A Second-Order Numerical Method for a Class of Optimal Control Problems

The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the class of control actions used. The first one is that c...

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Главные авторы:	Khandzel, A. V., Хандзель, А. В.
Формат:	Статья
Язык:	English
Опубликовано:	Multidisciplinary Digital Publishing Institute (MDPI) 2024
Темы:	Optimal control Newton’s method Functional gradient Hessian matrix Fast differentiation Gradient method
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/29300
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id	ir-123456789-29300
record_format	dspace
spelling	ir-123456789-293002025-03-06T12:37:33Z A Second-Order Numerical Method for a Class of Optimal Control Problems Khandzel, A. V. Хандзель, А. В. Optimal control Newton’s method Functional gradient Hessian matrix Fast differentiation Gradient method The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the class of control actions used. The first one is that controls are searched for in a given class of functions, which depend on unknown parameters to be found by minimizing an objective functional. The parameter values, in general, may be different at different time intervals. The second feature of the considered problem is that the boundaries of time intervals are also optimized with fixed values of the parameters of the control actions in each of the intervals. The special cases of the problem under study are relay control problems with optimized switching moments. In this work, formulas for the gradient and the Hessian matrix of the objective functional with respect to the optimized parameters are obtained. For this, the technique of fast differentiation is used. A comparison of numerical experiment results obtained with the use of first- and second-order optimization methods is presented. 2024-11-29T11:21:56Z 2024-11-29T11:21:56Z 2024 Статья Aida-zade, K., Handzel, A., Providas, E. A Second-Order Numerical Method for a Class of Optimal Control Problems // AXIOMS. - 2024. - 13 (10). - 679. - DOI: 10.3390/axioms13100679 https://dspace.ncfu.ru/handle/123456789/29300 en Axioms application/pdf Multidisciplinary Digital Publishing Institute (MDPI)
institution	СКФУ
collection	Репозиторий
language	English
topic	Optimal control Newton’s method Functional gradient Hessian matrix Fast differentiation Gradient method
spellingShingle	Optimal control Newton’s method Functional gradient Hessian matrix Fast differentiation Gradient method Khandzel, A. V. Хандзель, А. В. A Second-Order Numerical Method for a Class of Optimal Control Problems
description	The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the class of control actions used. The first one is that controls are searched for in a given class of functions, which depend on unknown parameters to be found by minimizing an objective functional. The parameter values, in general, may be different at different time intervals. The second feature of the considered problem is that the boundaries of time intervals are also optimized with fixed values of the parameters of the control actions in each of the intervals. The special cases of the problem under study are relay control problems with optimized switching moments. In this work, formulas for the gradient and the Hessian matrix of the objective functional with respect to the optimized parameters are obtained. For this, the technique of fast differentiation is used. A comparison of numerical experiment results obtained with the use of first- and second-order optimization methods is presented.
format	Статья
author	Khandzel, A. V. Хандзель, А. В.
author_facet	Khandzel, A. V. Хандзель, А. В.
author_sort	Khandzel, A. V.
title	A Second-Order Numerical Method for a Class of Optimal Control Problems
title_short	A Second-Order Numerical Method for a Class of Optimal Control Problems
title_full	A Second-Order Numerical Method for a Class of Optimal Control Problems
title_fullStr	A Second-Order Numerical Method for a Class of Optimal Control Problems
title_full_unstemmed	A Second-Order Numerical Method for a Class of Optimal Control Problems
title_sort	second-order numerical method for a class of optimal control problems
publisher	Multidisciplinary Digital Publishing Institute (MDPI)
publishDate	2024
url	https://dspace.ncfu.ru/handle/123456789/29300
work_keys_str_mv	AT khandzelav asecondordernumericalmethodforaclassofoptimalcontrolproblems AT handzelʹav asecondordernumericalmethodforaclassofoptimalcontrolproblems AT khandzelav secondordernumericalmethodforaclassofoptimalcontrolproblems AT handzelʹav secondordernumericalmethodforaclassofoptimalcontrolproblems
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A Second-Order Numerical Method for a Class of Optimal Control Problems

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