Optimal Guidance Laws for a Hypersonic Multiplayer Pursuit-Evasion Game Based on a Differential Game Strategy

The guidance problem of a confrontation between an interceptor, a hypersonic vehicle, and an active defender is investigated in this paper. As a hypersonic multiplayer pursuit-evasion game, the optimal guidance scheme for each adversary in the engagement is proposed on the basis of linear-quadratic differential game strategy. In this setting, the angle of attack is designed as the output of guidance laws, in order to match up with the nonlinear dynamics of adversaries. Analytical expressions of the guidance laws are obtained by solving the Riccati differential equation derived by the closed-loop system. Furthermore, the satisfaction of the saddle-point condition of the proposed guidance laws is proven mathematically according to the minimax principle. Finally, nonlinear numerical examples based on 3-DOF dynamics of hypersonic vehicles are presented, to validate the analytical analysis in this study. By comparing different guidance schemes, the effectiveness of the proposed guidance strategies is demonstrated. Players in the engagement could improve their performance in confrontation by employing the proposed optimal guidance approaches with appropriate weight parameters.