ℋ Optimal Estimation for Linear Coupled PDE Systems

Amritam Das, Sachin Shivakumar, Siep Weiland, Matthew M. Peet

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

Abstract

In this work, we present a Linear Matrix Inequality (LMI) based method to synthesize an optimal ℋ estimator for a large class of linear coupled partial differential equations (PDEs) utilizing only finite dimensional measurements. Our approach extends the newly developed framework for representing and analyzing distributed parameter systems using operators on the space of square integrable functions that are equipped with multipliers and kernels of semi-separable class. We show that by redefining the state, the PDEs can be represented using operators that embed the boundary conditions and input-output relations explicitly. The optimal estimator synthesis problem is formulated as a convex optimization subject to LMIs that require no approximation or discretization.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages262-267
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Externally publishedYes
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Das, A., Shivakumar, S., Weiland, S., & Peet, M. M. (2019). ℋ Optimal Estimation for Linear Coupled PDE Systems. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 262-267). [9029595] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029595