Adaptive control of multivariable fuzzy systems with unknown parameters

This paper presents a method to control multivariable nonlinear systems with unknown parameters using an adaptive technique. First, a fuzzy plant model with unknown membership functions is obtained to describe the unknown nonlinear plant. Then, an adaptive fuzzy controller is designed to close the feedback loop. An adaptive law is derived based on the Lyapunov's stability theory to update the grades of membership such that the membership functions of the fuzzy plant model and the fuzzy controller are made the same with guaranteed close-loop system stability. An application example on stabilizing a nonlinear mass-spring-damper system with unknown parameters is given to illustrate the merits of the proposed adaptive fuzzy controller.