UDC 517.977
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 g.chikrii@gmail.com
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2 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
jeffrappoport@gmail.com
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A MODIFIED METHOD OF RESOLVING FUNCTIONS FOR CONTROL
GAME PROBLEMS WITH INTEGRAL CONSTRAINTS
Abstract. The paper considers linear differential games with integral constraints. Sufficient conditions for the game termination in a finite guaranteed time are formulated for the case where Nikolsky’s condition is not satisfied. Multivalued mappings that generate the upper and lower resolving functions of special type are introduced. The modified schemes of Nikolsky’s direct method and the method of resolving functions are proposed, which ensure the game termination in a finite guaranteed time in the class of quasi-strategies and stroboscopic strategies. The most recent theoretical results are illustrated by the reference Pontryagin’s example with objects of the same type.
Keywords: linear differential game, integral constraints, multivalued mapping, resolving functions, stroboscopic strategy.
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