Anti-Disturbance Lyapunov-Based Model Predictive Control for Trajectory Tracking of Dynamically Positioned Ships

Abstract

Trajectory tracking is a fundamental task of the dynamic positioning (DP) system. This paper studies the problem of trajectory tracking of DP ships constrained by control inputs under environmental disturbances. To solve this problem, we develop a novel anti-disturbance Lyapunov-based model predictive control (ADLMPC) scheme. Firstly, an extended state observer (ESO) is designed to estimate environmental disturbances. By combining the ESO with Lyapunov-based model predictive control, the ADLMPC scheme is devised. Secondly, a virtual controller which satisfies input constraints is developed by backstepping and the auxiliary dynamic system, and it is integrated into the Lyapunov contraction constraint in ADLMPC. We show that if the parameters for the virtual controller are appropriately determined, the recursive feasibility of ADLMPC is theoretically guaranteed, and the uniform ultimate boundedness of all signals in the trajectory tracking control system is achieved. Finally, the simulation results display the efficacy and superiorities of the ADLMPC scheme.