Sub-Predictors for Finite-Dimensional Observer-Based Control of Stochastic Semilinear Parabolic PDEs

Pengfei Wang, Emilia Fridman

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

Abstract

We study output-feedback control of 1D stochastic semilinear heat equation with constant input delay and nonlinear multiplicative noise where the nonlinearities satisfy globally Lipschitz condition. We consider the Neumann actuation and nonlocal measurement. To compensate delay r, we construct a chain of M+1 sub-predictors in the form of ODEs that correspond to the delay fraction r/M. Differently from the deterministic case, we add an additional sub-predictor to the chain that leads to the closed-loop system with the stochastic infinite-dimensional tail and the finite-dimensional part that consists of non-delayed stochastic equations and delayed deterministic ones. The latter essentially simplifies the Lyapunov-based mean-square L2 exponential stability analysis of the full-order closed-loop system. We employ corresponding Itô's formulas for stochastic ODEs and PDEs, respectively. Our stability analysis leads to LMIs which are shown to be feasible for any input delay provided M and the observer dimension are large enough and Lipschitz constants are small enough. A numerical example demonstrates the efficiency of the proposed approach.

Original languageEnglish
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2943-2949
Number of pages7
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: 13 Dec 202315 Dec 2023

Publication series

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

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period13/12/2315/12/23

Fingerprint

Dive into the research topics of 'Sub-Predictors for Finite-Dimensional Observer-Based Control of Stochastic Semilinear Parabolic PDEs'. Together they form a unique fingerprint.

Cite this