Section
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Mathematics
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Title
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The programmed iterations method in a game problem of guidance
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Author(-s)
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Chentsov A.G.ab
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Affiliations
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Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa,
Ural Federal Universityb
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Abstract
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The solution of a differential game of guidance-evasion on the basis of the programmed iterations method is considered. The basic goal consists in the construction of a set of positional absorption corresponding to alternative partition following from the fundamental alternative theorem of N.N. Krasovskii and A.I. Subbotin. For construction, an operator of programmed absorption defined by the target set in a guidance problem is used. The set defining phase constraints is gradually transformed by the above-mentioned operator; therefore, the sequence for which the corresponding limit coincides with the set of positional absorption is realized. It is assumed that the target set is closed and the set defining phase constraints of initial problem has closed sections corresponding to fixation of time. Properties having the sense of one-sided continuity of the positional absorption set under variation of sets defining initial differential game are established. It is shown that the limit of iterated procedure coincides with the set of successful solvability in a class of set-valued generalized quasistrategies.
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Keywords
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differential game, programmed iterations method, set of positional absorption
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UDC
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519.6
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MSC
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28A33
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DOI
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10.20537/vm160213
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Received
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6 May 2016
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Language
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Russian
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Citation
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Chentsov A.G. The programmed iterations method in a game problem of guidance, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 271-282.
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References
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- Krasovskii N.N, Subbotin A.I. An alternative for the game problem of convergence, Journal of Applied Mathematics and Mechanics, 1970, vol. 34, issue 6, pp. 948-965.
- Krasovskii N.N, Subbotin A.I. Pozitsionnye differentsial'nye igry (Positional differential games), Мoscow: Nauka, 1974, 456 p.
- Kryazhimskii A.V. On the theory of positional differential games of convergence-evasion, Soviet Mathematics. Doklady, 1978, vol. 19, pp. 408-412.
- Chentsov A.G. On the structure of a game problem of convergence, Soviet Mathematics. Doklady, 1975, vol. 16, pp. 1404-1408.
- Chentsov A.G. On a game problem of guidance, Soviet Mathematics. Doklady, 1976, vol. 17, pp. 73-77.
- Čencov A.G. On a game problem of converging at a given instant of time, Mathematics of the USSR - Sbornik, 1976, vol. 28, no. 3, pp. 353-376.
- Ukhobotov V.I. Construction of a stable bridge for a class of linear games, Journal of Applied Mathematics and Mechanics, 1977, vol. 41, issue 2, pp. 350-354.
- Chistyakov S.V. On solving pursuit game problems, Journal of Applied Mathematics and Mechanics, 1977, vol. 41, issue 5, pp. 845-852.
- Chentsov A.G. About an alternative to the class of quasistrategies for differential pursuit-evasion game, Differ. Uravn., 1980, vol. 16, no. 10, pp. 1801-1808 (in Russian).
- Chentsov A.G. The programmed iterations method for differential pursuit-evasion game, Sverdlovsk: Institute of Mathematics and Mechanics, Ural Research Centre of RAS, 1979, 103 p. Deposited in VINITI 04.06.1979, no. 1933-79 (in Russian).
- Chentsov A.G. Programmed iteration method and sets of positional absorption, Doklady Mathematics, 2016, vol. 93, no. 2, pp. 144-148.
- Engelking R. General topology, Warszawa: PWN, 1985, 752 p.
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