total Abstracts: 4

**Tutorial session on Monday July 4th, a full day 9AM-5PM **

** The Beauty of Simple Adaptive Control and Old and New results in Stability Analysis of Nonlinear Systems**

**Intructors**: Itzhak Barkana. Haim Weiss, Ilan Rusnak

**Keywords:**Control, Adaptive Control, Positive Realness and Passivity, Lyapunov methods; Barbalat’s Lemma, LaSalle’s Invariance Principle, New Theorem of Stability

**Abstract**Simple Adaptive Control (SAC) techniques have initially been conceived because of the need for adaptive control methods in large-scale systems, where the use of models and controllers of the order of the plant was naturally excluded. While initially SAC was considered (even by its own developers) to be just a modest version of the standard MRAC, the workshop shows that it was only before appropriate mathematical tools of analysis (that could reveal its real potential yet were missing at the time) had been developed. Further developments showed that they can easily be applied to such applications as robots, planes, missiles, satellites, fine motion control, etc. The talk explains how various drawbacks related to the classical Model Reference Adaptive Control (MRAC) methodology have been addressed and eliminated. To this end, it will be shown that the conditions needed for robust stability have been significantly mitigated. Recent developments in nonlinear systems stability analysis tools lead to clear proofs of SAC stability in real-world application and realistic environments. Previously unstable “counterexamples” to MRAC are revisited and shown to be just simple, successful, and stable applications of SAC. Realistic examples from various domains of flight control, guidance and aerospace are also used to show that indeed SAC is the Stable Direct MRAC methodology. A non-minimum-phase

*and*unstable UAV will be used as a detailed case-study to illustrates show the simplicity of implementation of SAC as an Add-On to classical control design towards improving performance beyond anything that could be obtained otherwise.

To this end, although Lyapunov stability theory is the customary basis of any modern stability analysis, its direct application requires fitting to the system a Positive Definite function whose derivative ”along all trajectories of the system” is Negative Definite. If this is the case, it is easy to see that both the Lyapunov function and its derivative ultimately vanish and therefore, one can reach the desired conclusion of asymptotic stability. However, because in most non-trivial problems the derivative is at most Negative Semi-Definite, various extensions to the basic Lyapunov stability theory have been sought. Because early extensions of Lyapunov stability theory were only covering autonomous systems of the form , various alternatives were sought for nonautonomous systems of the form . In particular, a successful alternative has been provided by Barbalat Lemma that under some conditions allowed concluding that the Lyapunov derivative ultimately vanishes and therefore, as many examples illustrated, asymptotic stability conclusions could be drawn. Texts on Nonlinear Control gave various formulations intending to mitigate prior conditions that would facilitate application of Barbalat Lemma to stability analysis. However, Barbalat Lemma that deals with

*function*theory and

*not necessarily*with theory of

*systems*stability imposes conditions of uniform continuity of functions and even continuity of derivatives that again could limit its applicability. Besides, even when applicable, it only ends with partial results. As even recent publications illustrate, although extensions of LaSalle's Invariance Principle to nonautonomous systems have been available at least since 1976, they have remained surprisingly unknown for large circles of the nonlinear control community. Moreover, even if assumably known, misinterpretations of its larger mathematical scope (that covers much more than mere asymptotic stability) may have misled the prospective users with respect to its usefulness. It is hoped that the review of LaSalle’s Invariance Principle along with a new extended Invariance Principles and the comparative parallel presentation of various alternatives to stability analysis may help showing the extreme efficiency of the new Theorems of Stability to nonlinear systems stability analysis.

**Outline**Review of need for adaptation Life is with uncertainty: need various gains for various situation, either change in nominal parameters or various operational conditions Nonstationary gains: right gains at right times. Good idea, yet… must be careful. Example: The danger of “safe” fixed control in nonstationary environments Model Reference Adaptive Control (MRAC) First Adaptive Control ideas: ingenious and failure Basic MRAC: First rigorous proofs, problematic SPR conditions “Classical” MRAC: Stability in ideal situations , problems otherwise:- Persistent excitation - Bursting, etc. - Unmodeled dynamics Simple Adaptive Control (SAC) From MRAC towards

**Simple**Adaptive Control (SAC) - Can Adaptive Control use and extend ideas from Optimization to the world of uncertainty? The Simple Adaptive Control (SAC)-Minimum Phase and conditions on CB-Claim and Proof: Same conditions that allow LTI design also guarantee stability with SAC. Advantage: the guarantee of stability allows reaching superior performance.-Nonstationary and Nonlinear systems-On Robustness

