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## Archive of Issues

Russia Izhevsk
Year
2013
Issue
4
Pages
20-26
 Section Mathematics Title Capture of a group of evaders in a conflict-controlled process Author(-s) Blagodatskikh A.I.a Affiliations Udmurt State Universitya Abstract The present paper deals with the problem of pursuit of the group of $m$ evaders $(m \geqslant 1)$ in a conflict-controlled process 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 multiple capture of one evader requires that capture moments coincide. We say that the simultaneous multiple capture of the whole group of evaders $(m \geqslant 2)$ holds if the simultaneous multiple capture of every evader holds at 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/vm130403 Received 1 November 2013 Language Russian Citation Blagodatskikh A.I. Capture of a group of evaders in a conflict-controlled process, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 20-26. 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 over 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. Blagodatskikh A.I. Simultaneous multiple capture in a conflict control process, Prikl. Mat. Mekh., 2013, vol. 77, no. 3, pp. 433-440. Blagodatskikh A.I. Simultaneous multiple capture of evaders in a simple group pursuit problem, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 3, pp. 13-18. Bannikov A.S. Nonstationary group pursuit problem, Izv. Vyssh. Uchebn. Zaved., Mat., 2009, no. 5, pp. 3-12. Full text