Control of semilinear dissipative distributed parameter systems with minimum feedback information

Davood B. Pourkargar, Antonios Armaou

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

Abstract

We focus on Lyapunov-based output feedback control for a class of distributed parameter systems with spatiotemporal dynamics described by input-affine semilinear dissipative partial differential equations (DPDEs). The control problem is addressed via adaptive model order reduction. Galerkin projection is applied to discretize the DPDE and derive low-dimensional reduced order models (ROMs). The empirical basis functions needed for this discretization are updated using adaptive proper orthogonal decomposition (APOD) which needs measurements of the complete profile of the system state (called snapshots) at revision times. The main objective of this paper is to minimize the demand for snapshots from the spatially distributed sensors by the control structure while maintaining closed-loop stability and performance. A control Lyapunov function is defined and its value is monitored as the system evolves. Only when the value violates a closed-loop stability threshold, snapshots are requested for a brief period by APOD after which the ROM is updated and the controller is reconfigured. The proposed approach is applied to stabilize the Kuramoto-Sivashinsky equation.

Original languageEnglish (US)
Title of host publication2020 American Control Conference, ACC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2685-2691
Number of pages7
ISBN (Electronic)9781538682661
DOIs
StatePublished - Jul 2020
Event2020 American Control Conference, ACC 2020 - Denver, United States
Duration: Jul 1 2020Jul 3 2020

Publication series

NameProceedings of the American Control Conference
Volume2020-July
ISSN (Print)0743-1619

Conference

Conference2020 American Control Conference, ACC 2020
CountryUnited States
CityDenver
Period7/1/207/3/20

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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