Adaptive Model-Based Control of Information-Poor Systems
11.1 Robust Adaptive Fuzzy Control
Nearly all robust adaptive fuzzy control schemes use a fuzzy model (a T-S or defuzzified Mamdani FLS) for function approximation and the control design assumes a non-fuzzy norm-bounded representation of the uncertainties. Some schemes can deal with unstructured uncertainties (Yang and Ren, 2003) but others are only able to deal with structured uncertainties (Zheng et al., 2004). Early schemes require the matching conditions to be satisfied or make simplifying assumptions (e.g. norm-bounded external disturbances, no uncertainties in the controller input matrix, full state feedback) or the T-S fuzzy model is used to approximate the non-linear uncertainties and robust stability of only the associated fuzzy model (not the real system) is guaranteed. More recently however, methods based on backstepping (Yang and Feng, 2004; Zhou et al., 2005; Liu et al., 2009; Tong and Li, 2009; Tong et al., 2009a, b; Tong et al., 2010) have been developed that have no such limitations although their application is restricted to a particular class of non-linear systems (strict feedback systems). A major concern is that all of the robust adaptive fuzzy control schemes are too computationally demanding or require too much prior knowledge to be of much use in practice.
The use of T-S fuzzy models allows robust, and robust adaptive, techniques (feedback linearization, Lyapunov stability analysis, LMI optimization, ...