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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 128–142
(Mi timm1121)
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This article is cited in 5 scientific papers (total in 5 papers)
Stable bridge construction in games with simple motions in the plane
L. V. Kamnevaab, V. S. Patskoba a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University
Abstract:
It is known that the solvability set (the maximal stable bridge) in a zero-sum differential game with simple motions, fixed terminal time, geometric constraints on the controls of the first and second players, and convex terminal set can be constructed by means of a program absorption operator. In this case, a backward procedure for the construction of $t$-sections of the solvability set does not need any additional partition times. We establish the same property for a game with simple motions, polygonal terminal set (which is generally nonconvex), and polygonal constraints on the players's controls in the plane. In the particular case of a convex terminal set, the operator used in the article coincides with the program absorption operator.
Keywords:
differential games with simple motions in the plane, solvability set, backward procedure.
Received: 09.08.2014
Citation:
L. V. Kamneva, V. S. Patsko, “Stable bridge construction in games with simple motions in the plane”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 128–142; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 125–139
Linking options:
https://www.mathnet.ru/eng/timm1121 https://www.mathnet.ru/eng/timm/v20/i4/p128
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