**and**Perfect Tracking -Robustness with Noise -Discrete-time systems -Continuous mitigation of stability conditions -Gentle introduction of Stability conditions in Engineering terms Brief review of stability analysis for nonlinear systems. Lyapunov stability approach: examples and limitations Simple example and LTI example First extensions: Krasovskii and LaSalle, The Invariance Principle for Autonomous systems only First extension for Nonautonomous systems: Barbalat’s Lemma: the apparent need for uniform continuity (and the implied ‘threat” of discontinuity). Further extensions: (The real and ignored) LaSalle’s Invariance Principle for Nonautonomous systems The new Invariance Principle The new Theorem of Stability: simple and safe tool for proofs of stability Example problems Application of SAC Approach Unstable MRAC “counterexamples” become simple examples for SAC Explicit design case: Combining Classical LTI design and SAC guarantee stability and lead to superior performance for Non-minimum Phase UAV. Missile Flexible structures: new developments relax the need for collocation Example Problems Advanced issues (time permitting): gain convergence, participants proposed examples

**RECOMENDED REFERENCES**

1) H. Kaufman, I. Barkana, K. Sobel:

*Direct Adaptive Control Algorithms*, Springer 1998 (2nd edition)

2) I. Barkana: "Parallel Feedforward and Simplified Adaptive Control,"

*International Journal of Adaptive Control and Signal Processing,*Vol. 1, No. 2, pp. 95-109, 1987.

3) I. Barkana: "Classical and Simple Adaptive Control Design for a Non-Minimum Phase Autopilot,"

*AIAA Journal of Guidance, Control*

*and Dynamics*, Vol. 28, No. 4, pp. 631-638, 2005.

4) I. Barkana: “Extensions on Adaptive Model Tracking with Mitigated Passivity Conditions,”

*Chinese Journal of Aeronautics*, Vol. 26, No. 1, 2013, pp. 136-150.

5) I. Barkana: “Simple Adaptive Control - A Stable Direct Model Reference Adaptive Control Methodology- Brief Survey,”

*International Journal of Adaptive Control and Signal Processing,*Vol. 28, No. 7-8, pp. 567-603, July 2014, (Published On-Line 17 June 2013) DOI: 10.1002/acs.2411.

6) I. Barkana: “Robustness and Perfect Tracking in Simple Adaptive Control,”

*International Journal of Adaptive Control and Signal Processing*, Published On-Line in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2411.

7) I. Barkana: “Parallel Feedforward and Simple Adaptive Control of Flexible Structures: First order-pole instead of collocated velocity sensors?,”

*ASCE’s Journal of Aerospace Engineering*(Published On-Line). DOI: 10.1061/(ASCE)AS.1943-5525.0000538.

8) LaSalle JP: “Stability of Nonautonomous systems,”

*Nonlinear Analysis, Theory, Methods and Applications*1976; 1(1): 83–90.

7) LaSalle JP.

*The Stability of Dynamical Systems*, 2nd ed. SIAM: New York, 1976.

9) Z. Artstein: “Limiting equations and stability of nonautonomous ordinary differential equations,” Appendix A in: LaSalle,

*The Stability of Dynamical Systems*, 2nd ed., SIAM, New York, 1976.

10) Z. Artstein: "Uniform asymptotic stability via the limiting equations,"

*J. Differential Equations*, vol. 25, pp. 184–202, 1977.

11) Z. Artstein: "Uniform asymptotic stability via the limiting equations,"

*J. Differential Equations*, vol. 27, pp. 172â˘A ¸ S-189, 1978.

12) I. Barkana: “Defending the Beauty of the Invariance Principle,"

*International Journal of Control,*Vol. 87, No. 1, pp. 186-206, 2014.

13) Ilan Rusnak, Haim Weiss and Itzhak Barkana: “Improving the Performance of Existing Missile Autopilot using Simple Adaptive Control,”

*International Journal of Adaptive Control and Signal Processing,*Vol. 28, No. 7-8, pp. 732-759, July 2014. DOI: 10.1002/acs.2457.

