Abstract:
A differential approach-evasion game with fixed termination time is studied. It is assumed that the phase vector of the conflict-control system is subjected to constraints that form a closed set in the position space. The ideology of stable bridges is used for solving the problem.
A method of convolution is proposed, which is used in several problems for constructing explicitly the stable absorption operator defining the stable bridges. A method of approximate construction of the maximal stable bridge in this game is suggested. The relations are written down that define a system of sets approximating the maximal stable bridge, and a control procedure with a guide is described, which can be used for obtaining an approximate solution of the approach problem.
Citation:
S. V. Grigor'eva, V. Yu. Pakhotinskikh, A. A. Uspenskii, V. N. Ushakov, “Construction of solutions in certain differential games with phase constraints”, Sb. Math., 196:4 (2005), 513–539
\Bibitem{GriPakUsp05}
\by S.~V.~Grigor'eva, V.~Yu.~Pakhotinskikh, A.~A.~Uspenskii, V.~N.~Ushakov
\paper Construction of solutions in certain differential games with phase constraints
\jour Sb. Math.
\yr 2005
\vol 196
\issue 4
\pages 513--539
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https://doi.org/10.1070/SM2005v196n04ABEH000890
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This publication is cited in the following 25 articles:
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V. N. Ushakov, A. M. Tarasyev, A. A. Ershov, “A Supplement to Krasovskii's Unification Method in Differential Game Theory”, Dokl. Math., 2024
V. N. Ushakov, A. V. Ushakov, O. A. Kuvshinov, “Sblizhenie konfliktno upravlyaemykh sistem na konechnom promezhutke vremeni”, Izv. IMI UdGU, 64 (2024), 70–96
V. N. Ushakov, A. M. Tarasyev, A. A. Ershov, “Concerning one supplement to unification method of N.N. Krasovskii in differential games theory”, Dokl. RAN. Math. Inf. Proc. Upr., 519 (2024), 65–71
V. N. Ushakov, A. A. Ershov, “On the Construction of Solutions to a Game Problem with a Fixed End Time”, Proc. Steklov Inst. Math., 327:S1 (2024), S239
V. N. Ushakov, A. M. Tarasyev, A. V. Ushakov, “Minimax Differential Game with a Fixed End Moment”, Dokl. Math., 110:S2 (2024), S495
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V. N. Ushakov, A. V. Ushakov, “O sblizhenii upravlyaemoi sistemy na konechnom promezhutke vremeni”, Izv. IMI UdGU, 60 (2022), 111–154
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