Indirect adaptive fuzzy control scheme based on observer for nonlinear systems: A novel SPR-filter approach

Abstract

In this paper, a novel fuzzy indirect adaptive controller based on observer for uncertain nonlinear perturbed systems is proposed. A tracking-error observer is introduced to resolve the problem of the unavailability of state variables. Adaptive fuzzy systems are employed to approximate the unknown smooth nonlinear functions. The control system is augmented by a low-pass filter designed to meet a SPR condition of a transfer function of the observation error dynamics. The SPR condition is used in the Lyapunov stability analysis to construct the adaptation laws using only available measurements (i.e. the output observation error and the output tracking error). The main contributions of this paper lie in the following: (a) The SPR-filter approach used here avoids the filtering of the fuzzy basis functions. (b) Unlike in the previous works, the stability analysis is rigorously proven by using a SPR-based Lypunov approach. Finally, numerical simulation results are presented to verify the feasibility and effectiveness of the proposed controller.