Prescribed-Time Nash Equilibrium Seeking for Pursuit–Evasion Game Under Intermittent Control With Undirected/Directed Graph

This paper studies the prescribed-time Nash equilibrium (PTNE) seeking problem of the pursuit-evasion game (PEG) with second-order dynamics under the intermittent control (IC) strategy. To achieve Nash equilibrium (NE) in a user-defined prescribed-time, a time-varying high-gain function is incorporated into the design. The core challenge lies in applying IC to NE seeking, which complicates the convergence analysis and control design. To address this sticking point, we construct an auxiliary function and propose a Lyapunov function considering second-order dynamics to solve the PTNE seeking problem of PEG. Building upon the results for undirected graphs, we further extend our findings to directed graphs, demonstrating that the proposed method can reach the NE of PEG under IC in the prescribed-time. Moreover, we generalize the approach to non-cooperative games, indicating that the prescribed-time intermittent control framework can effectively solve PTNE seeking problem in such competitive scenarios. The numerical simulations validate the practicality of the proposed method.