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A Two-on-One Linear Pursuit–Evasion Game with Bounded Controls

Author

Listed:
  • Shmuel Y. Hayoun

    (Technion-Israel Institute of Technology)

  • Tal Shima

    (Technion-Israel Institute of Technology)

Abstract

A linearized engagement with two pursuers versus a single evader is considered, in which the adversaries’ controls are bounded and have first-order dynamics and the pursuers’ intercept times are equal. Wishing to formulate the engagement as a zero-sum differential game, a suitable cost function is proposed and validated, and the resulting optimization problem and its solution are presented. Construction and analysis of the game space is shown, and the players’ closed-form optimal controls are derived for the case of two “strong” pursuers. The results are compared to those of a 1-on-1 engagement with a “strong” pursuer, and it is shown that the addition of a second pursuer enlarges the capture zone and introduces a new singular zone to the game space, in which the pursuers can guarantee equal misses, regardless of the evader’s actions. Additionally, it is concluded that in the regular zones the closed-form optimal pursuit strategies are unchanged compared to two 1-on-1 engagements, whereas the optimal evasion strategy is more complex. Several simulations are performed, illustrating the adversaries’ behavior in different regions of the game space.

Suggested Citation

  • Shmuel Y. Hayoun & Tal Shima, 2017. "A Two-on-One Linear Pursuit–Evasion Game with Bounded Controls," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 837-857, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1142-z
    DOI: 10.1007/s10957-017-1142-z
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    References listed on IDEAS

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    1. Sergey Ganebny & Sergey Kumkov & Stéphane Ménec & Valerii Patsko, 2012. "Model Problem in a Line with Two Pursuers and One Evader," Dynamic Games and Applications, Springer, vol. 2(2), pages 228-257, June.
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