A Pursuit-evasion Game with Hybrid Pursuer Dynamics

A pursuit-evasion differential game with hybrid pursuer dynamics and bounded controls of the players is considered. The duration of the game is prescribed. The pursuer has two possible dynamics while the dynamics of the evader is fixed. The pursuer can change its dynamics once during the game. The evader knows both possible pursuer dynamics, but not the actual one. A novel approach to the solution of this problem, taking into account the realistic discontinuous behavior of the zero-effort miss distance, is proposed. This leads to an auxiliary game with impulsive dynamics, providing a solution with both mathematical and practical meaning. Illustrative examples are presented.