On control of chaos: Higher periodic orbits
type: Item
instance of: scholarly article
title: On control of chaos: Higher periodic orbits
zbMATH Open document ID: 0845.93056
DOI: 10.1007/BF01968503
author: M. Paskota
author: Alistair Mees
author: Kok Lay Teo
published in: Dynamics and Control
publication date: 1996-01-22T00:00:00Z
review text: For a given dynamical system \(x_{k + 1} = f(x_k) + Bu_k\) the problem is to find the linear state feedback \(u_k = K^T (x_k - x^*)\) such that the system is stable in the fixed point \(x^*\). There is no major difference between stabilizing the system around the unstable \(m\)-periodic point and stabilizing it around an unstable fixed point. It suffices to consider the new system \(x_{k + 1} = f^m (x_k) + Bv_k\); for the fixed point, \(m = 1\). The examples are presented for the Hénon map, including the period-13 orbit and the Ikeda map.
reviewed by: A.Vaněček
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 836192
zbMATH Keywords: control of chaos
zbMATH Keywords: stabilization
zbMATH Keywords: periodic orbits
zbMATH Keywords: linear state feedback
zbMATH Keywords: Hénon map
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01968503
OpenAlex ID: W1978378433
description: scientific article; zbMATH DE number 836192