Bounded output feedback control of the Kuramoto-Sivashinsky equation with input constraints

Antonios Armaou, P. D. Christofides

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

This work focuses on the stabilization of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions at the zero solution in the presence of input constraints. Bounded nonlinear stabilizing controllers are synthesized on the basis of finite-dimensional Galerkin approximations of the KSE which capture the dominant dynamics of the equation for a given value of the instability parameter. The controller design accounts explicitly for the presence of input constraints and an explicit characterization of the limitations imposed by the input constraints on the allowable control actuator locations is provided. The theoretical results are successfully illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.

Original languageEnglish (US)
Pages (from-to)1936-1941
Number of pages6
JournalProceedings of the American Control Conference
Volume3
StatePublished - Jan 1 2001
Event2001 American Control Conference - Arlington, VA, United States
Duration: Jun 25 2001Jun 27 2001

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Feedback control
Controllers
Closed loop systems
Actuators
Stabilization
Boundary conditions
Computer simulation

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

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abstract = "This work focuses on the stabilization of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions at the zero solution in the presence of input constraints. Bounded nonlinear stabilizing controllers are synthesized on the basis of finite-dimensional Galerkin approximations of the KSE which capture the dominant dynamics of the equation for a given value of the instability parameter. The controller design accounts explicitly for the presence of input constraints and an explicit characterization of the limitations imposed by the input constraints on the allowable control actuator locations is provided. The theoretical results are successfully illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.",
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Bounded output feedback control of the Kuramoto-Sivashinsky equation with input constraints. / Armaou, Antonios; Christofides, P. D.

In: Proceedings of the American Control Conference, Vol. 3, 01.01.2001, p. 1936-1941.

Research output: Contribution to journalConference article

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T1 - Bounded output feedback control of the Kuramoto-Sivashinsky equation with input constraints

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AU - Christofides, P. D.

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N2 - This work focuses on the stabilization of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions at the zero solution in the presence of input constraints. Bounded nonlinear stabilizing controllers are synthesized on the basis of finite-dimensional Galerkin approximations of the KSE which capture the dominant dynamics of the equation for a given value of the instability parameter. The controller design accounts explicitly for the presence of input constraints and an explicit characterization of the limitations imposed by the input constraints on the allowable control actuator locations is provided. The theoretical results are successfully illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.

AB - This work focuses on the stabilization of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions at the zero solution in the presence of input constraints. Bounded nonlinear stabilizing controllers are synthesized on the basis of finite-dimensional Galerkin approximations of the KSE which capture the dominant dynamics of the equation for a given value of the instability parameter. The controller design accounts explicitly for the presence of input constraints and an explicit characterization of the limitations imposed by the input constraints on the allowable control actuator locations is provided. The theoretical results are successfully illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.

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