Sampled-data finite-dimensional observer-based boundary control of 1D stochastic parabolic PDEs

Pengfei Wang*, Emilia Fridman

*Corresponding author for this work

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

Abstract

Recently, finite-dimensional controllers were introduced for 1D stochastic parabolic PDEs via the modal decomposition method. In the present paper, we suggest a sampled-data implementation of a finite-dimensional observer-based boundary controller for 1D stochastic parabolic PDEs under discrete-time non-local measurement, where both the considered system and the measurement are subject to nonlinear multiplicative noise. We provide mean-square L2 exponential stability analysis of the full-order closed-loop system, where we employ Itô's formula. We consider sampled-data control that employs zero-order hold device and use the time-delay approach to the sampled-data system. We construct Lyapunov functional V, and further combine it with Halanay's inequality with respect to expected value of V to compensate sampling in the infinite-dimensional tail. We provide linear matrix inequalities (LMIs) for finding the observer dimension N and upper bounds on sampling intervals and noise intensities that preserve the exponential stability. We prove that the LMIs are always feasible for large enough N and small enough sampling intervals and noise intensities. A numerical example demonstrates the efficiency of our method.

Original languageEnglish
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1045-1050
Number of pages6
ISBN (Electronic)9781665467612
DOIs
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2022-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference61st IEEE Conference on Decision and Control, CDC 2022
Country/TerritoryMexico
CityCancun
Period6/12/229/12/22

Funding

FundersFunder number
Israel Science Foundation673/19
Tel Aviv University

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