Elmira ABDILDAYEVA

Article | 2015 | Eurasian Mathematical Journal6 ( 2 )

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, convergence, functional, the maximum pr . . .inciple, the optimality condition, nonlinear integral equations More less

Elmira ABDILDAYEVA

Chapter of Books | 2019 | Trends in Mathematics

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.

Elmira ABDILDAYEVA

Proceedings Paper | 2024 | AIP Conference Proceedings3085 ( 1 )

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.

Elmira ABDILDAYEVA

Article | 2016 | Applied Mathematics and Information Sciences10 ( 1 )

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 condition in the form of the system of . . .inequalities. Sufficient conditions for the existence of a unique solution of the problem of nonlinear optimization are given, and algorithm of its construction has been developed More less

Avıt ASANOV | Elmira ABDILDAYEVA | Kalıskan MATANOVA

Article | 2017 | Молодой учёный136 ( 2 )

In this paper we obtained a formula for the general solution for one class of Riccati equation. This formula was tested on the known results. The existence theorem of solution of Cauchy problem is proved. - Key words: Riccati equation, the general solution, the Cauchy problem

Elmira ABDILDAYEVA

Proceedings Paper | 2019 | Analysis and Partial Differential Equations: Perspectives from Developing Countries275

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 solution of the nonlinear optimization pr . . .oblem.Keywords: Optimal control. Fredholm integral equations. Boundary value problem More less

Elmira ABDILDAYEVA

Article | 2023 | Bulletin of the Karaganda University - Mathematics / Вестник Карагандинского университета. Серия Математика109 ( 1 )

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; nonlinear optimization; boundary vector c . . .ontrol; functional; optimal conditions; property of equal relation More less

Elmira ABDILDAYEVA

Chapter of Books | 2022 | Trends in Mathematics

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, Fredholm operator, Optimal control synthesis

Elmira ABDILDAYEVA

Proceedings Paper | 2018 | PROCEEDINGS of the 6th International Conference on CONTROL AND OPTIMIZATION WITH INDUSTRIAL APPLICATIONS, Volume II

Elmira ABDILDAYEVA

Proceedings Paper | 2018 | AIP Conference Proceedings1997 ( 1-UNSP 020070-1 )

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.

Elmira ABDILDAYEVA

Proceedings Paper | 2017 | IFIP Advances in Information and Communication Technology494

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 constructive and can be used in applications.

Elmira ABDILDAYEVA | Akılbek KERİMBEKOV

Article | 2019 | Filomat33 ( 5 )

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.