Adaptive variable structure control for chaos suppression of unified chaotic systems
type: Item
instance of: scholarly article
title: Adaptive variable structure control for chaos suppression of unified chaotic systems
zbMATH Open document ID: 1167.65071
author: Yung-Ching Hung
author: Teh-Lu Liao
author: Jun-Juh Yan
published in: Applied Mathematics and Computation
publication date: 2009-03-30T00:00:00Z
review text: The paper investigates the chaos suppression problem for the chaotic system \[ \begin{cases} x'= (25\alpha + 10)(y-x), \\ y'=(28-35\alpha) x +(29\alpha -1)y - xz, \\ z'=xy-\frac{8+\alpha}{3} z, \end{cases} \] where \(x\), \(y\) and \(z\) are states variables and \(\alpha\in [0,1]\) is a parameter. For \(\alpha\in [0,0.8)\) this is the Lorenz chaotic system, it is Lü's chaotic system for \(\alpha=0.8\) and Chen's chaotic system for \(\alpha\in (0.8,1]\). The authors consider the variable structure control technique which involves two major phases: first to select an appropriate switching surface for the system such that the sliding motion on this surface be asymptotically stable and second, design a control law to drive the system towards the surface even with unknown system parameters and control input nonlinearity. In particular, for this second step, the paper provides an scheme and a theorem that by means of the Lyapunov stability theory, the chaos suppression and the overall stability is proved. Finally the paper ends with some numerical results that validate the robustness of the proposed adaptive control scheme in any of Lorenz (\(\alpha=0\) is chosen), Lü and Chen (\(\alpha=1\) is chosen) chaotic systems.
reviewed by: Josep J. Masdemont
Mathematics Subject Classification ID: 65P20
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5534874
zbMATH Keywords: chaos suppression
zbMATH Keywords: dead-zone nonlinearity
zbMATH Keywords: variable structure control
zbMATH Keywords: switching surface
zbMATH Keywords: Lorenz chaotic system
zbMATH Keywords: Lü's chaotic system
zbMATH Keywords: Chen's chaotic system
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.amc.2008.12.058
OpenAlex ID: W2090598446
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DOI: 10.1016/J.AMC.2008.12.058
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description: scientific article; zbMATH DE number 5534874