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Home » Issues » Archive of Issues » 2021 - 4 issue » pp. 668-696

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Russia Yekaterinburg
Year
2021
Volume
31
Issue
4
Pages
668-696
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Section Mathematics
Title On properties of one functional used in software constructions for solving differential games
Author(-s) Chentsov A.G.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract Nonlinear differential game (DG) is investigated; relaxations of the game problem of guidance are investigated also. The variant of the program iterations method realized in the space of position functions and delivering in limit the value function of the minimax-maximin DG for special functionals of a trajectory is considered. For every game position, this limit function realizes the least size of the target set neighborhood for which, under proportional weakening of phase constraints, the player interested in a guidance yet guarantees its realization. Properties of above-mentioned functionals and limit function are investigated. In particular, sufficient conditions for realization of values of given function under fulfilment of finite iteration number are obtained.
Keywords differential game, program iteration method, value function
UDC 517.9
MSC 49L20, 90C39
DOI 10.35634/vm210410
Received 21 September 2021
Language Russian
Citation Chentsov A.G. On properties of one functional used in software constructions for solving differential games, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 4, pp. 668-696.
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