Control of the chaotic Duffing equation with uncertainty in all parameters

Author

Loria, Antonio ; Panteley, Elena ; Nijmeijer, Henk

Author_Institution

Fac. of Appl. Math., Twente Univ., Enschede, Netherlands

Volume

45

Issue

12

fYear

1998

fDate

12/1/1998 12:00:00 AM

Firstpage

1252

Lastpage

1255

Abstract

In this work, we deal with the open problem of controlling the periodically forced Duffing equation with uncertainty in all parameters. To date, several control schemes have been proposed to adapt for the linearly appearing unknown parameters but no solution exists for the case when the frequency of the periodic forcing is also unknown. We prove for the state feedback control case, global, asymptotic convergence for constant and time-varying references. We extend these results to the position feedback case and prove global ultimate boundedness

Keywords

adaptive control; chaos; closed loop systems; control system analysis; control system synthesis; convergence; feedback; stability; state feedback; three-term control; tracking; PID-based controller; adaptive tracking controller; chaotic Duffing equation; constant reference; control schemes; global asymptotic convergence; global ultimate boundedness; periodic forcing frequency; position feedback case; stable tracking; state feedback control; time-varying reference; Chaos; Chaotic communication; Communication system control; Control systems; Equations; Force control; Mathematics; Programmable control; State feedback; Uncertainty;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.736558

Filename

736558