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

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.