Constrained nonlinear control of parabolic PDE systems

Nael H. El-Farra, Antonios Armaou, Panagiotis D. Christofides

Research output: Contribution to journalConference article

Abstract

This paper focuses on the development of a general framework for analysis and control of parabolic PDE systems with manipulated input constraints. Initially, a nonlinear model reduction scheme based on combination of Galerkin's method with the concept of approximate inertial manifold is employed for the derivation of low-order ODE systems that yield solutions very close to those of the PDE system. These ODE systems are used as the basis for the explicit construction of bounded nonlinear optimal feedback controllers, via Lyapunov techniques, that enforce stability and provide an explicit characterization of the limitations imposed by input constraints on the allowable control actuator locations. Precise conditions that guarantee stability of the closed-loop parabolic PDE system in the presence of input constraints are provided. The proposed analysis and controller synthesis results are used to stabilize an unstable steady-state of a diffusion-reaction process.

Original languageEnglish (US)
Pages (from-to)2275-2279
Number of pages5
JournalProceedings of the American Control Conference
Volume4
StatePublished - Dec 1 2000
Event2000 American Control Conference - Chicago, IL, USA
Duration: Jun 28 2000Jun 30 2000

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Controllers
Galerkin methods
Actuators
Feedback

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

El-Farra, Nael H. ; Armaou, Antonios ; Christofides, Panagiotis D. / Constrained nonlinear control of parabolic PDE systems. In: Proceedings of the American Control Conference. 2000 ; Vol. 4. pp. 2275-2279.
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Constrained nonlinear control of parabolic PDE systems. / El-Farra, Nael H.; Armaou, Antonios; Christofides, Panagiotis D.

In: Proceedings of the American Control Conference, Vol. 4, 01.12.2000, p. 2275-2279.

Research output: Contribution to journalConference article

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