Robust Stabilization of an Autonomous Underwater Vehicle in Specified Finite-time with Disturbance Rejection

Abstract

This study investigates the robust finite-time stabilization of an autonomous underwater vehicle (AUV) with disturbance rejection, where the finite-time can be predetermined. The AUV is modeled as a rigid body moving within fluids, and the systems dynamics involves uncertain parameters arising from the hydrodynamic coupling between the AUV and fluid, along with unknown external disturbances. Direct compensation for the system’s dynamics, a common approach in controller design, is ineffective for AUVs with uncertainties. Therefore, a robust anti-disturbance control method without compensating for unknown dynamics is proposed. To begin, a time rescaling method is introduced to convert the specified finite-time stabilization of the system into an asymptotic stabilization for a time rescaling system. Then, an exponential PID controller is designed for the time rescaling system to handle unknown constant disturbances while a high-gain control strategy is used to suppress the uncertain dynamics, which also enhances the robustness against the uncertain dynamics. The specified finite-time stabilization control law is ultimately derived from the designed exponential control law of the time rescaling system. Numerical simulations are conducted to verify the results.