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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 3, Pages 383–387 (Mi vuu492)  

MATHEMATICS

To the problem of group pursuit on a plane

K. A. Shchelchkov

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

Abstract: The paper deals with two simple pursuit problems on a plane with a group of pursuers and one evader. All the participants have equal capabilities. In the first problem the admissible control for every participant takes the value in a non-degenerate triangle. Necessary and sufficient conditions on initial positions of all participants are obtained for capture by three pursuers of one evader. In the second problem the admissible control for every participants takes the value in a compact set with non-empty interior. Within this problem, necessary and sufficient conditions on the structure of this compact set are received for the existence of initial positions of two pursuers and one evader from which the capture occurs.

Keywords: differential game, simple motion, group pursuit.

Full text: PDF file (179 kB)
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UDC: 517.977
MSC: 49N70, 49N75
Received: 29.07.2015

Citation: K. A. Shchelchkov, “To the problem of group pursuit on a plane”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:3 (2015), 383–387

Citation in format AMSBIB
\Bibitem{Shc15}
\by K.~A.~Shchelchkov
\paper To the problem of group pursuit on a~plane
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 3
\pages 383--387
\mathnet{http://mi.mathnet.ru/vuu492}
\elib{http://elibrary.ru/item.asp?id=24237244}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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