Constructive finite-dimensional observer-based boundary control of stochastic parabolic PDEs

Pengfei Wang, Rami Katz, Emilia Fridman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs has been suggested by employing a modal decomposition approach. In the present paper, we aim to extend this method to the stochastic parabolic PDEs with nonlinear multiplicative noise. We consider the Neumann actuation and boundary measurement via dynamic extension. The controller dimension is defined by N0 unstable modes, whereas the observer may have a larger dimension N. We provide mean-square L2 stability analysis of the full-order closed-loop system leading to linear matrix inequality (LMI) conditions for finding N. We prove that the LMIs are always feasible for small enough noise intensity and large enough N. A numerical example demonstrates the efficiency of our method.

Original languageEnglish
Title of host publication2022 American Control Conference, ACC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1667-1672
Number of pages6
ISBN (Electronic)9781665451963
DOIs
StatePublished - 2022
Event2022 American Control Conference, ACC 2022 - Atlanta, United States
Duration: 8 Jun 202210 Jun 2022

Publication series

NameProceedings of the American Control Conference
Volume2022-June
ISSN (Print)0743-1619

Conference

Conference2022 American Control Conference, ACC 2022
Country/TerritoryUnited States
CityAtlanta
Period8/06/2210/06/22

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