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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2020, Volume 30, Issue 1, Pages 18–30 (Mi vuu707)  

MATHEMATICS

Discrete game problem with ring-shaped terminal set

I. V. Izmest'ev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

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. The aim of the first player is to lead a phase vector to the terminal set at fixed time. The aim of the second player is the opposite. In this paper, optimal controls of the players are constructed. Computer simulation of the game process is performed. A modification of the original problem, in which at an unknown time there is a change in the dynamics of the first player, is considered.

Keywords: game, control, terminal set, breakdown.

Funding Agency Grant Number
Russian Science Foundation 19-11-00105
This work supported by the Russian Science Foundation (grant no. 19-11-00105).


DOI: https://doi.org/10.35634/vm200102

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Full text: http://vm.udsu.ru/.../2020-1-2
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Bibliographic databases:

UDC: 517.977
MSC: 91A23, 49N75
Received: 20.11.2019

Citation: I. V. Izmest'ev, “Discrete game problem with ring-shaped terminal set”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:1 (2020), 18–30

Citation in format AMSBIB
\Bibitem{Izm20}
\by I.~V.~Izmest'ev
\paper Discrete game problem with ring-shaped terminal set
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 1
\pages 18--30
\mathnet{http://mi.mathnet.ru/vuu707}
\crossref{https://doi.org/10.35634/vm200102}


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