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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, Issue 3, Pages 52–58 (Mi vuu439)  

MATHEMATICS

On the interrelation of two linear stationary evasion problems with many evaders

N. N. Petrov, K. A. Shchelchkov

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: A linear stationary pursuit problem with a group of pursuers and a group of evaders is considered under the following conditions: the matrix of the system is a scalar matrix, among the pursuers there are participants whose set of admissible controls coincides with the set of admissible controls of evaders, and there are participants with fewer opportunities. The set of values of admissible controls of evaders is a ball with center at the origin. The pursuers' goal is to capture all evaders. The evaders' goal is to prevent this, i.e. to provide an opportunity for at least one of them to escape meeting. Pursuers and evaders use piecewise-program strategies. It is shown that if all participants of the game have equal opportunities and at least one of the evaders avoids meeting on the infinite time interval, then the addition of any number of pursuers with fewer opportunities leads to evasion of at least one evader on any finite time interval.

Keywords: differential game, group pursuit, pursuer, evader, the price of game.

Full text: PDF file (212 kB)
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UDC: 517.977
MSC: 49N70, 49N75
Received: 29.08.2014

Citation: N. N. Petrov, K. A. Shchelchkov, “On the interrelation of two linear stationary evasion problems with many evaders”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 3, 52–58

Citation in format AMSBIB
\Bibitem{PetShc14}
\by N.~N.~Petrov, K.~A.~Shchelchkov
\paper On the interrelation of two linear stationary evasion problems with many evaders
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2014
\issue 3
\pages 52--58
\mathnet{http://mi.mathnet.ru/vuu439}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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