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Index Type : Scopus ✕Researcher : Elmira ABDILDAYEVA ✕
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Doç. Dr. Elmira ABDILDAYEVAFen Fakültesi
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The Optimal Vector Control for the Elastic Oscillations Described by Fredholm Integral-Differential Equations

Elmira ABDILDAYEVA

In this paper, we investigate the nonlinear problem of the optimal vector control for oscillation processes described by Fredholm integro-differential equations in partial derivatives when function of external sources nonlinearly depend on control parameters. It was found that the system of nonlinear integral equations,which obtained relatively to the components of the optimal vector control, have the property of equal relations. This fact lets us to simplify the procedure of the constructing the solution of the nonlinear optimization problem. We have developed algorithm for constructing the s ...More

Proceedings Paper 2019 Fen Fakültesi Analysis and Partial Differential Equations: Perspectives from Developing Countries275 17 Views
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On the Solvability of the Synthesis Problem for Optimal Control Systems with Distributed Parameters

Elmira ABDILDAYEVA

The solvability of synthesis problem of external and boundary controls is investigated for optimization of oscillation process, described by partial differential equations with Fredholm integral operator. Functions of the external and boundary actions are nonlinearly with respect to control. An integro-differential equation is obtained in the specific type for Bellman functional. An algorithm is developed for constructing solutions to synthesis problem of external and boundary controls. Keywords: Generalized solution, Bellman functional, Frechet differential, Integro-differential equation, Fre ...More

Chapter of Books 2022 Fen Fakültesi Trends in Mathematics 59 Views
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On the solvability of a nonlinear optimization problem with boundary vector control of oscillatory processes = О разрешимости задачи нелинейной оптимизации при граничном векторном управлении колебательными процессами = Тербелмелi процестердi шекаралық векторлық басқарумен сызықтыемес оңтайландыру есебiнiң шешiмi туралы

Elmira ABDILDAYEVA

In the paper, the solvability of the nonlinear boundary optimization problem has been investigated for the oscillation processes, described by the integro-differential equation in partial derivatives with Fredholm integral operator. It has been established that the components of the boundary vector control are defined as a solution to a system of nonlinear integral equations of a specific form, and the equations of this system have the property of equal relations. An algorithm for constructing a solution to the problem of nonlinear optimization has been developed. Keywords: general solution; n ...More

Article 2023 Fen Fakültesi Bulletin of the Karaganda University - Mathematics / Вестник Карагандинского университета. Серия Математика109 ( 1 ) 38 Views
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On the Solvability of a Boundary Value Problem for Nonlinear Optimization of Oscillatory Processes

Elmira ABDILDAYEVA

The paper investigates the solvability of a boundary value problem in the control of an oscillatory process described by control in partial derivatives of the first order. It has been established that there are an infinite set of controls, as solutions to the system of nonlinear Fredholm integral equations of the first kind, each of which transfers the controlled process from the initial state to the final specified state in a specified time. Sufficient conditions for the existence of a nonlinear optimization solution are found.

Proceedings Paper 2024 Fen Fakültesi AIP Conference Proceedings3085 ( 1 ) 3 Views
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On Solvability of Optimization Problem for Elastic Oscillations with Multipoint Sources of Control

Elmira ABDILDAYEVA

In the paper we investigate the optimal control problem for elastic oscillation under multipoint influences of external forces when oscillation process is described by Fredholm integro-differential equation. Sufficient conditions for unique solvability of nonlinear optimization problem were found and the algorithm for constructing complete solution to this problem was developed.

