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Volume 58 >>> № 1 JANUARY — FEBRUARY 2022
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UDC 517.9
G.Ts. Chikrii1, A.О. Chikrii2


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

 g.chikrii@gmail.com

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

 g.chikrii@gmail.com

TIME DILATION PRINCIPLE IN DYNAMIC GAME PROBLEMS

Abstract. A method for solving the game problem of the trajectory of a quasi-linear non-stationary system approaching a cylindrical terminal set that varies with time is proposed. A case is considered where the Pontryagin condition (the condition of the first player’s advantage) is not satisfied. The time dilation function is introduced, which postpones the time of the game termination, and with its help 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 mappings and their selectors, strategies are generated, which guarantee the problem solution. The process of the trajectory approaching 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 function of time dilation. The scheme of the method is outlined and sufficient conditions for the game termination in a finite time are obtained.

Keywords: conflict-controlled process, set-valued mapping, modified Pontryagin’s condition, function of time dilation, measurable choice.


FULL TEXT

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