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Time Dilation Principle in Dynamic Game Problems

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors propose a method for solving the game problem where the trajectory of a quasi-linear non-stationary system approaches a cylindrical terminal set varying with time. The case is considered where Pontryagin’s condition (the condition of the first player’s advantage) is not satisfied. A time dilation function is introduced, which postpones the time of game termination and is used to introduce a modified Pontryagin’s condition, which allows making a measurable choice of control. The basic method is the method of resolving functions. Using the technique of set-valued map**s and their selectors, the strategies are generated, which guarantee the problem solution. The process of convergence of the trajectory and the terminal set consists of two sections: active and passive, where the control of the first player is selected using the control of the second player with a certain time delay, which depends on the time dilation function. The scheme of the method is outlined and sufficient conditions for the game termination in a finite time are obtained.

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Authors and Affiliations

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

    G. Ts. Chikrii & A. O. Chikrii

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  1. G. Ts. Chikrii
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  2. A. O. Chikrii
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Correspondence to G. Ts. Chikrii or A. O. Chikrii.

Additional information

The study was partially supported by the National Foundation of Ukraine, Grant # 2020.02/0121.

Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2022, pp. 45–54.

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Chikrii, G.T., Chikrii, A.O. Time Dilation Principle in Dynamic Game Problems. Cybern Syst Anal 58, 36–44 (2022). https://doi.org/10.1007/s10559-022-00433-6

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