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Direct Method for Solving Game Problems of Approach of Controlled Objects

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors analyze the problem of approach of controlled objects in dynamic game problems. The sufficient conditions for the game termination in a finite guaranteed time are obtained when the classical Pontryagin condition is not satisfied. Instead of the Pontryagin selection, which does not exist, some shift function is considered. With its help, a special set-valued map** is introduced, which generates a lower resolving function. The latter plays a key role in formulating the result and allows constructing the control based on theorems of the Filippov–Castaing kind. A modified scheme of Pontryagin’s first direct method is proposed, which ensures a 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 provided. The theoretical results are illustrated with a model example.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. A. Chikrii & I. S. Rappoport

Authors
  1. A. A. Chikrii
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  2. I. S. Rappoport
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Correspondence to A. A. Chikrii.

Additional information

The study was partially supported by the National Research Foundation of Ukraine, Grant No. 2020.02/0121.

Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2023, pp. 144–153.

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Chikrii, A.A., Rappoport, I.S. Direct Method for Solving Game Problems of Approach of Controlled Objects. Cybern Syst Anal 59, 812–820 (2023). https://doi.org/10.1007/s10559-023-00617-8

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