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Russia Izhevsk
Section Mathematics
Title To the problem of group pursuit on a plane
Author(-s) Shchelchkov K.A.a
Affiliations Udmurt State Universitya
Abstract The paper deals with two simple pursuit problems on a plane with a group of pursuers and one evader. All the participants have equal capabilities. In the first problem the admissible control for every participant takes the value in a non-degenerate triangle. Necessary and sufficient conditions on initial positions of all participants are obtained for capture by three pursuers of one evader. In the second problem the admissible control for every participants takes the value in a compact set with non-empty interior. Within this problem, necessary and sufficient conditions on the structure of this compact set are received for the existence of initial positions of two pursuers and one evader from which the capture occurs.
Keywords differential game, simple motion, group pursuit
UDC 517.977
MSC 49N70, 49N75
DOI 10.20537/vm150308
Received 29 July 2015
Language Russian
Citation Shchelchkov K.A. To the problem of group pursuit on a plane, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 3, pp. 383-387.
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