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Russia Izhevsk
Section  Mathematics 
Title  On the interrelation of two linear stationary evasion problems with many evaders 
Author(s)  Petrov N.N.^{a}, Shchelchkov K.A.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  A linear stationary pursuit problem with a group of pursuers and a group of evaders is considered under the following conditions: the matrix of the system is a scalar matrix, among the pursuers there are participants whose set of admissible controls coincides with the set of admissible controls of evaders, and there are participants with fewer opportunities. The set of values of admissible controls of evaders is a ball with center at the origin. The pursuers' goal is to capture all evaders. The evaders' goal is to prevent this, i.e. to provide an opportunity for at least one of them to escape meeting. Pursuers and evaders use piecewiseprogram strategies. It is shown that if all participants of the game have equal opportunities and at least one of the evaders avoids meeting on the infinite time interval, then the addition of any number of pursuers with fewer opportunities leads to evasion of at least one evader on any finite time interval. 
Keywords  differential game, group pursuit, pursuer, evader, the price of game 
UDC  517.977 
MSC  49N70, 49N75 
DOI  10.20537/vm140305 
Received  29 August 2014 
Language  Russian 
Citation  Petrov N.N., Shchelchkov K.A. On the interrelation of two linear stationary evasion problems with many evaders, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 3, pp. 5258. 
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