NDLI: Cheap Control in a Non-Scalarizable Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis

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Cheap Control in a Non-Scalarizable Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis

Content Provider	MDPI
Author	Turetsky, Vladimir Glizer, Valery Y.
Copyright Year	2022
Description	In this work, a finite-horizon zero-sum linear-quadratic differential game, modeling a pursuit-evasion problem, was considered. In the game’s cost function, the cost of the control of the minimizing player (the minimizer/the pursuer) was much smaller than the cost of the control of the maximizing player (the maximizer/the evader) and the cost of the state variable. This smallness was expressed by a positive small multiplier (a small parameter) of the square of the $L2-norm of the minimizer’s control in the cost function. Parameter-free sufficient conditions for the existence of the game’s solution (the players’ optimal state-feedback controls and the game value), valid for all sufficiently small values of the parameter, were presented. The boundedness (with respect to the small parameter) of the time realizations of the optimal state-feedback controls along the corresponding game’s trajectory was established. The best achievable game value from the minimizer’s viewpoint was derived. A relation between solutions of the original cheap control game and the game that was obtained from the original one by replacing the small minimizer’s control cost with zero, was established. An illustrative real-life example is presented.$
Starting Page	214
e-ISSN	20751680
DOI	10.3390/axioms11050214
Journal	Axioms
Issue Number	5
Volume Number	11
Language	English
Publisher	MDPI
Publisher Date	2022-05-05
Access Restriction	Open
Subject Keyword	Axioms Industrial Engineering Linear-quadratic Differential Game Cheap Control Singular (degenerate) Differential Game Pursuit-evasion Game
Content Type	Text
Resource Type	Article

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