Global tracking controller design for underactuated ships

This paper studies the global tracking problem for an underactuated ship with only two propellers. Under sufficient conditions of persistent excitation, two constructive solutions are proposed by application of Lyapunov's direct method. Both solutions exploit the inherent cascade-interconnected structure of the ship dynamics. The first solution yields tracking controllers with good transient performance and acceptable asymptotic convergence. The second solution, as the recent cascade approach of [13], achieves global exponential tracking, but at the expense of transient performance. Simulation results validate the proposed tracking methodology.