Robust Adaptive Control for Dynamic Positioning of Ships

In this paper, a robust adaptive control scheme with the global asymptotic stability with respect to positioning errors is proposed for dynamic positioning (DP) of ships in the presence of time-varying unknown bounded environmental disturbances. The unknown environmental disturbances are expressed as the outputs of a linear exosystem with unknown parameters and all eigenvalues of system matrix lying on the imaginary axis. On the basis of this exosystem, the disturbances are further represented as the outputs of a linear model of canonical form with unknown disturbances being inputs by a multivariate linear regression model whose regressor is the state vector of the linear model and whose regression parameters depend on unknown parameters of the linear exosystem. This representation allows us to construct an observer to estimate the unavailable state vector (regressor) in the linear model and hence convert the disturbance compensation control for the DP of ships to an adaptive control problem. Then, a robust adaptive control law for the DP of ships is designed incorporating the constructed observer and the projection algorithm into the vectorial backstepping method. The global asymptotic stability with respect to positioning errors of the DP closed-loop control system is proved applying Lyapunov stability theory and Barbalat's lemma. Finally, simulation results on a supply ship Northern Clipper in two different disturbance cases and simulation comparisons with an existing DP adaptive robust control scheme demonstrate more effectiveness and less conservativeness of our proposed control scheme.