Trajectory tracking for underactuated surface vessels with time delays and unknown control directions

Abstract

The problem of trajectory tracking control for underactuated surface vessels with time-delays, model uncertainty and unknown control directions has been considered in this paper. Firstly, an integration time delayed sliding mode controller is proposed, which decomposes the underactuated non-linear system into a cascading system consisting of a kinematics subsystem and a dynamics subsystem. Secondly, an adaptive backstepping control method for the heading angle system is proposed, which can drive the heading angle error into a preset interval. Then the Bouc-wen model is used to describe the hysteresis of the system, Nussbaum gain function is adopted to deal with unknown control directions, and the adaptive controller is designed by combining error transformation with Lyapunov function. Furthermore, a suitable Lyapunov-Krasovsky function is selected to analyse and prove the global stability of the closed-loop system. Finally, some numerical simulations show the effectiveness of the presented control methods.