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 proceedingConference contributionpeer-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 languageEnglish (US)
Title of host publication2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages1177-1186
Number of pages10
DOIs
StatePublished - 2009
Externally publishedYes
Event2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States
Duration: Sep 30 2009Oct 2 2009

Other

Other2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
CountryUnited States
CityMonticello, IL
Period09/30/0910/2/09

ASJC Scopus subject areas

  • Computer Science(all)
  • Control and Systems Engineering
  • Communication

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