Robust adaptive fuzzy control and its application to ship roll stabilization

Abstract

A robust adaptive fuzzy control (RAFC) scheme, which can be used to control a class of uncertain nonlinear systems in which the robust relative degree is equal to the system's degree, is proposed for the problem of ship roll stabilization. The uncertain system can be transformed into the controllability canonical form by the global diffeomorphism. Using the universal approximation capability of the fuzzy system, we construct a fuzzy system as the upper bound of uncertainties in the nonlinear uncertain system. Based on Lyapunov direct method, we prove that the RAFC scheme proposed in this paper can guarantee the closed-loop system to converge exponentially with a prescribed degree towards a residual ball around the equilibrium. Since only one parameter needs to be adapted on-line, the computing load of the proposed RAFC algorithm can be significantly reduced. We then demonstrate how to design a RAFC for ship roll stabilization. The feasibility of the proposed method is verified through a container ship simulation.