Title :
On quantized consensus by means of gossip algorithm - Part I: Convergence proof
Author :
Lavaei, Javad ; Murray, Richard M.
Author_Institution :
Dept. of Control & Dynamical Syst., California Inst. of Technol., Pasadena, CA, USA
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 properly. The expected value of the convergence time is lower and upper bounded in the second part of the paper.
Keywords :
graph theory; quantisation (signal); stochastic processes; arbitrary quantization; data exchange; distributed averaging problem; gossip algorithm; quantized consensus; steady-state properties; Computer networks; Computer science; Convergence; Distributed computing; Frequency synchronization; History; Java; Quantization; Stochastic processes; Tuning;
Conference_Titel :
American Control Conference, 2009. ACC '09.
Conference_Location :
St. Louis, MO
Print_ISBN :
978-1-4244-4523-3
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2009.5160485