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On Quantized Consensus by Means of Gossip Algorithm  Part II: Convergence Time 
Abstract 
This paper deals with the distributed aver … 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 numbers in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. In the first part of the paper, it was shown that the quantized consensus is reached by means of a stochastic gossip algorithm proposed in a recent paper, for any arbitrary quantization. The current part of the paper considers the expected value of the time at which the quantized consensus is reached. This quantity (corresponding to the worst case) is upper and lower bounded in terms of the topology of the graph, for uniform quantization. In particular, it is shown that these bounds are related to the principal minors of the weighted Laplacian matrix. A convex optimization is also proposed to determine the set of probabilities (used to pick a pair of agents) which leads to the fast convergence of the gossip algorithm. fast convergence of the gossip algorithm. +


Authors  Javad Lavaei, Richard M Murray + 
ID  2008q + 
Source  American Control Conference (ACC) + 
Tag  lm09bacc + 
Title  On Quantized Consensus by Means of Gossip Algorithm  Part II: Convergence Time + 
Type  Preprint + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:16:47 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/lm09bacc.pdf + 
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