Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
type: Item
instance of: scholarly article
title: Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
zbMATH Open document ID: 0859.93028
DOI: 10.1016/0005-1098(96)00065-9
published in: Automatica
publication date: 1996-12-09T00:00:00Z
review text: Compact conditions for the prediction and stability analysis of period-doubling bifurcations are obtained by the harmonic balance method. The implications of the results to control design are illustrated through the development of a design procedure for control design which can delay a given period-doubling bifurcation as well as meet stability objectives. This paper is organized as follows. Section 1 consists of an introduction. In Section 2 the class of systems investigated in the paper is specified and known harmonic balance results for this class are presented in a compact form. In Section 3, harmonic balance results are obtained for the prediction and stability analysis of period-doubling bifurcations. In Section 4 a control problem is defined and a design procedure for its solutions is outlined. Section 5 contains a detailed example illustrating the results; in this example, a controller is given that can delay or eliminate the period-doubling cascade to chaotic motion. Finally, concluding remarks are collected in Section 6.
reviewed by: He Chungyou
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 946987
zbMATH Keywords: stability analysis
zbMATH Keywords: period-doubling bifurcation
zbMATH Keywords: harmonic balance
author: Alberto Tesi
author: Eyad H. Abed
author: R. Genesio
author: Hua O. Wang
describes a project that uses: LOCBIF
MaRDI profile type: Publication
full work available at URL: 0005-1098(96)00065-9
OpenAlex ID: W2039041284
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description: scientific article; zbMATH DE number 946987