Direct and Indirect Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems

During the last two decades, there has been significant progress in the area of adaptive control design of nonlinear systems (Krstic et al., 1995; Sastry & Isidori, 1989; Slotine & Li 1991; Spooner et al., 2002). Most of the developed adaptive control schemes assume that an accurate model of the system is available and the unknown parameters appear linearly with respect to known nonlinear functions. However, this assumption is not sufficient for many practical situations, because it is difficult to precisely describe a nonlinear system by known nonlinear functions and, therefore, the problem of controlling nonlinear systems with incomplete model knowledge remains a challenging task. As a model free design method, fuzzy control has found extensive applications for complex and ill-defined plants (Passino & Yurkovich, 1998; Wang, 1994). Basically, fuzzy control is a human knowledge-based design methodology which is driven accordingly by fuzzy membership functions and fuzzy rules. However, it is sometimes difficult to find the matched membership functions and fuzzy rules for some plants, or the need may arise to tune the controller parameters if the plant dynamics change. In the hope to overcome this problem, based on the universal approximation theorem and on-line learning ability of fuzzy systems, several stable adaptive fuzzy control schemes have been developed to incorporate the expert knowledge systematically (Spooner & Passino, 1996; Spooner et al., 2002; Su & Stepanenko, 1994; Wang, 1994). The stability analysis in such schemes is performed by using the Lyapunov approach. Conceptually, there are two distinct approaches that have been formulated in the design of a fuzzy adaptive control system: direct and indirect schemes. The direct scheme uses fuzzy systems to approximate unknown ideal controllers (Chang, 2000; Chang, 2001; Labiod & Boucherit, 2003; Li & Tong, 2003; Ordonez & Passino, 1999; Spooner & Passino 1996; Wang, 1994), while the indirect scheme uses fuzzy systems to estimate the plant dynamics and then synthesizes a control law based 14