UDC 517.977
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 jeffrappoport@gmail.com
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SUFFICIENT APPROACHING CONDITIONS FOR CONTROLLED OBJECTS
IN THE GAME DYNAMIC PROBLEMS. I
Abstract. The problem of approach of control objects is solved on the basis of the method of resolving functions. Sufficient conditions for game ending in a final guaranteed time are proposed in the case when the Pontryagin condition is not satisfied. The upper and lower resolving functions of different types are introduced and used to develop two schemes of the method of resolving functions that ensure the completion of the differential game in the class of quasi-strategies and counter-controls.
Keywords: quasilinear differential game, multivalued mapping, measurable selector, stroboscopic strategy, resolving function.
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