Solution of a Linear Pursuit-Evasion Game with Variable Structure and Uncertain Dynamics
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.
KeywordsVariable Structure Positive Root Optimal Trajectory Differential Game Lateral Acceleration
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- Amato, F., Mattei, M. and Pironti, A. (1998), Robust Strategies for Nash Linear Quadratic Games Under Uncertain Dynamics, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, December 1998, pp. 1869–1870.Google Scholar
- Grigorenko, N.L. (1985), Differential Games of Pursuit by Several Objects with a Variable Structure, Some problems in modern mathematics and their applications to problems in mathematical physics, Moscow Fiz.-Tekhn.Inst., Moscow, pp. 54–61 (in Russian).Google Scholar
- Grigorenko, N.L. (1991), Game-Theoretic Problems of Control withVariable Structure, Moscow University Computational Mathematics and Cybernetics, no. 4, pp. 4–14.Google Scholar
- Grigorenko, N.L. (1998), Dynamic Game of Many Players with Variable Structure, Proceedings of International Conference Dedicated to the 90th Anniversary of L.S. Pontryagin, Moscow, August 31–September 6, 1998, pp. 74–77.Google Scholar
- Shinar, J. (1981), Solution Technics for Realistic Pursuit-Evasion Games, Advances in Control and Dynamic Systems, Edited by C.T. Leondes, Academic Press, New York, NY, Vol. 17, pp. 63–124.Google Scholar
- Shima, T. and Shinar, J. (2002), Time-Varying Linear Pursuit-Evasion Game Models with Bounded Controls, Journal of Guidance, Control and Dynamics, Vol. 25, pp. 425–432.Google Scholar
- Bryson, A.E. and Ho, Y.C. (1975), Applied Optimal Control, Hemisphere, New York, NY.Google Scholar