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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2024, Volume 64, Pages 70–96
DOI: https://doi.org/10.35634/2226-3594-2024-64-06 (Mi iimi471) 		 
MATHEMATICS

Convergence of conflict-controlled systems over a finite period of time

V. N. Ushakova, A. V. Ushakovab, O. A. Kuvshinova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
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DOI: https://doi.org/10.35634/2226-3594-2024-64-06
Abstract: A nonlinear conflict-controlled system is considered over a finite period of time and in a finite-dimensional Euclidean space. The problem of convergence with a compact target set at a fixed point in time is studied. Within the framework of the convergence problem, one of the key issues is investigated — the approximate construction of sets of solvability of the problem. An approach to approximate construction is discussed, the basis of which is a model that complements N.N. Krasovsky's unification method in the theory of differential games.
Keywords: control, conflict-controlled system, target set, differential inclusion, saddle point in a small game, convergence problem, solvability set of the convergence problem, maximum minimax $u$-stable bridge, maximum minimax $u$-stable path
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2024-1377
The study of the third author was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2024-1377).
Received: 30.07.2024
Accepted: 27.10.2024
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 93C15, 49N30
Language: Russian
Citation: V. N. Ushakov, A. V. Ushakov, O. A. Kuvshinov, “Convergence of conflict-controlled systems over a finite period of time”, Izv. IMI UdGU, 64 (2024), 70–96
Citation in format AMSBIB
\Bibitem{UshUshKuv24}
\by V.~N.~Ushakov, A.~V.~Ushakov, O.~A.~Kuvshinov
\paper Convergence of conflict-controlled systems over a finite period of time
\jour Izv. IMI UdGU
\yr 2024
\vol 64
\pages 70--96
\mathnet{http://mi.mathnet.ru/iimi471}
\crossref{https://doi.org/10.35634/2226-3594-2024-64-06}
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