Discretized Consensus 2012-12-03

Andrea Censi and Richard M. Murray. Real-valued consensus over noisy quantized channels. In Proceedings of the American Control Conference (ACC). St. Louis, Missouri, June 2009. pdfdoi supp. material slides


Abstract --- This paper concerns the average consensus problem with the constraint of quantized communication between nodes. A broad class of algorithms is analyzed, in which the transmission strategy, which decides what value to communicate to the neighbors, can include various kinds of rounding, probabilistic quantization, and bounded noise. The arbitrariness of the transmission strategy is compensated by a feedback mechanism which can be interpreted as a self-inhibitory action. The result is that the average of the nodes state is not conserved across iterations, and the nodes do not converge to a consensus; however, we show that both errors can be made as small as desired. Bounds on these quantities involve the spectral properties of the graph and can be proved by employing elementary techniques of LTI systems analysis.

Please link here using the PURL: http://purl.org/censi/2008/consensus.