Linear Quadratic Pursuit–Evasion Games on Time Scales

In this paper, we unify and extend the linear quadratic pursuit-evasion games to dynamic equations on time scales. Here we seek to a mixed strategy for a pair of linear players. We show that when the final state is fixed, these (open–loop) strategies can be written in terms of a zero-input state difference. On the other hand, when the final states are free, we find closed-loop strategies in terms of an extended state.