Abstract:
The paper deals with game problems on the approach of trajectories of a nonstationary quasilinear system to a variable cylindrical terminal set. The case is studied when Pontryagin's classical condition fails. The notions of upper and lower resolving functions are introduced in the form of selections of special set-valued mappings. These functions are used to derive sufficient solvability conditions, which differ from the known ones. The results are illustrated with a model example.
\Bibitem{Chi17}
\by A.~A.~Chikrii
\paper Upper and lower resolving functions in dynamic game problems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 1
\pages 293--305
\mathnet{http://mi.mathnet.ru/timm1403}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-1-293-305}
\elib{https://elibrary.ru/item.asp?id=28409387}
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https://www.mathnet.ru/eng/timm1403
https://www.mathnet.ru/eng/timm/v23/i1/p293
This publication is cited in the following 6 articles:
A. A Chikrii, I. S. Rappoport, “Modifications of the Pontryagin Conditions in the Problem of Approach of Conflict-Controlled Objects”, Cybern Syst Anal, 58:6 (2022), 935
I. S. Rappoport, “Solving the problem of approach of controlled objects in dynamic game problems”, Cybern. Syst. Anal., 57:5 (2021), 775–786
I. S. Rappoport, “Method of resolving functions for game problems of approach of controlled objects with different inertia”, Cybern. Syst. Anal., 57:2 (2021), 296–312
J. S. Rappoport, “The problem of approach of controlled objects in dynamic game problems with a terminal payoff function”, Cybern. Syst. Anal., 56:5 (2020), 820–834
I. S. Rappoport, “Sufficient conditions of approach of controlled objects in dynamic game problems. Ii”, Cybern. Syst. Anal., 55:6 (2019), 1027–1038
I. S. Rappoport, “Sufficient conditions of approach of controlled objects in dynamic game problems. I”, Cybern. Syst. Anal., 55:5 (2019), 828–839
Citation in format AMSBIB
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