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.
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
\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}
\crossref{https://doi.org/10.20537/vm130304}
Linking options:
https://www.mathnet.ru/eng/vuu388
https://www.mathnet.ru/eng/vuu/y2013/i3/p34
This publication is cited in the following 3 articles:
D. V. Kornev, “Chislennye metody resheniya differentsialnykh igr s neterminalnoi platoi”, Izv. IMI UdGU, 2016, no. 2(48), 82–151
M. I. Gomoyunov, “Lineino-vypuklye zadachi optimizatsii garantii pri zapazdyvanii v upravlenii”, Izv. IMI UdGU, 2015, no. 1(45), 37–105
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
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