Identification and adaptive control of a class of nonlinear systems with fuzzy system models

Identification and control of general nonlinear systems is a difficult but important problem. Various nonlinear model structures such as polynomials, Volterra series, splines, wavelets, neural networks and fuzzy systems have been used to represent the nonlinear mechanisms in the nonlinear systems in the literature. Fuzzy system models, compared with other schemes, have the advantages of incorporating human knowledge, being easy-to-understand and easy-to-implement, and fast convergence due to the convenience in parameter initialization.; In the existing fuzzy system approaches to identification and control of non-linear systems, fuzzy system models are viewed as black-boxes and the special features inside are not considered; this results in conservative identification and control schemes. The purpose of this research is to explore some particular internal properties of the fuzzy system models and develop more efficient and powerful methods for the identification and control of a broader class of nonlinear systems. In particular, we studied the following four problems with some fundamental results: (1) How to generate input signals for ensuring parameter convergence of the fuzzy system model. We established the persistent excitation conditions under which the parameters in the fuzzy system model converge to their true values, and presented several algorithms to generate input signals with the persistent excitation property for nonlinear moving average and second-order auto-regressive moving average systems. (2) How to design adaptive controllers based on fuzzy system models for a class of nonlinear systems that are not necessarily affine in the manipulated input. We developed a one-step-ahead adaptive control scheme by taking advantage of some specific features of the fuzzy system models. We also tested this control scheme on a set of data from a real steeling-heating furnace. (3) How to design long-range adaptive predictive controllers based on fuzzy system models for a class of nonlinear systems that are not necessarily affine in the manipulated input. We developed a multi-step-ahead adaptive fuzzy control scheme and proposed an algorithm to find a suboptimal solution to the nonlinear optimization problem involved in determining the control action. (4) How to identify fuzzy system models using the minimum number of fuzzy rules from the input-output data of an unknown system. We introduced the idea of nonuniformly partitioning the domain of interest according to the data and the error tolerance, and proposed a tunnel algorithm to construct fuzzy system models using the minimum number of rules from a limited number of input-output data.