Linear Differential Game with Two Pursuers and One Evader

  • Stéphane Le Ménec
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)


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).


Optimal Trajectory Differential Game Dynamic Game Capture Zone Game Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basar, T., Olsder, G.J.: Dynamic Non Cooperative Game Theory. Academic, London and San Diego (1982)Google Scholar
  2. 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. 3.
    Bryson, A.E., Ho, Y.C.: Applied Optimal Control. Hemisphere Publishing Corporation, USA (1975)Google Scholar
  4. 4.
    Cardaliaguet, P.: A differential game with two players and one target. SIAM J. Control Optimization 34(4), 1441–1460 (1996)MATHCrossRefMathSciNetGoogle Scholar
  5. 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. 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
  7. 7.
    Hagedorn, P., Breakwell, J.V.: A Differential Game with Two Pursuers and One Evader. Journal of Optimization Theory and Application 18(2), 15–29 (1976)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Isaacs, R.: Differential Games. Wiley, New York (1967)MATHGoogle Scholar
  9. 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. 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. 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. 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. 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. 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

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.EADS/MBDA FranceLe Plessis-Robinson CedexFrance

Personalised recommendations