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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, Issue 3, Pages 3–12 (Mi vuu435)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Linear non-stationary differential pursuit games with several evaders

A. S. Bannikov, N. N. Petrov

Department of Differential Equations, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: A linear non-stationary differential pursuit game with a group of pursuers and a group of evaders is considered. The pursuers' goal is to catch all evaders and the evaders' goal is at least for one of them to avoid contact with pursuers.
All players have equal dynamic capabilities, geometric constraints on the control are strictly convex compact set with smooth boundary. The point in question is the minimum number of evaders that is sufficient to evade a given number of pursuers from any initial position. Sufficient conditions for the solvability of the global problem of evasion are used as an upper estimate of this minimum. We assume that to capture one evader it suffices that the initial position of this evader lie in the interior of convex hull of initial positions of pursuers. Using this assumption we find a lower estimate of this minimum.
The obtained two-sided estimate of the number of evaders sufficient to avoid contact with a given number of pursuers from any initial position is illustrated by examples.

Keywords: differential game, group pursuit, evader, pursuer.

Full text: PDF file (235 kB)
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UDC: 517.977.8
MSC: 49N70, 49N75
Received: 25.08.2014

Citation: A. S. Bannikov, N. N. Petrov, “Linear non-stationary differential pursuit games with several evaders”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 3, 3–12

Citation in format AMSBIB
\Bibitem{BanPet14}
\by A.~S.~Bannikov, N.~N.~Petrov
\paper Linear non-stationary differential pursuit games with several evaders
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2014
\issue 3
\pages 3--12
\mathnet{http://mi.mathnet.ru/vuu435}


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    This publication is cited in the following articles:
    1. L. S. Chirkova, “Uklonenie ot vstrechi gruppy zhestko skoordinirovannykh ob'ektov v igre tretego poryadka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:3 (2015), 378–382  mathnet  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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