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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 1, Pages 12–20 (Mi vuu460)  

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

MATHEMATICS

On the capture of two evaders in a non-stationary pursuit–evasion problem with phase restrictions

M. N. Vinogradova

Department of Mathematics and Informatics, Udmurt State University, Branch in Votkinsk, ul. Raskovoi, 1a, Votkinsk, 427438, Russia

Abstract: We consider a linear problem of pursuing two evaders by a group of persecutors in case of equal dynamic opportunities of all participants and under phase restrictions imposed on the states of evaders. We assume that the evaders use the same control. The movement of each participant has the form $\dot z+a(t)z=w$. Geometric constraints on the control are strictly convex compact set with smooth boundary, and terminal sets are the origin of coordinates. It is assumed that the evaders do not leave the convex cone. The aim of a group of pursuers is to capture two evaders; the aim of a group of evaders is opposite. We say that a capture holds in the problem of pursuing two evaders if among the specified number of pursuers there are two of them who catch the evaders, possibly at different times. We obtain sufficient conditions for capturing two evaders in terms of initial positions. The results obtained are illustrated by examples.

Keywords: differential game, phase restrictions, piece-program strategy, counterstrategy.

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Document Type: Article
UDC: 517.977
MSC: 49N70, 49N75
Received: 25.02.2015

Citation: M. N. Vinogradova, “On the capture of two evaders in a non-stationary pursuit–evasion problem with phase restrictions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:1 (2015), 12–20

Citation in format AMSBIB
\Bibitem{Vin15}
\by M.~N.~Vinogradova
\paper On the capture of two evaders in a~non-stationary pursuit--evasion problem with phase restrictions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 1
\pages 12--20
\mathnet{http://mi.mathnet.ru/vuu460}
\elib{http://elibrary.ru/item.asp?id=23142045}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. N. Vinogradova, “Gruppovoe presledovanie dvukh ubegayuschikh v lineinoi igre s prostoi matritsei”, Izv. IMI UdGU, 50 (2017), 21–28  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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