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Russia Yekaterinburg
Year
2020
Volume
30
Issue
1
Pages
64-91
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Section Mathematics
Title Relaxation of pursuit-evasion differential game and program absorption operator
Author(-s) Chentsov A.G.ab, Khachai D.M.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract We consider some natural relaxation of pursuit-evasion differential game. For two closed sets, which are parameters, similar guidance problem for $\varepsilon$-neighborhoods is being solved. We are interested in finding a minimal size of such neighborhoods, which allows player I successfully solve his guidance problem in the class of generalized non-anticipating strategies. To resolve above-mentioned differential game, a modification of Program Iterations Method is implemented. Size of the neighborhoods is found as a position function and it's defined by application of special iterative procedure further below. As a corollary, it is shown that desired function is a fixed point of the open-loop operator, which defines the procedure.
Keywords pursuit-evasion differential game, program iterations method, guaranteed result
UDC 519.6
MSC 05A05, 97N70, 97N80
DOI 10.35634/vm200106
Received 2 January 2020
Language Russian
Citation Chentsov A.G., Khachai D.M. Relaxation of pursuit-evasion differential game and program absorption operator, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 1, pp. 64-91.
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