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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MODIFICATIONS OF THE PONTRYAGIN CONDITIONS IN THE PROBLEM
OF APPROACH OF CONFLICT-CONTROLLED OBJECTS
Abstract. The problem of approach of controlled objects in dynamic game problems is considered. Modified sufficient conditions for the game termination in a finite guaranteed time are formulated in the case where the Pontryagin condition is not satisfied. Instead of the Pontryagin selector, which does not exist, some shift functions are considered and used to introduce special multivalued mappings. They generate the upper and lower resolving functions of special type, and based on them, modified schemes of the first Pontryagin’s method and of the method of resolving functions are proposed, which ensures the completion of the conflict-controlled process in the class of quasi-strategies and counter-controls. The new theoretical results are illustrated by the control Pontryagin’s example of with objects of the same type.
Keywords: quasilinear differential game, multi-valued mapping, measurable selector, stroboscopic strategy, resolving function.
FULL TEXT
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