@conference {Topley2008Consensus-forma,
title = {Consensus formation in a switched Markovian dynamical system},
booktitle = {Decision and Control, 2008. CDC 2008. 47th IEEE Conference on},
year = {2008},
month = {dec.},
pages = {3547 -3552},
abstract = {We address the problem of distributively obtaining average-consensus among a connected network of sensors that each respectively track, by linear stochastic approximation, the stationary distribution of an ergodic Markov chain with slowly switching regimes. A hyper-parameter modeled as a Markov process on a slow time-scale modulates the regime of each observed Markov chain, thus at any given time the hyper-parameter determines what stationary distribution will be estimated by each sensor. If the Markov chains share a common stationary distribution conditional on the regime, it is shown the sequence of sensor state-values weakly-converge to an average-consensus under the distributed linear consensus-filter for all network communication graphs. Conversely, if the Markov chains have unique stationary distributions in each regime, then the average-consensus can be achieved only when sensors communicate state-values at a frequency that is on the same time-scale as the frequency at which they observe the fast Markov chain. In this scenario, unlike a static consensus filter, the state-value communication graph need not be connected for an average-consensus to be reached, however this is true only when the communication graph of observation data satisfies a specific connectivity condition. Simulations illustrate our conclusions and observation model.},
keywords = {ad hoc networks, connected network, consensus formation, distributed linear consensus-filter, ergodic Markov chain, graph theory, linear stochastic approximation, Markov processes, network communication graphs, sensor state-values, sensors, switched Markovian dynamical system},
issn = {0191-2216},
doi = {10.1109/CDC.2008.4739488},
url = {http://dx.doi.org/10.1109/CDC.2008.4739488},
author = {Topley, K. and Krishnamurthy, V. and Yin, G.}
}