Approximate Optimal Strategy for Multiagent System Pursuit–Evasion Game

In this article, we propose an approximate optimal control strategy for a class of nonlinear multiagent system pursuit–evasion games. Herein, multiple pursuers aim to capture multiple evaders trying to evade capture. Under the competitive framework, agents not only pursue their individual goals but also consider coordination with their teammates to achieve collective objectives. However, maintaining cohesion with teammates in existing distributed control methods has always been a challenge. To enhance team coordination, we employ a graph-theoretic approach to represent the relationships between agents. Based on this, we design a dynamic target graph algorithm to enhance the coordination among pursuers. The approximate optimal strategies for each agent are solved by utilizing the Hamilton–Jacobi–Isaacs equations of the system. As solving these equations becomes computationally intensive in multiagent scenarios, we propose a value-based single network adaptive critic network architecture. In addition, we consider scenarios where the numbers of agents on both sides are inconsistent and address the phenomenon of input saturation. Moreover, we provide sufficient conditions to prove the system's stability. Finally, simulations conducted in two representative scenarios, multiple-pursuer-one-evader and multiple-pursuer-multiple-evader, demonstrate the effectiveness of our proposed algorithm.