Minimal error certificates for detection of faulty sensors using convex optimization

Christian G. Claudel; Matthieu Nahoum; Alexandre M. Bayen

doi:10.1109/ALLERTON.2009.5394554

Minimal error certificates for detection of faulty sensors using convex optimization

Christian G. Claudel, Matthieu Nahoum, Alexandre M. Bayen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

This article proposes a new method for sensor fault detection, applicable to systems modeled by conservation laws. The state of the system is modeled by a Hamilton-Jacobi equation, in which the Hamiltonian is uncertain. Using a Lax-Hopf formula, we show that any local measurement of the state of the system restricts the allowed set of possible values of other local measurements. We derive these constraints explicitly for arbitrary Hamilton-Jacobi equations. We apply this framework to sensor fault detection, and pose the problem finding the minimal possible sensor error (minimal error certificate) as a set of convex programs. We illustrate the performance of the resulting algorithms for a highway traffic flow monitoring sensor network in the San-Francisco Bay Area.

Original language	English (US)
Title of host publication	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages	1177-1186
Number of pages	10
DOIs	https://doi.org/10.1109/ALLERTON.2009.5394554
State	Published - 2009
Externally published	Yes
Event	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States Duration: Sep 30 2009 → Oct 2 2009

Publication series

Name	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Other

Other	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Country/Territory	United States
City	Monticello, IL
Period	09/30/09 → 10/2/09

ASJC Scopus subject areas

General Computer Science
Control and Systems Engineering
Communication

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10.1109/ALLERTON.2009.5394554

Cite this

Claudel, C. G., Nahoum, M., & Bayen, A. M. (2009). Minimal error certificates for detection of faulty sensors using convex optimization. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 (pp. 1177-1186). Article 5394554 (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394554

@inproceedings{eadd0cd0d8e84cb1b862deafe07f3e9b,

title = "Minimal error certificates for detection of faulty sensors using convex optimization",

abstract = "This article proposes a new method for sensor fault detection, applicable to systems modeled by conservation laws. The state of the system is modeled by a Hamilton-Jacobi equation, in which the Hamiltonian is uncertain. Using a Lax-Hopf formula, we show that any local measurement of the state of the system restricts the allowed set of possible values of other local measurements. We derive these constraints explicitly for arbitrary Hamilton-Jacobi equations. We apply this framework to sensor fault detection, and pose the problem finding the minimal possible sensor error (minimal error certificate) as a set of convex programs. We illustrate the performance of the resulting algorithms for a highway traffic flow monitoring sensor network in the San-Francisco Bay Area.",

author = "Claudel, {Christian G.} and Matthieu Nahoum and Bayen, {Alexandre M.}",

year = "2009",

doi = "10.1109/ALLERTON.2009.5394554",

language = "English (US)",

isbn = "9781424458714",

series = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009",

pages = "1177--1186",

booktitle = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009",

note = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 ; Conference date: 30-09-2009 Through 02-10-2009",

}

Claudel, CG, Nahoum, M & Bayen, AM 2009, Minimal error certificates for detection of faulty sensors using convex optimization. in 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009., 5394554, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, pp. 1177-1186, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, Monticello, IL, United States, 09/30/09. https://doi.org/10.1109/ALLERTON.2009.5394554

Minimal error certificates for detection of faulty sensors using convex optimization. / Claudel, Christian G.; Nahoum, Matthieu; Bayen, Alexandre M.
2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. p. 1177-1186 5394554 (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - This article proposes a new method for sensor fault detection, applicable to systems modeled by conservation laws. The state of the system is modeled by a Hamilton-Jacobi equation, in which the Hamiltonian is uncertain. Using a Lax-Hopf formula, we show that any local measurement of the state of the system restricts the allowed set of possible values of other local measurements. We derive these constraints explicitly for arbitrary Hamilton-Jacobi equations. We apply this framework to sensor fault detection, and pose the problem finding the minimal possible sensor error (minimal error certificate) as a set of convex programs. We illustrate the performance of the resulting algorithms for a highway traffic flow monitoring sensor network in the San-Francisco Bay Area.

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Claudel CG, Nahoum M, Bayen AM. Minimal error certificates for detection of faulty sensors using convex optimization. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. p. 1177-1186. 5394554. (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). doi: 10.1109/ALLERTON.2009.5394554

Minimal error certificates for detection of faulty sensors using convex optimization

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