Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Anton Selivanov, Emilia Fridman

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

Abstract

The existing sampled-data observers for 2D heat equations use spatially averaged measurements, i.e., the state values averaged over subdomains covering the entire space domain. In this paper, we introduce an observer for a 2D heat equation that uses pointlike measurements, which are modeled as the state values averaged over small subsets that do not cover the space domain. The key result, allowing for an efficient analysis of such an observer, is a new inequality that bounds the L2-norm of the difference between the state and its point value by the reciprocally convex combination of the L2-norms of the first and second order space derivatives of the state. The convergence conditions are formulated in terms of linear matrix inequalities feasible for large enough observer gain and number of pointlike sensors. The results are extended to solve the H∞ filtering problem under continuous and sampled in time pointlike measurements.

Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages539-544
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - 2 Jul 2018
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: 17 Dec 201819 Dec 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Country/TerritoryUnited States
CityMiami
Period17/12/1819/12/18

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