Proceedings Paper 2017 Fen Fakültesi AIP Conference Proceedings1880 ( 1 ) 66 Views
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On the Solvability of a Nonlinear Tracking Problem Under Boundary Control for the Elastic Oscillations Described by Fredholm Integro-Differential Equations

Elmira ABDILDAYEVA

In the present paper we investigate nonlinear tracking problem under boundary control for the oscillation processes described by Fredholm integro-differential equations. When we investigate this problem we use notion of a weak generalized solution of the boundary value problem. Based on the maximum principle for distributed systems we obtain optimality conditions from which follow the nonlinear integral equation of optimal control and the differential inequality.We have developed an algorithm to construct the optimization problem solution. This solving method of a nonlinear tracking problem is ...More

Proceedings Paper 2017 Fen Fakültesi IFIP Advances in Information and Communication Technology494 66 Views
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On the Solvability of a Nonlinear Optimization Problem for Thermal Processes Described by Fredholm Integro-Differential Equations with External and Boundary Controls

Elmira ABDILDAYEVA

In the present paper we studied the problem of nonlinear optimal control of the thermal processes described by Fredholm integro-differential equations when the control parameters are nonlinearly included into the equation as well as into the boundary condition. The concept of weak generalized solution of the boundary value problem is introduced and the algorithm for its construction is indicated. It is established that optimal control is defined as the solution of the system of nonlinear integral equations which contain unknown functions under and out of the integral and satisfy the additional ...More

Article 2016 Fen Fakültesi Applied Mathematics and Information Sciences10 ( 1 ) 26 Views
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Optimal distributed control for the processes of oscillation described by Fredholm integro-differential equations

Elmira ABDILDAYEVA

In this paper we investigate the problem of distributed optimal control for the oscillation processes described by Fredholm integro-differential equations with partial derivatives when the function of the external source depends nonlinearly on the control parameters. We have developed an algorithm for finding approximate solutions of nonlinear optimization problems with arbitrary precision. The developed method of solving nonlinear optimization problems is constructive and can be used in applications. - Keywords and phrases: boundary value problem, generalized solution, approximate solutions, ...More

Article 2015 Fen Fakültesi Eurasian Mathematical Journal6 ( 2 ) 84 Views
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Solvability of Optimization Problem for the Oscillation Processes with Optimal Vector Controls

Elmira ABDILDAYEVA | Akılbek KERİMBEKOV

The optimal control problem is investigated for oscillation processes, described by integro-differential equations with the Fredholm operator when functions of external and boundary sources non-linearly depend on components of optimal vector controls. Optimality conditions having specific properties in the case of vector controls were found. A sufficient condition is established for unique solvability of the nonlinear optimization problem and its complete solution is constructed in the form of optimal control, an optimal process, and a minimum value of the functional.

Article 2019 Fen Fakültesi Filomat33 ( 5 ) 115 Views
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On the Solvability of Tracking Problem with Nonlinearly Distributed Control for the Oscillation Process

Elmira ABDILDAYEVA

In the paper we investigate the unique solvability of the tracking problem with the distributed optimal control for the elastic oscillations described by Fredholm integro-differential equations. The sufficient conditions are found for existence of a unique solution to the boundary value problem, also the class of functions of external influence for which the optimization problem has a solution. The algorithm was developed for constructing the complete solution of the tracking problem of nonlinear optimization.

Chapter of Books 2019 Fen Fakültesi Trends in Mathematics 55 Views
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Numerical Analysis of Convergence Rate of Approximation Solutions to Boundary Value Problem for Oscillation Processes

Elmira ABDILDAYEVA

In this paper, the dynamics of convergence rate is investigated for the approximations depending on the changes of the stiffness coefficient of the elastic fixation. The results of the numerical analysis show that with increasing of stiffness coefficient (parameter alpha) of the elastic fixation the radius of convergence of Neumann series increases, and the convergence rate of the approximations to the exact solution accelerates.

Proceedings Paper 2019 Fen Fakültesi AIP Conference Proceedings2183 ( 1-UNSP 070005 ) 103 Views
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Peculiarities of Constructing an Optimal Vector Distributed Control with Nonlinear Optimization of Oscillation Processes

Elmira ABDILDAYEVA

Nonlinear optimization problem is investigated for oscillation processes described by Fredholm integro-differential equations in partial derivatives when the function of the external source nonlinearly depends on vector distributed control. It is established that, the optimal control procedure is greatly simplified with vector control. Algorithm is developed for constructing a complete solution of the nonlinear optimization problem.

Proceedings Paper 2018 Fen Fakültesi AIP Conference Proceedings1997 ( 1-UNSP 020070-1 ) 90 Views
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