Control of the Lorenz chaos by the exact linearization
type: Item
instance of: scholarly article
title: Control of the Lorenz chaos by the exact linearization
zbMATH Open document ID: 0912.93016
DOI: 10.1007/BF02458982
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1999-05-19T00:00:00Z
review text: In a recent review of the book by \textit{G. Chen} and \textit{X. Dong}, From chaos to order (1998; Zbl 0908.93005), we mentioned that the only control method unused was the exact linearization. The paper is concerned with the exact linearization method to stabilize the Lorenz chaos near some off-center equilibrium point. The standard method based on the Lie bracket of the vector field gives \(\dot z_1= z_2\), \(\dot z_2 =z_3\), \(z_3=v\) and the linear feedback control law is \(v=\alpha_1z_1+ \alpha_2z_2 +\alpha_3 z_3\). Simulation results are given. To implement this control law, all three state components should be known and the initial state should be near the off-center equilibrium point. The Lorenz system has a smooth nonlinearity which is used for this Lie approach. On the other hand, the Chua system with piecewise nonlinearity gives a possibility for a state control law to stabilize it near any of the three equilibria. This, according to our knowledge, was never implemented because of limited possibilities of practical realization.
reviewed by: A.Vaněček
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1197095
zbMATH Keywords: Rayleigh number
zbMATH Keywords: chaos control
zbMATH Keywords: exact linearization
zbMATH Keywords: Lorenz chaos
author: Li-Qun Chen
author: Yan-Zhu Liu
MaRDI profile type: Publication
cites work: FROM CHAOS TO ORDER — PERSPECTIVES AND METHODOLOGIES IN CONTROLLING CHAOTIC NONLINEAR DYNAMICAL SYSTEMS
cites work: Taming chaos. II. Control
cites work: Q4861628
cites work: Deterministic Nonperiodic Flow
cites work: The Lorenz equations: bifurcations, chaos, and strange attractors
cites work: An open-plus-closed-loop (OPCL) control of complex dynamic systems
cites work: Control of a chaotic system
cites work: Nonliner regulation of a Lorenz system by feedback linearization techniques
cites work: Nonlinear feedback control with global stabilization
cites work: CONTROLLING CHAOS THROUGH ITERATION SEQUENCES AND INTERPOLATION TECHNIQUES
cites work: A CLASSICAL APPROACH TO CONTROLLING THE LORENZ EQUATIONS
cites work: Application of stochastic control techniques to chaotic nonlinear systems
cites work: Feedback control of chaotic systems
cites work: Q4003780
description: scientific article; zbMATH DE number 1197095