Command filtered backstepping control for dynamic positioning ships

Taking the dynamics of the thruster increases the order of the ship motion model and makes it difficult for researchers to obtain the derivative of the virtual control signal, and meanwhile the derivative complicates the control law for its complexity. A filter, which can approximate the virtual control signal and its derivative, is introduced to the backstepping controller design to avoid the derivation process and simplify the controller design. While the model parameters are unknown, an adaptive fuzzy logic system is utilized to estimate the unknown nonlinear functions which are necessary for the control law. It can compensate the system uncertainties and unmodeled dynamics due to its robustness. The closed-loop system is proved to be uniformly ultimate bounded by Lyapunov stable theory and simulation results verify the stability and effectiveness of the proposed controller.