Asymptotic mean ergodicity of average consensus estimators

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Dynamic average consensus estimators suitable for the decentralized computation of global averages of constant or slowly-varying local inputs include the proportional (P) and proportional-integral (PI) estimators. We analyze the convergence properties of these estimators when run on i.i.d. random graphs which are connected and balanced on average, but need not be connected or balanced at each time step. The statistics of the steady-state process are found using the Kronecker product covariance and an ergodic theorem is used to determine whether the steady-state process is mean ergodic. We show that for constant inputs the P estimator is asymptotically mean ergodic only for systems with non-zero forgetting factor which do not have zero steady-state error on average. The PI estimator has both the asymptotic mean ergodicity property and zero steady-state error in expectation for constant inputs independent of initial conditions, proving that the time-averaged output of each agent robustly converges to the correct average.

Original languageEnglish (US)
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4696-4701
Number of pages6
ISBN (Print)9781479932726
DOIs
StatePublished - Jan 1 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: Jun 4 2014Jun 6 2014

Other

Other2014 American Control Conference, ACC 2014
CountryUnited States
CityPortland, OR
Period6/4/146/6/14

Keywords

  • Decentralized control
  • Networked control systems
  • Stochastic systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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    Van Scoy, B., Freeman, R. A., & Lynch, K. M. (2014). Asymptotic mean ergodicity of average consensus estimators. In 2014 American Control Conference, ACC 2014 (pp. 4696-4701). [6859059] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2014.6859059