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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 76–92
(Mi tm3235)
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This article is cited in 35 scientific papers (total in 35 papers)
An analytical method in dynamic pursuit games
A. A. Chikrii V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Abstract:
The paper is devoted to quasilinear conflict-controlled processes of general form with a cylindrical terminal set. A specific feature is that, instead of a dynamical system, we start with representation of a solution in a form that allows one to include an additive term with the initial data and a control unit. This makes it possible to consider a broad spectrum of dynamic processes in a unified scheme. Our study is based on the method of resolving functions. We obtain sufficient conditions for the solvability of the pursuit problem at a certain guaranteed time in the class of strategies that use information on the behavior of the opponent in the past, as well as in the class of stroboscopic strategies. We also find conditions under which information on the prehistory of the evader does not matter. The guaranteed times of various schemes of the resolving function method are compared with the guaranteed time of Pontryagin's first direct method. The qualitative results are illustrated by an example of a game problem with simple motions and incomplete sweeping for special control domains in the Pontryagin condition.
Received in December 2009
Citation:
A. A. Chikrii, “An analytical method in dynamic pursuit games”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 76–92; Proc. Steklov Inst. Math., 271 (2010), 69–85
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https://www.mathnet.ru/eng/tm3235 https://www.mathnet.ru/eng/tm/v271/p76
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Abstract page: | 520 | Full-text PDF : | 121 | References: | 129 |
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