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Uzbekistan Andijan; Tashkent
Year
2023
Volume
33
Issue
1
Pages
103-118
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Section Mathematics
Title The method of resolving functions for solving a pursuit problem with integral constraints on player controls
Author(-s) Mamadaliev N.A.ab, Mustapokulov Kh.Ya.bc, Abdualimova G.M.d
Affiliations Institute of Mathematics, National Academy of Sciences of Uzbekistana, National University of Uzbekistanb, Tashkent State Technical Universityc, Andijan State Universityd
Abstract In this paper, we study pursuit game problems described by a system of equations with a retarded argument under integral constraints on the players' controls. The proposed scheme uses the ideas of the method of resolving functions. Modifications of methods (i.e., the first and so-called third methods) [1,3,12] of pursuit are proposed in the case when integral constraints are imposed on the players' controls. Sufficient conditions are obtained for the possibility of completing the pursuit in a finite time.
Keywords differential game, pursuit game, integral constraint, resolving function, conflict-controlled process, multivalued mapping, control, pursuer, evader
UDC 517.977
MSC 35F46, 35K51, 35R12, 49N25, 93C20
DOI 10.35634/vm230107
Received 12 September 2022
Language Russian
Citation Mamadaliev N.A., Mustapokulov Kh.Ya., Abdualimova G.M. The method of resolving functions for solving a pursuit problem with integral constraints on player controls, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 1, pp. 103-118.
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