Sufficient Conditions of Approach of Controlled Objects in Dynamic Game Problems. I
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The problem of approach of control objects is solved on the basis of the method of resolving functions. Sufficient conditions for game termination in a guaranteed finite time are proposed for the case where the Pontryagin condition is not satisfied. The upper and lower resolving functions of different types are introduced and are used to develop two schemes of the method of resolving functions that ensure termination of the differential game in the class of quasi-strategies and counter-controls.
Keywordsquasilinear differential game multivalued mapping measurable selector stroboscopic strategy resolving function
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