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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 1, Pages 50–59 (Mi vuu310)  

This article is cited in 7 scientific papers (total in 7 papers)

MATHEMATICS

On two differential games of simple group pursuit

D. V. Sakharov

Department of Differential Equations, Udmurt State University, Izhevsk, Russia

Abstract: Two differential games of the simple pursuit of a group of evaders by a group of pursuers are considered. The first problem is devoted to the pursuit of a group of rigidly co-ordinated evaders by a group of pursuers with equal possibilities for all participants. It is supposed that the evaders remain in the bounds of the convex polyhedral set, terminal sets are convex compacts and the aim of the group of pursuers is to capture at least one evader. The solvability conditions of the problem of pursuit and the problem of evasion are obtained in the terms of initial positions and parameters of the game.
The second problem is devoted to the pursuit of a group of evaders by a group of pursuers under condition that the evaders use program strategies and one pursuer can catch only one evader. The aim of a group of pursuers is to capture a specified number of evaders. Terminal sets are convex compacts, the set of possible controls is an arbitrary convex compact. Necessary and sufficient solvability conditions of the problem of pursuit are obtained.

Keywords: differential game, simple motion, group pursuit, rigidly co-ordinated evaders.

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Document Type: Article
UDC: 517.977
MSC: 49N70, 49N75
Received: 19.10.2011

Citation: D. V. Sakharov, “On two differential games of simple group pursuit”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 1, 50–59

Citation in format AMSBIB
\Bibitem{Sak12}
\by D.~V.~Sakharov
\paper On two differential games of simple group pursuit
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 1
\pages 50--59
\mathnet{http://mi.mathnet.ru/vuu310}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Sakharov, “Dve zadachi prostogo gruppovogo presledovaniya”, Izv. IMI UdGU, 2012, no. 1(39), 121–122  mathnet
    2. Denis V. Sakharov, “Odna zadacha gruppovogo presledovaniya v lineinoi pochti periodicheskoi differentsialnoi igre”, MTIP, 4:3 (2012), 86–100  mathnet
    3. N. N. Petrov, K. A. Schelchkov, “K zadache Chernousko”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 62–67  mathnet
    4. L. S. Chirkova, “Uklonenie ot gruppy inertsionnykh ob'ektov v igre chetvertogo poryadka”, Izv. IMI UdGU, 2013, no. 2(42), 58–101  mathnet
    5. Lyubov S. Chirkova, “Uklonenie ot vstrechi v konuse v differentsialnoi igre tretego poryadka”, MTIP, 6:3 (2014), 93–104  mathnet
    6. L. S. Chirkova, “Uklonenie v konuse ot “myagkoi poimki” v igre chetvertogo poryadka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 526–533  mathnet  elib
    7. N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache prostogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 193–198  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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