Huang, Minyi and Dey, Subhrakanti and Nair, Girish N. and Manton, Jonathan H.
(2010)
Stochastic consensus over noisy networks with Markovian and arbitrary switches.
Automatica, 46 (10).
pp. 1571-1583.
ISSN 0005-1098
Abstract
This paper considers stochastic consensus problems over lossy wireless networks. We first propose a
measurement model with a random link gain, additive noise, and Markovian lossy signal reception,
which captures uncertain operational conditions of practical networks. For consensus seeking, we
apply stochastic approximation and derive a Markovian mode dependent recursive algorithm. Mean
square and almost sure (i.e., probability one) convergence analysis is developed via a state space
decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum
condition.Subsequently,we consider a model with arbitrary random switching and a common stochastic
Lyapunov function technique is used to prove convergence. Finally,our method is applied to models with
heterogeneous quantizers and packet losses, and convergence results are proved.
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