Stochastic consensus over noisy networks with Markovian and arbitrary switches

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...

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Bibliographic Details
Published in:Automatica (Oxford) 2010-10, Vol.46 (10), p.1571-1583
Main Authors: Huang, Minyi, Dey, Subhrakanti, Nair, Girish N., Manton, Jonathan H.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Automation
Coefficients
Computer science
control theory
systems
Computer systems and distributed systems. User interface
Consensus
Convergence
Exact sciences and technology
Markovian lossy channels
Measurement noises
Networks
Packet losses
Quantized data
Signal reception
Software
Stochastic approximation
Stochasticity
Switching theory
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2010.06.016