Adaptive nonlinear controller design for course-tracking of ships based on dynamic surface control and backstepping

A new approach is proposed for the nonlinear course control problem of ships with parameter uncertainties and completely unknown control gain based on backstepping. Nussbaum function is used to deal with the unknown sign of uncertain control gain and avoid the possible controller singularity problem. Dynamic surface control is combined with backstepping technique to overcome the problem of “explosion of terms”. By means of Lyapunov function and the lemma of Nussbaum function, it is proved theoretically that the designed adaptive nonlinear controller can guarantee the global uniform boundedness of all signals of the resulting ship course tracking control system and make the course tracking error arbitrarily small by an appropriate choice of the design parameters. The simulations on the mathematical models of two ships are carried out. The simulation results demonstrate the effectiveness of the proposed control scheme.