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

Shmuel Y. Hayoun, Tal Shima

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)837-857
Number of pages21
JournalJournal of Optimization Theory and Applications
Volume174
Issue number3
DOIs
StatePublished - 1 Sep 2017

Keywords

  • Differential games
  • Missile guidance
  • Pursuit–evasion

All Science Journal Classification (ASJC) codes

  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

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