An overview of bifurcation, chaos and nonlinear dynamics in control systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

43 Scopus Citations
View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)819-858
Journal / PublicationJournal of the Franklin Institute
Volume331
Issue number6
Publication statusPublished - Nov 1994
Externally publishedYes

Abstract

This article offers a brief review of the fundamental concepts of bifurcation and chaos in nonlinear dynamical and control systems. Both the time-domain and frequency-domain versions of the classical Hopf bifurcation theory are studied in detail. Generalized (or degenerate) Hopf bifurcation is also discussed. Theoretical analysis and potential applications of the bifurcation theory in power systems are introduced. Meanwhile, chaos and the route to chaos from period-doubling bifurcations are described. In particular, chaos and bifurcations in feedback control systems and adaptive control systems are addressed. Because a nonlinear control system is by nature a very complex nonautonomous dynamical system due essentially to the involving of the control input, understanding and utilizing the rich dynamics of nonlinear control systems have an important impact in the modern technology. It calls for new effort and endeavor devoted to this scientific and engineering challenge. © 1995.