Abstract
A class of pursuit-evasion differential games with bounded controls and a prescribed duration is considered. Two finite sets of possible dynamics of the pursuer and evader, known for both players, are given. The evader chooses his dynamics once before the game starts. This choice is unavailable for the pursuer, which causes a dynamics uncertainty. The pursuer can change his dynamics a finite number of times during the game, yielding a variable structure dynamics. The solution of this game is derived including optimal strategies of the players. The existence of a saddle point is shown. The game value and the shape of the maximal capture zone are obtained. Illustrative examples are presented.
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Shinar, J., Glizer, V.Y., Turetsky, V. (2007). Solution of a Linear Pursuit-Evasion Game with Variable Structure and Uncertain Dynamics. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_10
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DOI: https://doi.org/10.1007/978-0-8176-4553-3_10
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