A pursuit-evasion game with hybrid pursuer dynamics

A pursuit-evasion differential game of hybrid dynamics with bounded controls and a prescribed duration is considered. The pursuer has a finite set of possible dynamics while the dynamics of the evader is fixed. The pursuer can change its dynamics a finite number of times during the game. The evader knows the set of possible pursuer dynamics, but not the actual one. Two approaches to the solution of this problem are proposed. In both approaches, a new state variable - the zero-effort miss distance (ZEM) - is introduced, leading to a reduced order auxiliary differential game. The first approach is based on the theoretical assumption of ZEM continuity, yielding a game solution of mathematical importance. The second approach takes into account the realistic discontinuous behavior of the ZEM. This leads to an auxiliary game with impulsive dynamics, providing a solution with both mathematical and practical meaning. Illustrative examples are presented.