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Russia; Uzbekistan Izhevsk; Tashkent
Year
2018
Volume
28
Issue
2
Pages
193-198
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Section Mathematics
Title Multiple capture of a given number of evaders in the problem of a simple pursuit
Author(-s) Petrov N.N.a, Narmanov A.Ya.b
Affiliations Udmurt State Universitya, National University of Uzbekistanb
Abstract In the finite-dimensional Euclidean space, the problem of a group of pursuers pursuing a group of evaders is considered, which is described by the system $$\dot z_{ij} = u_i - v_j,\quad u_i, v_j \in V.$$ The set of admissible controls is a convex compact, and the target's sets are the origin of coordinates. The aim of the group of pursuers is to carry out an $r$-fold capture of at least $q$ evaders. Additionally, it is assumed that the evaders use program strategies and that each pursuer can catch no more than one evader. We obtain necessary and sufficient conditions for the solvability of the pursuit problem. For the proof we use the Hall theorem on the system of various representatives.
Keywords differential game, group pursuit, pursuer, evader
UDC 517.977
MSC 49N75, 91A23
DOI 10.20537/vm180205
Received 3 June 2018
Language Russian
Citation Petrov N.N., Narmanov A.Ya. Multiple capture of a given number of evaders in the problem of a simple pursuit, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 2, pp. 193-198.
References
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