Adaptive Control Methods Based on Fuzzy Basis Function Vectors

Abstract

There have been some attempts to design fuzzy controllers and explain their performance based on a variety of nonlinear control theories in recent years. Kiriakidis et al. [6] studied quadratic stability analysis methods in which the Takagi-Sugeno (T-S) model was analyzed as a linear system, subject to a class of nonlinear perturbations. However, it is sometimes difficult to determine a positive definite matrix that solves the Lyapunov equation. A robust controller for the T-S fuzzy model was presented in [5] and stability and robustness analysis results were also established. The main result of [5] is about the global stability of closed-loop system and the robustness with respect to unstructured uncertainty, which may include modeling errors and disturbances. The main limitation is that the unstructured uncertainty in the system must be relatively small compared to the inputs and outputs. Recently, model-reference adaptive control based on fuzzy basis function networks has been proposed as an alternative method to solve the above problems [7], [8], [11], but the emphasis has been placed on the single-input single-output (SISO) plants.