Abstract

The analysis of a distributed consensus algorithm for estimating the maximum of the node initial state values in a network is considered in the presence of communication noise. Conventionally, the maximum is estimated by updating the node state value with the largest received measurements in every iteration at each node. However, due to additive channel noise, the estimate of the maximum at each node has a positive drift at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used to study this ergodic process, wherein, at each iteration, the state values are multiplied by a random matrix characterized by the noise distribution. The growth rate of the state values due to noise is studied by analyzing the Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is bounded by a constant which depends on the spectral radius of the network and the noise variance. Simulation results supporting the theory are also presented.

Original languageEnglish (US)
Title of host publicationConference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1408-1412
Number of pages5
ISBN (Electronic)9781538692189
DOIs
StatePublished - Feb 19 2019
Event52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 - Pacific Grove, United States
Duration: Oct 28 2018Oct 31 2018

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2018-October
ISSN (Print)1058-6393

Conference

Conference52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
CountryUnited States
CityPacific Grove
Period10/28/1810/31/18

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Keywords

  • Lyapunov exponent
  • Max consensus
  • max-plus algebra
  • wireless sensor networks

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

Cite this

Muniraju, G., Tepedelenlioglu, C., Spanias, A., Zhang, S., & Banavar, M. K. (2019). Max Consensus in the Presence of Additive Noise. In M. B. Matthews (Ed.), Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 (pp. 1408-1412). [8645297] (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.1109/ACSSC.2018.8645297