Program iterations method and relaxation of a pursuit-evasion differential game. (English) Zbl 1426.91037

Chentsov, Alexander; Khachay, Daniel

Kondratenko, Yuriy P. (ed.) et al., Advanced control techniques in complex engineering systems: theory and applications. Dedicated to Professor Vsevolod M. Kuntsevich. Cham: Springer. Stud. Syst. Decis. Control 203, 129-161 (2019).

Summary: We consider special case of nonlinear zero-sum pursuit-evasion differential game. This game is defined by two closed sets – target set and one defining state constraints. We find an optimal non-anticipating strategy for player I (the pursuer). Namely, we construct his successful solvability set specified by limit function of the iterative procedure in space of positions. For positions outside of the successful solvability set, we consider relaxation of our game by determining the smallest size of a neighborhoods of two mentioned sets, for which the pursuer can solve his problem. Then, we construct his successful solvability set in terms of those neighborhoods.
For the entire collection see [Zbl 1416.93005].

MSC:

91A24

Positional games (pursuit and evasion, etc.)

Keywords:

pursuit-evasion differential game; nonlinear zero-sum pursuit-evasion game

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