Adaptive H8 Fuzzy Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Introduction

The fuzzy controllers provide a systematic and efficient framework to incorporate linguistic fuzzy information from human expert (Wang 1993, 1994; Wang & Mendal, 1992; Buckley, 1992). Furthermore, fuzzy control is a model free approach, i.e., it does not require a mathematical model of the system under control. Control engineers are now facing more and more complex systems, and the mathematical models of these systems are more and more difficult to obtain. Thus, in control engineering, model free approaches become more important. There are some model free approaches in conventional control, such as nonlinear adaptive control and PID control. Fuzzy control gives another model free approach (Hwang & Lin, 1992; Wang, Liu, et al., 2002; Wang, Lin, et al., 2002; Lin, Wang, et al., 2004; Chen, Lee, et al., 1996; Leu, Lee, et al., 1999).

In the last two decades, optimal control theory has been well developed and found extensive application to efficiently treat the robust stabilization and disturbance rejection problems (Lin, Wang, et al., 2004; Wang, Liu, et al., 2002; Wang, Lin, et al., 2002). In the conventional optimal control, the plant model must be known beforehand. In this study, the optimal control design will be extended toward the nonlinear systems with unknown or uncertain models via fuzzy technique. However, several adaptive fuzzy sliding mode control systems have been developed for continuous-time systems (Chang, Park, et al., 2002; Lee, Kim, et al., 2001; Yu, Man, et al., 1998; Utkin, 1977), which cannot be expanded into discrete-time systems directly. Only a few of them are devoted to discrete-time systems (Shi, 2007; Sarpturk, Istefanopulos, et al., 1987; Han, Su, et al., 2000; Shaocheng & Tianyou, 1998; Fuchun, Zengqi, et al., 1998; Guo, Shi, et al., 2009; Spooner, Ordonez, et al., 1997a, 1997b).