Optimal event-triggered trajectory tracking control for under-actuated autonomous underwater vehicles with adaptive dynamic programming

In this study, the optimal event-triggered trajectory tracking control problem for under-actuated autonomous underwater vehicles (AUVs) is investigated. First, a virtual velocity control law is designed for the position and attitude tracking error system using the backstepping approach. Next, the velocity tracking error is derived. By integrating the position, attitude, and velocity-tracking errors, a comprehensive tracking error system is constructed, and a corresponding cost function for the system is defined. Then, the optimal event-triggered control law is designed using event-triggered adaptive dynamic programming, employing only a single critic network. The approximation error of the critic network and the stability of the tracking error system are analyzed using Lyapunov theory. Finally, simulation results demonstrate the effectiveness of the proposed optimal event-triggered control law.