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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 2, Pages 304–321
DOI: https://doi.org/10.21538/0134-4889-2016-22-2-304-321 (Mi timm1315) 		 
This article is cited in 15 scientific papers (total in 15 papers)

The program iteration method in a game problem of guidance

A. G. Chentsovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Institute of Radio Engineering and Information Technologies, Ural Federal University, Ekaterinburg
Full-text PDF (271 kB) Citations (15)
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DOI: https://doi.org/10.21538/0134-4889-2016-22-2-304-321
Abstract: A variant of the program iteration method for solving a game problem of guidance to a target set under state constraints is considered. We study a procedure for the construction of a positional absorption set corresponding to N.N. Krasovskii and A.I. Subbotin's theorem of alternatives, which underlies the modern theory of differential games. Important results on the alternative solvability of differential games for systems with distributed parameters and aftereffect belong to Yu.S. Osipov. These results are an essential complement to the ideas related to the alternative for dynamic problems of infinite-dimensional nature. The solution method from the present paper is intended for the “finite-dimensional” case of a differential game of approach-evasion.
Keywords: differential game, generalized program control, iteration method.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00505
16-01-00649
Received: 07.12.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 297, Issue 1, Pages 43–61
DOI: https://doi.org/10.1134/S0081543817050066
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 49J15, 49K15, 93C15, 49N70
Language: Russian
Citation: A. G. Chentsov, “The program iteration method in a game problem of guidance”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 304–321; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 43–61
Citation in format AMSBIB
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