Abstract
The authors consider the problem of approach of controlled objects with different inertia in dynamic game problems on the basis of the modern version of the method of resolving functions. For such objects, it is characteristic that the Pontryagin condition is not satisfied on a certain time interval, which significantly complicates the application of the method of resolving functions to this class of dynamic game problems. A method for solving such problems is proposed, which is associated with the construction of some scalar (resolving) functions, which qualitatively characterize the course of approach of controlled objects with different inertia and the efficiency of the decisions made. The method of resolving functions allows efficient use of the modern technique of multi-valued mappings in substantiating game constructions and obtaining meaningful results on their basis. The guaranteed times of game termintion are compared for different schemes of approaching of controlled objects. An illustrative example is given.
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Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2021, pp. 147–166.
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Rappoport, I.S. Method of Resolving Functions for Game Problems of Approach of Controlled Objects with Different Inertia. Cybern Syst Anal 57, 296–312 (2021). https://doi.org/10.1007/s10559-021-00355-9
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DOI: https://doi.org/10.1007/s10559-021-00355-9