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Russia Izhevsk
Section  Mathematics 
Title  Linear nonstationary differential pursuit games with several evaders 
Author(s)  Bannikov A.S.^{a}, Petrov N.N.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  A linear nonstationary differential pursuit game with a group of pursuers and a group of evaders is considered. The pursuers' goal is to catch all evaders and the evaders' goal is at least for one of them to avoid contact with pursuers. All players have equal dynamic capabilities, geometric constraints on the control are strictly convex compact set with smooth boundary. The point in question is the minimum number of evaders that is sufficient to evade a given number of pursuers from any initial position. Sufficient conditions for the solvability of the global problem of evasion are used as an upper estimate of this minimum. We assume that to capture one evader it suffices that the initial position of this evader lie in the interior of convex hull of initial positions of pursuers. Using this assumption we find a lower estimate of this minimum. The obtained twosided estimate of the number of evaders sufficient to avoid contact with a given number of pursuers from any initial position is illustrated by examples. 
Keywords  differential game, group pursuit, evader, pursuer 
UDC  517.977.8 
MSC  49N70, 49N75 
DOI  10.20537/vm140301 
Received  25 August 2014 
Language  Russian 
Citation  Bannikov A.S., Petrov N.N. Linear nonstationary differential pursuit games with several evaders, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 3, pp. 312. 
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