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Russia Yekaterinburg
Section  Mathematics 
Title  The programmed iterations method in a game problem of guidance 
Author(s)  Chentsov A.G.^{ab} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a}, Ural Federal University^{b} 
Abstract  The solution of a differential game of guidanceevasion 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 abovementioned 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 onesided 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 setvalued generalized quasistrategies. 
Keywords  differential game, programmed iterations method, set of positional absorption 
UDC  519.6 
MSC  28A33 
DOI  10.20537/vm160213 
Received  6 May 2016 
Language  Russian 
Citation  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. 271282. 
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