Nash Equilibrium Strategies for Multicluster Pursuit–Evasion Game With Disturbances: A Prescribed-Time Convergence Approach

This article investigates the problem of prescribed-time Nash equilibrium (NE) seeking for a multicluster pursuit-evasion game (PEG) subject to external disturbances. To mitigate the impact of disturbances and reach the NE within a user-defined prescribed time, a prescribed-time disturbance observer (PTDO) is devised to estimate and compensate for them. Based on this observation, a novel control algorithm is developed, which facilitates collaboration among multiple pursuers to capture multiple evaders within the prescribed time. It is theoretically demonstrated that the designed algorithm ensures prescribed-time convergence to the NE of the multicluster PEG with disturbances. Finally, numerical simulations are conducted to verify the effectiveness of the algorithm under different initial conditions, further demonstrating the flexibility of the user-specified convergence time.