Backstepping Control Using Barrier Lyapunov Function for Dynamic Positioning Control System with Passive Observer

Abstract

This paper presents a backstepping controller using barrier Lyapunov function (BLF) for dynamic positioning (DP) system. For safety reasons, the position and heading of DP ship are to be maintained in certain range. Thus, in this paper, a control law based on BLF and backstepping technique is proposed to limit the position and heading. The closed-loop system is proved stable in the sense of Lyapunov stability theories. In addition, since the velocities of ship are not measurable and the wave frequency (WF) motion is unavailable, a passive observer is adopted to estimate the velocities and the effect of WF motion. The simulation results show that the proposed controller can limit the position and heading of the vessel in a predefined range and verify the performance of the proposed controller and the passive observer.