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CALCULATION OF EXTREMALS IN AN OPTIMAL CONTROL PROBLEM WITH A HIGHER-ORDER STATE CONSTRAINT
- Authors: Zhukova A.A.1, Karamzin D.Y.1
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Affiliations:
- Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences
- Issue: Vol 65, No 12 (2025)
- Pages: 1995-2008
- Section: Optimal control
- URL: https://ogarev-online.ru/0044-4669/article/view/369548
- DOI: https://doi.org/10.7868/S3034533225120028
- ID: 369548
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Abstract
The problem of controlling the k-th derivative of an object state under a linear state constraint, where k is an arbitrary natural number, is studied. According to the existing terminology in literature, this is a so-called state-constrained control problem of order k (the term 'of depth k' is also used). This paper applies Pontryagin's maximum principle to the problem under study and conducts a theoretical analysis of the resulting optimality conditions. Based on this analysis, a computational scheme for finding extremals is proposed.
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About the authors
A. A. Zhukova
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences
Email: Azhukova@frccs.ru
Moscow, Russia
D. Yu. Karamzin
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences
Email: dmitry_karamzin@mail.ru
Moscow, Russia
References
- Дикусар В.В., Милютин А.А. Качественные и численные методы в принципе максимума. М.: Наука, 1989.
- Robbins H. Junction phenomena for optimal control with state-variable inequality constraints of third order // J. Optim. Theory Appl. 1980. V. 31. P. 85-99.
- Борисов В.Ф., Гаель В.В., Зеликин М.И. Режимы с учащающимися переключениями и лагранжевы многообразия в задачах с фазовыми ограничениями // Изв. РАН. Сер. матем. 2012. 76:1. С. 3–42.
- Karamzin D.Y. On regularity conditions in higher-order state-constrained control problems // J. Comp. Appl. Math. 2024. V. 452, P. 104-116.
- Karamzin D., Pereira F.L. On higher-order state constraints // SIAM J. Cont. Opt. 2023. V. 61 (4). P. 1913-1933.
- Karamzin D., Zhukova A. One example of a k-order state-constrained control problem // 10th International Conference on Control, Decision and Information Technologies (CoDIT). 2024. P. 884-887.
- Arutyunov A.V. Optimality conditions: Abnormal and Degenerate Problems. Mathematics and Its Application. Kluwer Academic Publisher, 2000.
- Mordukhovich B.S. Maximum principle in the problem of time optimal response with nonsmooth constraints // J. Appl. Math. Mech. 1976. V. 40 (6). P. 960-969.
- Филиппов А.Ф. О некоторых вопросах теории оптимального регулирования // Вестник МГУ. Сер. Матем. и мех. 1959. № 2. С. 25–32.
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