A pursuit-evasion game with hybrid evader dynamics

A pursuit-evasion differential game of hybrid dynamics with bounded controls and a prescribed duration is considered. The evader has two possible dynamics, while the dynamics of the pursuer is fixed. The evader can change its dynamics once during the game. The pursuer knows the set of possible evader dynamics, but not the actual one. The solution of this game is obtained by introducing a new state variable - the zero-effort miss distance (ZEM) which leads to a reduced order auxiliary differential game. The hybrid dynamics of the evader creates a discontinuity of the ZEM, yielding an auxiliary game with impulsive dynamics. The game solution illustrates that by optimal use of the hybrid dynamics the evader can extend the escape zone of the game.