Adaptive Fuzzy Control of Nonlinear Systems Based on T-S fuzzy Hyperbolic Model

Abstract

In this paper, a design scheme is proposed for a class of nonlinear systems, which can be modeled by a T-S fuzzy hyperbolic model of stable fuzzy control. Firstly, the parallel distributed compensation (PDC) method is employed to design the fuzzy controller for the system without considering the error caused by fuzzy modeling, and the sufficient conditions of stability are given by using linear matrix inequalities (LMI). Then the error caused by fuzzy modeling is considered and the method of adaptive control is employed to reduce the effect of the modeling error. Simultaneously, the closed-loop system has better dynamic performance. According to Lyapunov stability theory, the resulting closed-loop system is proved to be asymptotically stable. Finally, an illustrative example is given to verify the effectiveness of the results proposed in this paper.