Linear Differential Game with Two Pursuers and One Evader
We study the situation involving two pursuers and one evader in the framework of DGL/1 (Linear Differential Game with bounded controls and first order dynamics for both players). The criterion of the one-on-one DGL/1 game is the terminal miss distance (perpendicular to the initial pursuer/evader Line Of Sight). The pursuer is minimizing this outcome meantime the evader is maximizing the same criterion. We introduce one pursuer more and analyze the changes. A new optimal evasion strategy is then derived to compromise the terminal miss distance with respect to each pursuer. This trade-off strategy and the resulting 2 ×1 No Escape Zone have been computed when the pursuers have the same time-to-go as well as with different times-to-go (equal and different durations of the individual games).
KeywordsOptimal Trajectory Differential Game Dynamic Game Capture Zone Game Parameter
Unable to display preview. Download preview PDF.
- 1.Basar, T., Olsder, G.J.: Dynamic Non Cooperative Game Theory. Academic, London and San Diego (1982)Google Scholar
- 2.Ben-Asher, J., Cliff, E.M., Kelly, H.J.: Optimal Evasion with a Path-Angle Constraint and Against Two Pursuers. Journal of Guidance, Control and Dynamics 11(4), (1988)Google Scholar
- 3.Bryson, A.E., Ho, Y.C.: Applied Optimal Control. Hemisphere Publishing Corporation, USA (1975)Google Scholar
- 5.Cardaliaguet, P., Quincampoix, M., Saint-Pierre, P.: Set-valued numerical analysis for optimal control and differential games. In: Bardi, M., Raghavan, T.E.S., Parthasarathy, T. (eds) Annals of the International Society of Dynamic Games, Vol. 4, pp. 177–247. Birkhäuser (1999)Google Scholar
- 6.Ge, J., Tang, L., Reimann, J., Vachtsevanos, G.: Suboptimal Approaches to Multiplayer Pursuit-Evasion Differential Games. AIAA 2006-6786 Guidance, Navigation, and Control Conference, 21–24 August 2006, Keystone, ColoradoGoogle Scholar
- 9.Jang, J.S., Tomlin, C.J.: Control Strategies in Multi-Player Pursuit and Evasion Game. AIAA 2005-6239 Guidance, Navigation, and Control Conference, 15–18 August 2005, San Francisco, CaliforniaGoogle Scholar
- 10.Mitchel, M., Bayen, A., Tomlin, C.J.: A Time Dependent Hamilton-Jacobi Formulation of Reachable Sets for Continuous Dynamic Games. IEEE Transactions on Automatic Control 50(7) (2005)Google Scholar
- 11.Rusnak, I.: The Lady, The Bandits, and The Bodyguards – A Two Team Dynamic Game. Proceedings of the 16th World IFAC Congress (2005)Google Scholar
- 12.Shinar, J., Shima, T.: Nonorthodox Guidance Law Development Approach for Intercepting Maneuvering Targets. Journal of Guidance, Control and Dynamics 25(4) (2002)Google Scholar
- 13.Stipanovic, D.M., Melikyan, A., Hovakimyan, N.: Some Sufficient Conditions for Multi-Player Pursuit-Evasion Games with Continuous and Discrete Observations. 12th ISDG Conference, Sophia-Antipolis, France (2006)Google Scholar
- 14.Stipanovic, D.M., Sriram, S., Tomlin, C.J.: Strategies for Agents in Multi-Player Pursuit-Evasion Games. 11th ISDG Conference, Tucson, Arizona (2004)Google Scholar