Robust fixed-time trajectory tracking control of the dynamic positioning ship with actuator saturation

Abstract

This paper addresses the fixed-time trajectory tracking control and setpoint regulation problems for dynamic positioning (DP) ships subject to unknown time-varying disturbances, system uncertainties, and actuator saturation. To meet the resistance of the low-frequency disturbances and system uncertainties, a continuous fixed-time disturbance observer (FTDO) based on integral sliding mode and fixed-time control is constructed. A nonlinear auxiliary dynamic system is introduced to mitigate the inconsistency between command forces and actual control forces, in which the feedback of the bias Δτ guarantees the input constraints for the design of the proposed controller. The explosion-of-complexity problem inherent in traditional backstepping is addressed based on a nonlinear first-order filter. Furthermore, a robust fixed-time control law with constraints is developed to track the predefined trajectory and the desired setpoint. Theoretical analyses demonstrate the fixed-time stability of the closed-loop system via Lyapunov analysis. Numerical simulation results illustrate the effectiveness and robustness of the proposed control approach.