Self-Adjusting Prescribed Performance H∞ Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles

A predefined-time $H_{\mathrm {\infty }}$ trajectory tracking control scheme based on self-adjusting prescribed performance functions and dynamic relative threshold event-triggered mechanism is proposed for a five-degree-of-freedom underactuated autonomous underwater vehicle (AUV) with unknown external disturbances and actuators saturated. First, a new self-adjusting prescribed performance function is designed to ensure that the tracking errors do not exceed the prescribed bounds and to solve the singularity problem of general prescribed performance control (PPC) due to actuator saturation. Second, a predefined-time $H_{\mathrm {\infty }}$ controller combined with a predefined-time dynamic surface control (DSC) method is proposed to guarantee that system signals converge to the neighborhood of zero in a predefined time without adjusting the control parameters and to improve system robustness to uncertain disturbances. Third, an improved dynamic relative threshold event-triggered method is designed to save the communication resources of an underactuated AUV system. Then, the Lyapunov stability proof indicates that all signals in the closed-loop system are predefined-time bounded, and the trajectory tracking errors can converge to the neighborhood of zero within the set desired time. Finally, the simulations not only demonstrate the performance of the proposed controller-controlled system but also verify the effectiveness of the proposed scheme.