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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2022, Volume 60, Pages 111–154
DOI: https://doi.org/10.35634/2226-3594-2022-60-07 (Mi iimi438) 		 
MATHEMATICS

On the approach problem for a control system on a finite time interval

V. N. Ushakova, A. V. Ushakovba

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/10.35634/2226-3594-2022-60-07
Abstract: A conflict-controlled system in a finite-dimensional Euclidean space is considered. We study the game problem of approaching the system to the goal set in the phase space over a finite time interval. The study of the problem is based on methods developed in the theory of positional differential games. Within the framework of this theory, an approach to constructing approximate solutions to the approach problem is presented.
Keywords: control, target set, conflict-controlled system, differential inclusion, approach problem, solution set, minimax $u$-stable bridge.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-01265-22-00, проект FEWS-2020-0010
This research was funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of state assignment No. 075-01265-22-00, project FEWS-2020-0010.
Received: 31.10.2022
Accepted: 10.11.2022
Bibliographic databases:
Document Type: Article
UDC: 517.958, 530.145.6
MSC: 93C15, 49N30, 49N35
Language: Russian
Citation: V. N. Ushakov, A. V. Ushakov, “On the approach problem for a control system on a finite time interval”, Izv. IMI UdGU, 60 (2022), 111–154
Citation in format AMSBIB
\Bibitem{UshUsh22}
\by V.~N.~Ushakov, A.~V.~Ushakov
\paper On the approach problem for a control system on a finite time interval
\jour Izv. IMI UdGU
\yr 2022
\vol 60
\pages 111--154
\mathnet{http://mi.mathnet.ru/iimi438}
\crossref{https://doi.org/10.35634/2226-3594-2022-60-07}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4521464}
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