Sampled-Data Consensus Over Random Networks
2016 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 17, 4479-4492 p.Article in journal (Refereed) Published
This paper considers the consensus problem for a network of nodes with random interactions and sampled-data control actions. We first show that consensus in expectation, in mean square, and almost surely are equivalent for a general random network model when the inter-sampling interval and maximum node degree satisfy a simple relation. The three types of consensus are shown to be simultaneously achieved over an independent or a Markovian random network defined on an underlying graph with a directed spanning tree. For both independent and Markovian random network models, 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 critical value on the intersampling interval, below which a global mean-square consensus is achieved and above which the system diverges in a mean-square sense for some initial states. Finally, we establish an upper bound on the intersampling interval below which almost sure consensus is reached, and a lower bound on the intersampling interval above which almost sure divergence is reached. Some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter-sampling intervals for the mean-square consensus are provided.
Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016. Vol. 64, no 17, 4479-4492 p.
Consensus, Markov chain, sampled-data, random networks
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-193191DOI: 10.1109/TSP.2016.2568168ISI: 000381434700008ScopusID: 2-s2.0-84982805925OAI: oai:DiVA.org:kth-193191DiVA: diva2:1034637
QC 201610122016-10-122016-09-302016-10-12Bibliographically approved