Adaptive control and synchronization of a modified Chua's circuit system.
type: Item
instance of: scholarly article
title: Adaptive control and synchronization of a modified Chua's circuit system.
zbMATH Open document ID: 1038.34041
DOI: 10.1016/S0096-3003(01)00318-6
author: M. T. Yassen
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The problem of chaos control is considered for the modified Chua circuit \[ x'=p(y-\frac{1}{7}(2x^3 -x )), \qquad y' = x-y+z, \qquad z=-qy. \] Conditions are given for the asymptotic stabilization of a fixed-point in the presence of the feedback control term \(-k(x-\bar x)\), which is introduced in the equation for the \(x\) variable. \(\bar x\) is the \(x\)-component of the fixed-point under consideration. This point is shown to be unstable in the absence of a controller. Then, the author derives conditions for the stabilization of the fixed-point in the presence of adaptive controller \(-g(x-\bar x)\), where \(g\) is updated according to the following algorithm \(g'=\gamma (x-\bar x)^2\). Finally, adaptive synchronization of two unidirectionally coupled identical Chua systems is considered.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 93C99
Mathematics Subject Classification ID: 94C05
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 1861330
zbMATH Keywords: Chua's system
zbMATH Keywords: synchronization
zbMATH Keywords: feedback control
zbMATH Keywords: adaptive control
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00318-6
OpenAlex ID: W1969594279
description: scientific article; zbMATH DE number 1861330