On time-delayed feedback control of chaotic systems

Author

Chen, Guanrong ; Yu, Xinghuo

Author_Institution

Dept. of Electr. & Comput. Eng., Houston Univ., TX, USA

Volume

46

Issue

6

fYear

1999

fDate

6/1/1999 12:00:00 AM

Firstpage

767

Lastpage

772

Abstract

A time-delayed feedback control (TDFC) system is, by nature, a rather special version of the familiar autoregressive moving-average (ARMA) control or the canonical state-space control systems. Despite some of its inherent limitations, TDFC can be quite successful in many chaos control applications. To understand to what extent the TDFC method is useful, some analytic (sufficient) conditions for chaos control from the TDFC approach are derived in this paper for both stabilization and tracking problems. A gradient-descent-based search algorithm is incorporated with the TDFC to estimate the time-delay constant for tracking unstable periodic orbits. The established theoretical results and estimation method are further clarified via a case study of the typical chaotic Rossler system with computer simulations

Keywords

Lyapunov methods; chaos; control system analysis; delay systems; feedback; stability; tracking; chaos control application; chaotic Rossler system; chaotic systems; estimation method; gradient-descent-based search algorithm; stabilization problems; time-delayed feedback control; tracking problems; unstable periodic orbits; Chaos; Chaotic communication; Control systems; Feedback control; Filters; Frequency; Orbits; Signal processing algorithms; State-space methods; Target tracking;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.768837

Filename

768837