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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RESOLVING FUNCTIONS MODIFIED METHOD FOR GAME PROBLEMS OF APPROACH
OF CONTROLLED OBJECTS WITH DIFFERENT INERTIA
Abstract. The problem of approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in the finite guaranteed time in the case where the Pontryagin condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multivalued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type and, based on them, two types of modified schemes of the first Pontryagin method and the method of resolving functions are proposed, which ensure the completion of the conflict-controlled process for objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example.
Keywords: controlled objects with different inertia, quasilinear differential game, multi-valued mapping, measurable selector, stroboscopic strategy, resolving function.
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