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Russian Universities Reports. Mathematics, 2020, Volume 25, Issue 132, Pages 359–369 (Mi vtamu204)  

Scientific articles

Minimax differential game with delay

A. V. Kima, G. A. Bocharovb

a N. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences
b Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences

Abstract: The paper considers a minimax positional differential game with aftereffect based on the $i$-smooth analysis methodology. In the finite-dimensional (ODE) case for a minimax differential game, resolving mixed strategies can be constructed using the dynamic programming method. The report shows that the $i$-smooth analysis methodology allows one to construct counterstrategies in a completely similar way to the finite-dimensional case. Moreover as it is typical for the use of $i$-smooth analysis, in the absence of an aftereffect, all the results of the article pass to the corresponding results of the finite-dimensional theory of positional differential games.

Keywords: differential games, systems with delays.

Funding Agency Grant Number
Russian Foundation for Basic Research 20-01-00352_
The work is partially supported by the Russian Foundation for Basic Research (project no. 20-01-00352_).


DOI: https://doi.org/10.20310/2686-9667-2020-25-132-359-369

Full text: PDF file (500 kB)
References: PDF file   HTML file

UDC: 517.977.8
Received: 28.05.2020

Citation: A. V. Kim, G. A. Bocharov, “Minimax differential game with delay”, Russian Universities Reports. Mathematics, 25:132 (2020), 359–369

Citation in format AMSBIB
\Bibitem{KimBoc20}
\by A.~V.~Kim, G.~A.~Bocharov
\paper Minimax differential game with delay
\jour Russian Universities Reports. Mathematics
\yr 2020
\vol 25
\issue 132
\pages 359--369
\mathnet{http://mi.mathnet.ru/vtamu204}
\crossref{https://doi.org/10.20310/2686-9667-2020-25-132-359-369}


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