Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds

Panagiotis D. Christofides, Prodromos Daoutidis

Research output: Contribution to journalConference articlepeer-review

25 Scopus citations

Abstract

This paper introduces a methodology for the synthesis of nonlinear finite-dimensional output feedback controllers for systems of quasi-linear parabolic partial differential equations (PDEs), for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast one. Combination of Galerkin's method with a novel procedure for the construction of approximate inertial manifolds for the PDE system is employed for the derivation of ordinary differential equation (ODE) systems (whose dimension is equal to the number of slow modes) that yield solutions which are close, upto a desired accuracy, to the ones of the PDE system, for almost all times. These ODE systems are used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed-loop system to follow up to a desired accuracy, a prespecified response for almost all times.

Original languageEnglish (US)
Pages (from-to)1068-1073
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
StatePublished - 1997
EventProceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5) - San Diego, CA, USA
Duration: Dec 10 1997Dec 12 1997

Bibliographical note

Funding Information:
Financial support for this work from the National Science Foundation, CTS-9624725, is gratefully acknowledged.

Fingerprint

Dive into the research topics of 'Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds'. Together they form a unique fingerprint.

Cite this