\(H_{\infty}\) variable universe adaptive fuzzy control for chaotic system
type: Item
instance of: scholarly article
title: \(H_{\infty}\) variable universe adaptive fuzzy control for chaotic system
zbMATH Open document ID: 1083.93013
author: Jiang Wang
author: Guo-Dong Qiao
author: Bin Deng
published in: Chaos, Solitons and Fractals
publication date: 2005-05-12T00:00:00Z
review text: The \(H_{\infty}\) control technique is combined with an adaptive control algorithm and the fuzzy approximate method in this study to achieve a desired attenuation of disturbance due to an approximation error and an external disturbance in a class of nonlinear system under a large uncertainty or unknown variation in plant parameter and structure. More precisely, the system under consideration is of the form: \[ \dot x= Ax+B(f(x)+g(x)u+d), \] \[ y=C^Tx \] where \((A,B,C)\) is the canonical minimal realization of a transfer function and \(f(x)\) and \(g(x)\) are unknown but bounded functions, \(u\in{\mathbb R}, y\in{\mathbb R}\) are control input and output of the system, respectively. \(d\) denotes an external bounded disturbance which is unknown. A new adaptive fuzzy control algorithm is proposed in the study, so that not only the stability of the adaptive fuzzy control system is guaranteed but also the influence of matching error and external disturbance on the tracking error is attenuated to an arbitrarly desired level via an \(H_{\infty}\) tracking design technique. The proposed design method attempts to combine the attenuation technique, a fuzzy logical approximation method and an adaptive algorithm for the robust tracking control design. The simulation results of the Duffing chaotic system are given to confirm that the control algorithm is feasible for practical application.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93D09
zbMATH DE Number: 2167920
zbMATH Keywords: \(H_{\infty}\)-control
zbMATH Keywords: fuzzy logical approximation method
zbMATH Keywords: adaptive algorithm
zbMATH Keywords: Duffing chaotic system
zbMATH Keywords: adaptive fuzzy control
zbMATH Keywords: matching error
zbMATH Keywords: robust tracking
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.09.056
OpenAlex ID: W2023295713
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DOI: 10.1016/J.CHAOS.2004.09.056
description: scientific article; zbMATH DE number 2167920