A PROBLEM OF OPTIMAL CONTROL OF LOADING POINTS AND THEIR REACTION FUNCTIONS FOR A PARABOLIC EQUATION-Reference-Cited by-同舟云学术

A PROBLEM OF OPTIMAL CONTROL OF LOADING POINTS AND THEIR REACTION FUNCTIONS FOR A PARABOLIC EQUATION

Published:2024 Issue: Volume: Page:120-134
ISSN:1019-5262
Container-title:Kibernetyka ta Systemnyi Analiz
language:
Short-container-title:KCA

Author:

,Abdullayev V.M., ,Hashimov V.A.,

Abstract

We consider the problem of optimal control of loading points and the corresponding reaction functions described by a loaded parabolic equation. Optimality conditions for control actions are obtained. The objective functional gradient formulas contained in these conditions are used in the algorithm for numerically solving the problem of optimization of loading points and reaction functions based on first-order optimization methods. The results of numerical experiments are provided. Keywords: distributed-parameter system, loaded differential equation, necessary optimality condition, functional gradient.

Publisher

V.M. Glushkov Institute of Cybernetics

Reference32 articles.

1. 1. Nakhushev A.M. Loaded equations and their applications [in Russian]. Moscow: Nauka, 2012. 232 p.

2. 2. Dzhenaliev M.T. Optimal control of linear loaded parabolic equations. Differential equations. 1989. Vol. 25, N 4. P. 641-651.

3. 3. Dzhenaliev M.T. On the theory of linear boundary value problems for loaded differential equations [in Russian]. Almaty: ITPM Computer Center, 1995. 270p.

4. 4. Mardanov M.J., Sharifov Y.A., Zeynalli F.M. Existence and uniqueness of the solutions to impulsive nonlinear integro-differential equations with nonlocal boundary conditions. Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 2019. Vol. 45, N 2. P. 222-233. https://doi.org/ 10.29228/proc.6.

5. 5. Abdullayev V.M., Aida-zade K.R. Approach to the numerical solution of optimal control problems for loaded differential equations with nonlocal conditions. Comput. Math. Math. Phys. 2019. Vol. 59, N 5. P. 696-707. https://doi.org/10.1134/S0965542519050026.