On quantized consensus by means of gossip algorithm: part i: convergence proof

  • Authors:
  • Javad Lavaei;Richard M. Murray

  • Affiliations:
  • Department of Control and Dynamical Systems, California Institute of Technology, Pasadena;Department of Control and Dynamical Systems, California Institute of Technology, Pasadena

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

This paper is concerned with the distributed averaging problem subject to a quantization constraint. Given a group of agents associated with scalar numbers, it is assumed that each pair of agents can communicate with a prescribed probability, and that the data being exchanged between them is quantized. In this part of the paper, it is proved that the stochastic gossip algorithm proposed in a recent paper leads to reaching the quantized consensus. Some important steady-state properties of the system (after reaching the consensus) are also derived. The results developed here hold true for any arbitrary quantization, provided that the tuning parameter of the gossip algorithm is chosen properiy. The expected value of the convergence time is lower and upper bounded in the second part of the paper.