Two-Step Stackelberg Approach for the Two Weak Pursuers and One Strong Evader Closed-Loop Game

• 成果类型: Article
• 署名作者: Zhang, Pengfei; Zhang, Yiqun
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3300365
• 发表日期: 2024
• 页码: 1309-1315
• 关键词: games; Missiles; trajectory; Nash equilibrium; Level set; differential games; State feedback; Closed-loop game; n-step Stackelberg; two weak pursuers one strong evader

摘要

In this article, we aim to study the analytical solution of two identical weak pursuers and one strong evader closed-loop game with a one-/two-step Stackelberg approach. Toward this, the basic idea is presented, that is, the solutions of the closed-loop game and an n-step Stackelberg game might be identical. In particular, we develop the optimal one-/two-step Stackelberg strategy for the evader, as well as the optimal state feedback/closed-loop strategy for the pursuers. On this basis, we proceed to prove that the underlying one-/two-step Stackelberg strategy and the state feedback/closed-loop strategy constitute a Nash equilibrium, indicating that the one-/two-step Stackelberg solution implies the closed-loop one. As an application, a simulation case of the homing missile interception in head-on scenarios considering the first-order link of the actuators is delivered and the results agree with the theoretical analysis.