Adaptive Finite-Time Controller Design for T–S Fuzzy Systems

This paper studies the adaptive finite-time stabilization problem for a class of nonlinear systems described by Takagi-Sugeno (T-S) fuzzy dynamic models with parametric uncertainties. A novel adaptive state feedback control scheme for the T-S fuzzy systems is proposed, and the scheme is developed based on finite-time Lyapunov theorem and adaptive backstepping-like method. Augmented dynamics are introduced in the design of finite-time stabilization controllers to construct suitable finite-time Lyapunov functions. It is shown that finite-time convergence of the closed-loop adaptive control system can be achieved, and the potential controller singularity problem caused by the augmented dynamics can be avoided. In addition, constructive procedures to obtain such an adaptive finite-time controller are given. Convergence time as a transient performance specification is also taken into account, and a finite upper bound on the convergence time is estimated. Finally, two numerical examples are provided to illustrate the effectiveness and practicality of the proposed adaptive control approach.

I. Introduction

Over the past few decades, a great number of control methods based on Takagi–Sugeno (T–S) fuzzy models have been widely adopted to handle complex nonlinear systems (see [1]–[8]). In these control methods, nonlinear systems are represented by a set of local linear models and fuzzy controllers are then designed. Typically, global fuzzy controllers can be synthesized from corresponding local fuzzy controllers. Moreover, it has been proved that T–S fuzzy models have universal function approximation capability (see [9], [10] for details). Therefore, T–S fuzzy models provide systematic and effective approaches to deal with complex nonlinear systems in view of their universal function approximation capability and powerful conventional control theory.