Template-based stabilization of relative equilibria

Sunil Ahuja, Yannis Kevrekidis, Clarence Worth Rowley

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present an approach to the design of feedback control laws that stabilize the relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original system are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. Assuming equivariant actuation, we derive feedback laws for the reduced system that are optimal in the sense that they minimize a quadratic cost function. We illustrate the method by stabilizing unstable traveling waves of a dissipative PDE possessing translational invariance.

Original languageEnglish (US)
Title of host publicationProceedings of the 2006 American Control Conference
Pages3606-3611
Number of pages6
StatePublished - Dec 1 2006
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: Jun 14 2006Jun 16 2006

Publication series

NameProceedings of the American Control Conference
Volume2006
ISSN (Print)0743-1619

Other

Other2006 American Control Conference
CountryUnited States
CityMinneapolis, MN
Period6/14/066/16/06

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Ahuja, S., Kevrekidis, Y., & Rowley, C. W. (2006). Template-based stabilization of relative equilibria. In Proceedings of the 2006 American Control Conference (pp. 3606-3611). [1657278] (Proceedings of the American Control Conference; Vol. 2006).