A Method for Solving the Optimal Strategy of a Class of Pursuit-evasion Problem

Based on the zero-sum game model, this paper is concerned with the optimal strategy for the pursuit-evasion problem under the worst conditions of players. Firstly, aiming at the situation of obstacle-free and complete information, the model of the pursuit-evasion problem including motion differential equation, strategy set and objective function under the game framework is established. Secondly, a strategy evaluation method is established by using the minimum maximum principle. As a consequence, the optimal strategy for the pursuit-evasion problem in which one pursuer pursues many evaders is obtained. The method is also valid in a slightly simplified case where many pursuers pursue many evaders. Finally, simulation examples are illustrated to verify the effectiveness of the proposed method.