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Critical sampling rate for sampled-data consensus over random networks
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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2016 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2016, 412-417 p.Conference paper (Refereed)Text
Abstract [en]

In this paper, we consider the consensus problem for a network of nodes with random interactions and sampled-data control actions. Each node independently samples its neighbors in a random manner over a directed graph underlying the information exchange of different nodes. The relationship between the sampling rate and the achievement of consensus is studied. We first establish a sufficient condition, in terms of the inter-sampling interval, such that consensus in expectation, in mean square, and in almost sure sense are simultaneously achieved provided a mild connectivity assumption for the underlying graph. Necessary and sufficient conditions for mean-square consensus are derived in terms of the spectral radius of the corresponding state transition matrix. These conditions are then interpreted as the existence of a critical value on the inter-sampling interval, below which global mean-square consensus is achieved and above which the system diverges in mean-square sense for some initial states. Finally, we establish an upper bound of the inter-sampling interval, below which almost sure consensus is reached, and a lower bound, above which almost sure divergence is reached. An numerical example is given to validate the theoretical results.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2016. 412-417 p.
National Category
Signal Processing Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-188263DOI: 10.1109/CDC.2015.7402235ScopusID: 2-s2.0-84962016843ISBN: 9781479978861OAI: diva2:937387
54th IEEE Conference on Decision and Control, CDC 2015, 15 December 2015 through 18 December 2015

QC 20160615

Available from: 2016-06-15 Created: 2016-06-09 Last updated: 2016-06-15Bibliographically approved

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Wu, JunfengJohansson, Karl Henrik
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