14) Ulrich, S., and Sasiadek, J. Z., “Decentralized Simple Adaptive Control for Nonlinear Systems,”

*International Journal of Adaptive Control and Signal Processing*, Vol. 28, No. 7-8, pp. 750-763, 2014. doi:10.1002/acs.2446

15) I. Barkana:

*The new Theorem of Stability – Direct Extension of Lyapunov Theorem*.

*Mathematics in Engineering, Science and Aerospace*(

*MESA),*Vol. 6, no. 3, pp. 519-535, 2015.

16) I. Barkana:

*The*Beauty of Simple Adaptive Control and New Results in

*Stability Analysis of Nonlinear Systems*. ICNPAA 2014.

17) I. Barkana: “Parallel Feedforward and Simple Adaptive Control of Flexible Structures: First order-pole instead of collocated velocity sensors?”

*ASCE’s Journal of Aerospace Engineering*(Published On-Line) DOI: 10.1061/(ASCE)AS.1943-5525.0000538.

18) I. Barkana: “Robustness and Perfect Tracking in Simple Adaptive Control,”

*International Journal of Adaptive Control and Signal Processing*(2015). Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2573).

19) I. Barkana:

*Barbalat’s Lemma and Stability - Misuse of a correct mathematical result?*BARKANA Consulting Technical Report, 2015.

**Lecturers:**

**Itzhak Barkana**Itzhak Barkana received his B.Sc. and M.Sc. degrees in electrical engineering from Technion—Israel Institute of Technology and his PhD degree in 1983 from Rensselaer Polytechnic Institute (RPI). He presently is a Consulting for high-tech industry, after retiring from his job as a Fellow with Kulicke and Soffa Industries, Inc., Fort Washington, PA, USA. In this job he had been an internal technical consultant and authority for all problems related to systems and controls of fine machines motion control, design of optimal trajectories of motion, system analysis for both power consumption and performance. Between 1988 and 2000 has also been Visiting and Adjunct Professor with Drexel University in Philadelphia. Has developed self-tuning algorithms and specialized feedback and feedforward control techniques that had pushed forward and permanently maintained the K&S bonding machines as the fastest and the most precise in the world. Has been a leading developer of the Simple Adaptive Control (SAC) methodology and has developed the fine theoretical points needed to guarantee robust stability of the adaptive control systems. Has defined and clarified the underlying theoretical “almost strictly positive real (ASPR)” and “almost strict passivity (ASP)” conditions needed for stable adaptation and has invented the so called “Parallel Feedforward Configuration (PFC) that has become the main tool that allows implementation of Adaptive Control in real-world systems. Has continued to develop the theory related to implications of adaptive control techniques, including extensions and modified versions of the LaSalle’s Invariance Principle, with new and valuable implications for the guarantee of stability of adaptive controllers and of general nonlinear systems in practical applications.

In 2002 has received the Benjamin Franklin Key Award from Philadelphia Chapter of IEEE for “advancing the theory and practice of adaptive control, and in so doing, making major contributions to improving the speed and accuracy of specialty robotics for the semiconductor industry.” These techniques helped to extend the life of wire bonding technology. As a result of this work, the challenge of portability – the ability to repeatedly perform the same task on different machines – was solved. The time duration of bond table motion was reduced by more than 60%, dramatically increasing productivity, and the accuracy limit was lowered from more than 100 microns in the late 1990s to 35 microns in the current generation of bonders. The robustness of the algorithms has been proven over the last 17 years by its successful implementation in tens of thousands of machines representing various platforms. It is one of the major innovations that have made these wire bonders the world industry leaders. Is co-author of the book: “Direct Adaptive Control Algorithms – Theory and Applications” and has published 3 chapters in books and more than 100 papers in Journals and major Technical Conferences.

**Ilan Rusnak**Ilan Rusnak holds B.Sc. and M.Sc. in electrical engineering from Technion Haifa, Israel, and Ph.D. in ECE from Drexel University, Philadelphia, USA. He is currently with RAFAEL, Israel, holding the position of senior research fellow, and holding position of adjunct senior lecturer at Technion, Haifa, Israel. His current interests are Systems Engineering, Guidance, Control Theory, Motion Control, Estimation Theory, Architecture of the Feedback, Simulation and Signal Processing.

