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International Theoretical Science Journal
Volume 59 >>> № 5 SEPTEMBER — OCTOBER 2023
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UDC 517.977
A.A Chikrii1, I.S. Rappoport2


1 V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv, Ukraine

 g.chikrii@gmail.com

2 V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv, Ukraine

 jeffrappoport@gmail.com

DIRECT METHOD FOR SOLVING GAME PROBLEMS
OF APPROACH OF CONTROLLED OBJECTS

Abstract. The issue of approaching controlled objects in game problems of dynamics is analyzed. The sufficient conditions for the game termination in a finite guaranteed time are obtained in the case where the classical Pontryagin condition is not satisfied. Instead of the Pontryagin selection, which does not exist, some shift function is considered. With its help, special set-valued mapping is introduced, which generates a lower resolving function. The latter plays a decisive role in the formulation of the result and allows realizing a control construction based on theorems of the Filippov-Castaing kind. A modified scheme of Pontryagin’s first direct method is proposed, which ensures the successful completion of the conflict-controlled process in the class of counter-controls. To compare the guaranteed times, the upper resolving function is introduced and the corresponding scheme of the method is presented. The theoretical results are illustrated with a model example.

Keywords: quasilinear differential game, multi-valued mapping, measurable selector, stroboscopic strategy, resolving function.


full text

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