Abstract:
For conflict-controlled dynamical systems satisfying the conditions of generalized uniqueness and uniform boundedness, the solvability of the minimax problem in the class of generalized controls is studied. The issues of consistency of such an extension are considered; i. e., the possibility of approximating generalized controls in the space of strategic measures by embeddings of ordinary controls is analyzed. For this purpose, the dependence of the set of measures on the general marginal distribution specified on one of the factors of the base space is studied. The continuity of this dependence in the Hausdorff metric defined by the metric corresponding to the $*$-weak topology in the space of measures is established. The density of embeddings of ordinary controls and control-noise pairs in sets of corresponding generalized controls in the $*$-weak topologies is also shown.
The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2024-1377).
Citation:
A. G. Chentsov, D. A. Serkov, “Continuous dependence of sets in a space of measures and a program minimax problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 2, 2024, 277–299; Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S76–S98
\Bibitem{CheSer24}
\by A.~G.~Chentsov, D.~A.~Serkov
\paper Continuous dependence of sets in a space of measures and a program minimax problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2024
\vol 30
\issue 2
\pages 277--299
\mathnet{http://mi.mathnet.ru/timm2098}
\crossref{https://doi.org/10.21538/0134-4889-2024-30-2-277-299}
\elib{https://elibrary.ru/item.asp?id=67234343}
\edn{https://elibrary.ru/zywfas}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2024
\vol 325
\issue , suppl. 1
\pages S76--S98
\crossref{https://doi.org/10.1134/S0081543824030064}
Citation in format AMSBIB
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