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Quantized Consensus by Means of Gossip Algorithm

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2 Author(s)
Javad Lavaei ; Department of Control and Dynamical Systems, California Institute of Technology, Pasadena, United States of America ; Richard M. Murray

This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own states in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. It is shown that a quantized consensus is reached for an arbitrary quantizer by means of the stochastic gossip algorithm proposed in a recent paper. The expected value of the time at which a quantized consensus is reached is lower and upper bounded in terms of the topology of the graph for a uniform quantizer. In particular, it is shown that these bounds are related to the principal submatrices of the weighted Laplacian matrix. A convex optimization is also proposed to determine a set of probabilities used to pick a pair of agents that leads to a fast convergence of the gossip algorithm.

Published in:

IEEE Transactions on Automatic Control  (Volume:57 ,  Issue: 1 )