**Haim Weiss**Haim Weiss received his B.Sc. and M.Sc. degrees in electrical engineering, in 1966 and 1971, respectively, both from Technion—Israel Institute of Technology. In 1979 he received Ph.D. degree from University of Newcastle, Australia, also in electrical engineering. From 1966 to 1970 he served as an electronic engineer in the Israeli Air Force. In 1972 he joined RAFAEL where he is now a research fellow. From 1999–2001 he was Lady Davis visiting scientist at Faculty of Aerospace Engineering, Technion, Israel. Currently he holds the position of adjunct senior teaching fellow. His research interests include estimation, guidance, adaptive control and spacecraft attitude determination and control.

**Registration:**Tutorial session fee 70 Euros should be added to regular conference registration fee

**Multivariate Function Decomposition and Data Analysis with a Basic Focus on HDMR and EMPR**

**Lecturers: (oral presentations)**Metin Demiralp, İstanbul Technical University, (Chairman)

Süha Tuna, İstanbul Technical University, (Organizing Assistant to Chairman)

Alper Tunga, Bahçeşehir University

Burcu Tunga, İstanbul Technical University

Evrim Korkmaz Özay, Aydın University

**Lecturers: (focusing on certain specific topics in core sessions composed of oral presentations)**

Zeynep Gündoğar, İstanbul Technical University

Ayla Okan, İstanbul Technical University

Derya Bodur, İstanbul Technical University

**Implementative Session(s) Devoted to Only (Poster Presentations)**

Evrim Korkmaz Özay, Zeynep Gündoğar, Ayla Okan, and, Derya Bodur

**Assistive instructors:**

Berfin Kalay, İstanbul Technical University

Melike Ebru Kırkın, İstanbul Technical University

Elif Tataroğlu, İstanbul Technical University

**If any application comes from outside the above team for the announcement**

**of special expertises then some of instructively important ones will be**

**selected to be presented in this session via poster(s).**

The original findings including one will be redirected to the special ICNPAA 2016

session organized by Demiralp.

**ABSTRACT:**The topics of this pre-ICNPAA 2016 organization will be focused on the following areas:

* ANOVA and basic conceptualism of High Dimensional Model Representation (HDMR). Sobol's definition and related works.

* Weights and orthogonal geometry in HDMR, the works of Rabitz and his group. Cut-HDMR, Random Sampling HDMR, Multicut HDMR.

* Orthogonality, truncation approximants, quality measurers. How to increase truncation approximation quality.

* Other HDMR varieties from Demiralp Group: HDMR with Generalized Weights, Factorized HDMR, Hybrid HDMR, Discrete and discretized HDMR applications.

* Further HDMR developments from Demiralp group: Logarithmic HDMR, Transformational HDMR (under various transformations like affine, quadratic, cubic, Moebius type).

* Ascending approximation quality via multivariance enhancement. Supporting element concept. Enhanced Multivariance Products Representation (EMPR = Supported HDMR) as introduced in Demiralp group works.

* EMPR in practical applications. EMPR varieties as extended counterparts of HDMR. What does EMPR bring new extension and capabilities against HDMR's limited structure.

* Support function and support array optimisation. Integral equations related issues. Multiway array related issues.

* Supportive hybridization in EMPR. Developments outside Sobol's, Rabitz group's, and, Demiralp group's studies. Future work possibilities.

**Core Sessions Devoted to Oral Presentations**

**DOCUMENTATION and WEB SITE:**The construction of a tutorial/textbook type book has been started and will be, at least, ready to the online access of participants. The distribution of the printed version of this book is also under consideration. The ultimate status will be announced quite before of the tutorial/workshop day.

Almost all of the abovementioned contributors will give certain level of support to this documentation in both printed and online versions.

**Event support to the documentation**. * N. Abdülbaki Baykara, Marmara University

* Coşar Gözükırmızı, İstanbul Technical University

* Muzaffer Ayvaz, İstanbul Technical University

* Semra Bayat, İstanbul Technical University

**Organizers:**Metin Demiralp, İstanbul Technical University, (Chairman)

**Informatics Institute, Computational Science and Engineering Department.**Süha Tuna, İstanbul Technical University, (Organizing Assistant to Chairman) Alper Tunga, Bahçeşehir University, Burcu Tunga, İstanbul Technical University, Evrim Korkmaz Özay, Aydın University

**URL for further information about this activity in english and turkish (choose and click on relevant flag therein): bebbyt.be.itu.edu.tr/empr. You can also leave a message in that site if you need.**

**Registration:**Tutorial session fee 70 Euros should be added to regular conference registration fee