The paper studies a novel method for real-time solutions of the two-player pursuit-evasion game. The min-max principle is adopted to confirm the Nash equilibrium of the game. As agents in the game can form an Internet of Things (IoT) system, the real-time control law of each agent is obtained by taking a linear-quadratic cost function in adaptive dynamic programming. By introducing the Lyapunov function, we consider the scenario when capture occurs. Since most actual systems are continuous, the policy iteration algorithm is used to make the real-time policy converge to the analytical solution of the Nash equilibrium. Furthermore, we employ the value function approximation method to calculate the neural network parameters without directly solving the Hamilton–Jacobi–Isaacs equation. Simulation results depict the method’s feasibility in different scenarios of the pursuit-evasion game.

This paper presents a new scheme for the online solution of a networked multi-agent pursuit–evasion game based on an online adaptive dynamic programming method. As a multi-agent in the game can form an Internet of Things (IoT) system, by incorporating the relative distance and the control energy as the performance index, the expression of the policies when the agents reach the Nash equilibrium is obtained and proved by the minmax principle. By constructing a Lyapunov function, the capture conditions of the game are obtained and discussed. In order to enable each agent to obtain the policy for reaching the Nash equilibrium in real time, the online adaptive dynamic programming method is used to solve the game problem. Furthermore, the parameters of the neural network are fitted by value function approximation, which avoids the difficulties of solving the Hamilton-Jacobi–Isaacs equation, and the numerical solution of the Nash equilibrium is obtained. Simulation results depict the feasibility of the proposed method for use on multi-agent pursuit–evasion games.