Adaptive and robust controller design for uncertain nonlinear systems via fuzzy modeling approach

The issue for designing robust adaptive stabilizing controllers for nonlinear systems in Takagi-Sugeno fuzzy model with both parameter uncertainties and external disturbances is studied in this paper. It is assumed that the parameter uncertainties are norm-bounded and may be of some structure properties and that the external disturbances satisfy matching conditions and, besides, are also norm-bounded, but the bounds of the external disturbances are not necessarily known. Two adaptive controllers are developed based on linear matrix inequality technique and it is shown that the controllers can guarantee the state variables of the closed loop system to converge, globally, uniformly and exponentially, to a ball in the state space with any pre-specified convergence rate. Furthermore, the radius of the ball can also be designed to be as small as desired by tuning the controller parameters. The effectiveness of our approach is verified by its application in the control of a continuous stirred tank reactor.

I. Introduction

Since the 1980s, fuzzy technique has been widely adopted to model complex nonlinear plants. Theoretical justification of fuzzy model as a universal approximator has been given in the last decade [9], [12], [23]. A very important class of fuzzy systems, which has gained much popularity recently because of its success in functional approximation, is the so-called Takagi-Sugeno (T-S) fuzzy system [15]. The basic idea in this kind of fuzzy systems is first to decompose the model of a nonlinear system or other kinds of complex systems into linear systems in accordance with the cases for which linear models are suitable to describe and then to aggregate (fuzzy blend) each individual model (linear model) into a single nonlinear model in terms of their membership function. As is well known, the key problem in this approach is to what degree the nonlinear system can be approximated by a convex (fuzzy) blending of several linear systems. Now T-S model has found wide applications in the control of complex systems, for example, in the control of robot manipulators [10] and complex processes [6].