Controller Design for Tracking Control of an Under-Actuated Surface Ship

 Abstract—In this paper an output feedback controller for tracking control of surface ships based on Euler-Lagrange equations has been proposed. It has been assumed that a surface ship is moving in a horizontal plane and under-actuated in sway direction. The change of coordinate's method is applied to overcome the third order component that arises in the Lyapunov function derivatives due to Coriolis and centripetal forces term. The design of the controller is based on the backstepping control technique and Lyapunov stability theory. Firstly, the observer is derived using the change of coordinate method. Next, backstepping control technique is employed to derive the control law. Finally, a global asymptotic convergence is proven using Lyapunov stability theorems. Simulations are provided to demonstrate the performance of the designed controller and prove tracking error of the controller convergence.