Boundary Observers for a Reaction-Diffusion System Under Time-Delayed and Sampled-Data Measurements

Anton Selivanov; Emilia Fridman

doi:https://doi.org/10.1109/TAC.2018.2877381

Boundary Observers for a Reaction-Diffusion System Under Time-Delayed and Sampled-Data Measurements

Anton Selivanov, Emilia Fridman

School of Electrical Engineering

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We construct finite-dimensional observers for a one-dimensional reaction-diffusion system with boundary measurements subject to time-delays and data sampling. The system has a finite number of unstable modes approximated by a Luenberger-type observer. The remaining modes vanish exponentially. For a given reaction coefficient, we show how many modes one should use to achieve a desired rate of convergence. The finite-dimensional part is analyzed using appropriate Lyapunov-Krasovskii functionals that lead to linear matrix inequalitie (LMI)-based convergence conditions feasible for small enough time-delay and sampling period. The LMIs can be used to find appropriate injection gains.

Original language	English
Article number	8502078
Pages (from-to)	3385-3390
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	64
Issue number	8
DOIs	https://doi.org/10.1109/TAC.2018.2877381
State	Published - Aug 2019

Keywords

Boundary measurements
data sampling
observers
partial differential equations
time-delays

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Access to Document

https://doi.org/10.1109/TAC.2018.2877381

Cite this

@article{e1d9d7135bcf40adbc12d587fb08a6d1,

title = "Boundary Observers for a Reaction-Diffusion System Under Time-Delayed and Sampled-Data Measurements",

abstract = "We construct finite-dimensional observers for a one-dimensional reaction-diffusion system with boundary measurements subject to time-delays and data sampling. The system has a finite number of unstable modes approximated by a Luenberger-type observer. The remaining modes vanish exponentially. For a given reaction coefficient, we show how many modes one should use to achieve a desired rate of convergence. The finite-dimensional part is analyzed using appropriate Lyapunov-Krasovskii functionals that lead to linear matrix inequalitie (LMI)-based convergence conditions feasible for small enough time-delay and sampling period. The LMIs can be used to find appropriate injection gains.",

keywords = "Boundary measurements, data sampling, observers, partial differential equations, time-delays",

author = "Anton Selivanov and Emilia Fridman",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.",

year = "2019",

month = aug,

doi = "https://doi.org/10.1109/TAC.2018.2877381",

language = "الإنجليزيّة",

volume = "64",

pages = "3385--3390",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

number = "8",

}

TY - JOUR

T1 - Boundary Observers for a Reaction-Diffusion System Under Time-Delayed and Sampled-Data Measurements

AU - Selivanov, Anton

AU - Fridman, Emilia

PY - 2019/8

Y1 - 2019/8

N2 - We construct finite-dimensional observers for a one-dimensional reaction-diffusion system with boundary measurements subject to time-delays and data sampling. The system has a finite number of unstable modes approximated by a Luenberger-type observer. The remaining modes vanish exponentially. For a given reaction coefficient, we show how many modes one should use to achieve a desired rate of convergence. The finite-dimensional part is analyzed using appropriate Lyapunov-Krasovskii functionals that lead to linear matrix inequalitie (LMI)-based convergence conditions feasible for small enough time-delay and sampling period. The LMIs can be used to find appropriate injection gains.

AB - We construct finite-dimensional observers for a one-dimensional reaction-diffusion system with boundary measurements subject to time-delays and data sampling. The system has a finite number of unstable modes approximated by a Luenberger-type observer. The remaining modes vanish exponentially. For a given reaction coefficient, we show how many modes one should use to achieve a desired rate of convergence. The finite-dimensional part is analyzed using appropriate Lyapunov-Krasovskii functionals that lead to linear matrix inequalitie (LMI)-based convergence conditions feasible for small enough time-delay and sampling period. The LMIs can be used to find appropriate injection gains.

KW - Boundary measurements

KW - data sampling

KW - observers

KW - partial differential equations

KW - time-delays

UR - http://www.scopus.com/inward/record.url?scp=85055183966&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/TAC.2018.2877381

DO - https://doi.org/10.1109/TAC.2018.2877381

M3 - مقالة

SN - 0018-9286

VL - 64

SP - 3385

EP - 3390

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 8

M1 - 8502078

ER -

Boundary Observers for a Reaction-Diffusion System Under Time-Delayed and Sampled-Data Measurements

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this