On Explicit Optimal Strategies for Two Pursuit-evasion Problems under Distance Condition in Frame of Differential Games

This paper studies two pursuit-evasion problems under distance conditions in frame of differential game. In particular, a zero-sum differential game with the objective of distance and a nonzero-sum differential game with objective of both distance and azimuth adjustment are presented. The two players in the games are described by a nonlinear dynamics model subject to both speed and acceleration constraints in the two-dimensional plane. Instead of numerical solutions, the explicit equilibrium solutions of these two differential games are given under the condition that the distance between two players is larger than a certain value. Finally, the simulation results of these two differential games under typical cases demonstrate the effectiveness of our method.