Geodesic
On numerical solution of differential games with nonterminal payoff in classes of mixed strategies
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 34-48

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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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     author = {D. V. Kornev and N. Yu. Lukoyanov},
     title = {On numerical solution of differential games with nonterminal payoff in classes of mixed strategies},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {34--48},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_3_a3/}
}
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D. V. Kornev; N. Yu. Lukoyanov. On numerical solution of differential games with nonterminal payoff in classes of mixed strategies. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2013), pp. 34-48. http://geodesic.mathdoc.fr/item/VUU_2013_3_a3/