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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 3, Pages 34–48 (Mi vuu388)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

On numerical solution of differential games with nonterminal payoff in classes of mixed strategies

D. V. Korneva, N. Yu. Lukoyanovb

a Department of Computational Mathematics, Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620083, Russia
b Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: A zero-sum linear-convex differential game with a quality index that estimates a set of deviations of a motion trajectory at given instants of time from given target points is considered. A case when the saddle point condition in a small game, also known as Isaac's condition, does not hold, is studied. The game is formalized in classes of mixed control strategies of players. A numerical method for approximate computation of the game value and optimal strategies is elaborated. The method is based on the recurrent construction of upper convex hulls of auxiliary program functions. The results of numerical experiments in model examples are given.

Keywords: differential games, game value, saddle point, mixed stategies.

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Document Type: Article
UDC: 517.977
MSC: 49N70
Received: 22.07.2013

Citation: D. V. Kornev, N. Yu. Lukoyanov, “On numerical solution of differential games with nonterminal payoff in classes of mixed strategies”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 3, 34–48

Citation in format AMSBIB
\Bibitem{KorLuk13}
\by D.~V.~Kornev, N.~Yu.~Lukoyanov
\paper On numerical solution of differential games with nonterminal payoff in classes of mixed strategies
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 3
\pages 34--48
\mathnet{http://mi.mathnet.ru/vuu388}


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    This publication is cited in the following articles:
    1. M. I. Gomoyunov, D. V. Kornev, N. Yu. Lukoyanov, “On the numerical solution of a minmax control problem with a positional functional”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 77–95  mathnet  crossref  mathscinet  isi  elib
    2. M. I. Gomoyunov, “Lineino-vypuklye zadachi optimizatsii garantii pri zapazdyvanii v upravlenii”, Izv. IMI UdGU, 2015, no. 1(45), 37–105  mathnet  elib
    3. D. V. Kornev, “Chislennye metody resheniya differentsialnykh igr s neterminalnoi platoi”, Izv. IMI UdGU, 2016, no. 2(48), 82–151  mathnet  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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