~ y r ~ ELSEVIER Fuzzy Sets and Systems 101 (1999) 31 39 FU2Z'Y sets and systems Fuzzy adaptive control for a class of nonlinear systems 1 Shao Cheng Tong*, Qingguo Li, Tianyou Chai Research Center of Automation, Northeastern University, Shenyang, Liaoning 110006, People's Republic of China Received March 1996; receivedin revised form January 1997 Abstract An adaptive tracking control architecture is proposed for a class of continuous-time nonlinear dynamic systems, for which an explicit linear parameterization of the uncertainty in the dynamic is either unknown or impossible. The architecture employs fuzzy systems to approximate nonlinear functions, uses fuzzy sliding controller to compensate for the plant uncertainties. Global asymptotic stability is established in the Lyapunov sense, with the tracking errors converging to a neighborhood of zero. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Fuzzy control; Adaptive control; Nonlinear systems; Fuzzy sliding mode 1. Introduction Fuzzy logic control as one of the most useful approaches for utilizing expert knowledge, has been an active field of research the past decade [5]. Fuzzy logic control is generally applicable to plants that are mathematically poorly modeled and where experienced operators are available for providing qualitative guidance. Although it achieved much practical success, fuzzy control has not been viewed as a rigorous science, and it is due to a lack of formal synthesis techniques which guarantee the very basic requirements of global stability and acceptable performance [11]. In the stability analysis I-3, 4], it is commonly assumed that the mathematical model of the plants are known. This assumption contradicts the very basic premise of fuzzy control systems, which is to control processes that are poorly modeled from a mathematical view. The design of the globally stable fuzzy control system was an open problem until recently, till the efforts presented in [11]. Based on fuzzy systems which are capable of approximating, with arbitrary accuracy, any real continuous function on a compact set, a globally stable adaptive controller is firstly synthesized from a collect of fuzzy IF-THEN rules 1-11]. The fuzzy system, used to approximate an optimal controller, is adjusted by an adaptive law based on a Lyapunov function synthesis approach. However, since this kind of direct adaptive law is limited to the nonlinear system with control gain unity, it is difficult to extend it to *Corresponding author• 1 This paper is supported by the funds of the Natural Scienceof China and Liaoning. 0165-0114/99/$ - see front matter © 1999 ElsevierScienceB.V. All rights reserved. PII: S0165-01 14(97)00055-9