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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2021, Volume 58, Pages 48–58
DOI: https://doi.org/10.35634/2226-3594-2021-58-03 (Mi iimi420) 		 
MATHEMATICS

On a discrete game problem with non-convex control vectograms

I. V. Izmestyevab, V. I. Ukhobotovba

a Chelyabinsk State University, ul. Brat'ev Kashirinykh, 129, Chelyabinsk, 454001, Russia
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
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DOI: https://doi.org/10.35634/2226-3594-2021-58-03
Abstract: In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.
Keywords: game, control, vectogram, terminal set.
Funding agency Grant number
Russian Science Foundation 19-11-00105
The study was funded by the Russian Science Foundation (project no. 19-11-00105).
Received: 03.11.2021
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 91A23, 49N75
Language: Russian
Citation: I. V. Izmestyev, V. I. Ukhobotov, “On a discrete game problem with non-convex control vectograms”, Izv. IMI UdGU, 58 (2021), 48–58
Citation in format AMSBIB
\Bibitem{IzmUkh21}
\by I.~V.~Izmestyev, V.~I.~Ukhobotov
\paper On a discrete game problem with non-convex control vectograms
\jour Izv. IMI UdGU
\yr 2021
\vol 58
\pages 48--58
\mathnet{http://mi.mathnet.ru/iimi420}
\crossref{https://doi.org/10.35634/2226-3594-2021-58-03}
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