Dynamic Event‐Triggered Adaptive Dynamic Programming for Nonlinear Multiplayer Nonzero‐Sum Games With Time Delays

ABSTRACT In this study, we propose a dynamic event‐triggered (DET) optimal control method for nonlinear continuous‐time multiplayer nonzero‐sum (NZS) games with time delays using adaptive dynamic programming (ADP). To mitigate the adverse effects of time delays on the system state, a Lyapunov–Krasovskii function that incorporates historical state information is integrated into the cost function. To reduce computational burden and enhance control efficiency, a DET mechanism is introduced to formulate coupled Hamilton–Jacobi (HJ) equations. The ADP technique is utilized to derive event‐triggering optimal strategies by employing a single‐critic neural network architecture. The weights of the neural network are adjusted according to the rules obtained from a gradient descent procedure, and these adjustments are enhanced by employing experience replay (ER) methods to mitigate the stringent conditions of the persistent excitation. The Lyapunov method is applied to ensure the stability of the system state and the convergence of the neural network weights. Finally, the effectiveness of the proposed control method is confirmed via a simulation involving a three‐player differential game.