High-Gain Disturbance Observer-Based Backstepping Control or Dynamic Positioning Ships Using Contraction Theory

A contraction-based backstepping control with disturbance observer is proposed for dynamic positioning ship under environmental disturbances induced by waves, wind and ocean current. A high gain disturbance observer is built to compensate the environmental disturbances. Contraction theory is adopted to design backstepping controller and study the convergence of system trajectories with respect to another. At each step of recursive design, subsystem is made contracting, and its error state is global exponential convergent. Using coordinate transformation for contraction analysis, it is proved that ship's position and heading of dynamic positing ship can globally exponential convergence to desired value. Numerical simulations on a ship are given to demonstrate the proposed controller has strong robustness to different sea conditions.