Design a robust adaptive trajectory tracking controller for underactuated ships

Tracking control is an issue of vital practical importance to the ship. In this paper, an adaptive robust tracking controller is developed for underactuated ships to cope with parametric and nonparametric uncertainties in the ships model. At first, an adaptive nonlinear control law is developed based on backstepping and Lyapunov synthesis. Then, the controller is modified to increase the robustness of the controller. The adaptive robust controller is developed such that it estimates the unknown constants of an upper bounding function of the uncertainty due to disturbances and unmodeled dynamics. It is also proved that the proposed algorithm could guarantee the closed-loop system to be globally asymptotically converge to zero. Numerical simulations are provided to illustrate the robustness and tracking performance of the controller.