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Russia Izhevsk
Year
2012
Issue
1
Pages
50-59
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Section Mathematics
Title On two differential games of simple group pursuit
Author(-s) Sakharov D.V.a
Affiliations Udmurt State Universitya
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
UDC 517.977
MSC 49N70, 49N75
DOI 10.20537/vm120106
Received 19 October 2011
Language Russian
Citation Sakharov D.V. On two differential games of simple group pursuit, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 50-59.
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