Stochastic consensus over noisy networks with Markovian and arbitrary switches

  • Authors:

  • Minyi Huang;Subhrakanti Dey;Girish N. Nair;Jonathan H. Manton

  • Affiliations:

  • School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada;Department of Electrical and Electronic Engineering, University of Melbourne, Victoria 3010, Australia;Department of Electrical and Electronic Engineering, University of Melbourne, Victoria 3010, Australia;Department of Electrical and Electronic Engineering, University of Melbourne, Victoria 3010, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2010

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Abstract

This paper considers stochastic consensus problems over lossy wireless networks. We first propose a measurement model with a random link gain, additive noise, and Markovian lossy signal reception, which captures uncertain operational conditions of practical networks. For consensus seeking, we apply stochastic approximation and derive a Markovian mode dependent recursive algorithm. Mean square and almost sure (i.e., probability one) convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition. Subsequently, we consider a model with arbitrary random switching and a common stochastic Lyapunov function technique is used to prove convergence. Finally, our method is applied to models with heterogeneous quantizers and packet losses, and convergence results are proved.