13 - Techniques and Applications of Fuzzy Theory Via H∞ Control Techniques for Tracking Algorithms for Uncertain Nonlinear Systems

Abstract

Fuzzy control has recently found extensive application for a wide variety of industrial systems and consumer products and has attracted the attention of many control researchers because of its model free approach. This chapter describes the Fuzzy logic systems, H∞ tracking performance designs in both indirect and direct adaptive fuzzy systems, and provides two simulation examples to illustrate the performance of the proposed methods. The H∞ control technique is combined with an adaptive control algorithm and a fuzzy approximation method in this study to achieve the desired attenuation of disturbance because of the approximation error and external noise in a class of nonlinear system under a large uncertainty or unknown variation in plant parameter and structure. Both indirect and direct adaptive fuzzy control algorithms have been employed to treat this H∞ tracking design problem. The solvability conditions and the corresponding adaptive fuzzy control laws are both derived. The results indicate that an arbitrarily small attenuation level can be achieved, if the magnitude of weighting factor r can be chosen to be as small as possible. Simulation results confirm that the H∞ tracking performance can be achieved via the proposed adaptive fuzzy control algorithms. However, further works are still required to apply the proposed adaptive fuzzy H∞ tracking algorithm to the more general nonlinear systems.