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Archive of Issues

Russia Izhevsk
Year
2012
Issue
3
Pages
13-18
 Section Mathematics Title Simultaneous multiple capture of evaders in a simple group pursuit problem Author(-s) Blagodatskikh A.I.a Affiliations Udmurt State Universitya Abstract The present paper deals with the problem of simple pursuit of group of $m$ evaders $(m\geqslant 1)$ with equal opportunities. We say that a multiple capture in the problem of pursuit of one evader $(m = 1)$ holds if the specified number of pursuers catch him, possibly at different times. The problem of the simultaneous capture of one evader requires that capture moments coincide. We introduce the concept of multiple simultaneous capture of the whole group of evaders $(m \geqslant 2).$ We say that the simultaneous multiple capture of the whole group of evaders holds if the simultaneous multiple capture of every evader holds in the same time. We obtain necessary and sufficient conditions for simultaneous multiple capture of the whole group of evaders in terms of initial positions of the participants. Keywords capture, multiple capture, simultaneous multiple capture, pursuit, evasion, differential games, conflict controlled processes UDC 517.977 MSC 49N70, 49N75 DOI 10.20537/vm120302 Received 24 May 2012 Language Russian Citation Blagodatskikh A.I. Simultaneous multiple capture of evaders in a simple group pursuit problem, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 13-18. References Pshenichnyi B.N. Simple pursuit by several objects, Kibernetika, 1976, no. 3, pp. 145-146. Grigorenko N.L. Matematicheskie metody upravleniya neskol'kimi dinamicheskimi protsessami (Mathematical methods of control multiple dynamic processes), Moscow: Moscow State University, 1990, 197 p. Chikrii A.A. Konfliktno upravlyaemye protsessy (Conflict controlled processes), Kiev: Naukova dumka, 1992, 380 p. Petrov N.N. Multiple capture in Pontryagin's problem with phase restrictions, Prikl. Mat. Mekh., 1997, vol. 61, no. 5, pp. 747-754. Blagodatskikh A.I., Petrov N.N. Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob''ektov (Conflict interaction of groups of controlled objects), Izhevsk: Udmurt State University, 2009, 266 p. Blagodatskikh A.I. Simultaneous multiple capture in a simple pursuit problem, Prikl. Mat. Mekh., 2009, vol. 73, no. 1, pp. 54-59. Full text