Abstract
The authors consider the problem of approach of controlled objects in dynamic game problems and formulate modified sufficient conditions for the game termination in a finite guaranteed time 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 map**s. 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. Pontryagin’s control example with objects of the same type illustrates the new theoretical results.
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Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2022, pp. 95–105.
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Chikrii, A.A., Rappoport, I.S. Modifications of the Pontryagin Conditions in the Problem of Approach of Conflict-Controlled Objects. Cybern Syst Anal 58, 935–944 (2022). https://doi.org/10.1007/s10559-023-00527-9
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DOI: https://doi.org/10.1007/s10559-023-00527-9