Consensus formation in a switched Markovian dynamical system

TitleConsensus formation in a switched Markovian dynamical system
Publication TypeConference Paper
Year of Publication2008
AuthorsTopley, K., V. Krishnamurthy, and G. Yin
Conference NameDecision and Control, 2008. CDC 2008. 47th IEEE Conference on
Pagination3547 -3552
Date Publisheddec.
Keywordsad 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

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.


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