NONLINEAR MODEL FOLLOWING CONTROL In Chapter 9, the model following control for chaotic systems based on the Takagi-Sugeno fuzzy models with the common B matrix is discussed. In this chapter, we present a more general framework w1, 2x to address the nonlinear model following control problem for the fuzzy descriptor systems introduced in Chapter 10. Specifically, these extended results deal with nonlinear model following control for fuzzy descriptor systems with different B matrices. | Fuzzy Control Systems Design and Analysis A Linear Matrix Inequality Approach Kazuo Tanaka Hua O. Wang Copyright 2001 John Wiley Sons Inc. CHAPTER 11 ISBNs 0-471-32324-1 Hardback 0-471-22459-6 Electronic NONLINEAR MODEL FOLLOWING CONTROL In Chapter 9 the model following control for chaotic systems based on the Takagi-Sugeno fuzzy models with the common B matrix is discussed. In this chapter we present a more general framework 1 2 to address the nonlinear model following control problem for the fuzzy descriptor systems introduced in Chapter 10. Specifically these extended results deal with nonlinear model following control for fuzzy descriptor systems with different B matrices. A new parallel distributed compensation the so-called twin parallel distributed compensation TPDC is proposed to solve the nonlinear model following control. The TPDC fuzzy controller mirrors the structures of the fuzzy descriptor systems which represent a nonlinear plant and a nonlinear reference model. A design procedure based on the TPDC is presented. As in the usual spirit of this book all design conditions are rendered in terms of LMIs. The proposed method represents a unified approach to nonlinear model following control. It contains the regulation and servo control problems as special cases. Several design examples are included to show the utility of the nonlinear model following control. INTRODUCTION This chapter presents a unified approach to nonlinear model following control that is much more difficult than the regulation problem. In this chapter the nonlinear model following control means nonlinear control to reduce the error between the states of a nonlinear system and those of a nonlinear reference model that is limt x t - xR t 0 where x t and 217 218 NONLINEAR MODEL FOLLOWING CONTROL xR t denote the states of the nonlinear system and those of the nonlinear reference model respectively. The important feature is that xR t is not necessarily zero or a constant. The nonlinear .
