Clark, R., Punzo, G. orcid.org/0000-0003-4246-9045 and Macdonald, M. (2016) Consensus speed optimisation with finite leadership perturbation in k-nearest neighbour networks. In: 2016 IEEE 55th Conference on Decision and Control (CDC). 55th IEEE Conference on Decision and Control, 12-14 Dec 2016, Las Vegas, NV, USA. IEEE (Institute of Electrical and Electronics Engineers) , pp. 879-884. ISBN 9781509018383
Abstract
Near-optimal convergence speeds are found for perturbed networked systems, with N interacting agents that conform to k-nearest neighbour (k-NNR) connection rules, by allocating a finite leadership resource amongst selected nodes. These nodes continue averaging their state with that of their neighbours while being provided with the resources to drive the network to a new state. Such systems are represented by a directed graph Laplacian with two newly presented semi-analytical approaches used to maximise the consensus speed. The two methods developed typically produce near-optimal results and are highly efficient when compared with conventional numerical optimisation, where the asymptotic computational complexity is O(n ^3 ) and O(n ^4 ) respectively. The upper limit for the convergence speed of a perturbed k-NNR network is identified as the largest element of the first left eigenvector (FLE) of a graph's adjacency matrix. The first semi-analytical method exploits this knowledge by distributing leadership resources amongst the most prominent nodes highlighted by this FLE. The second method relies on the FLEs of manipulated versions of the adjacency matrix to expose different communities of influential nodes. These are shown to correspond with the communities found by the Leicht-Newman detection algorithm, with this method enabling optimal leadership selection even in low outdegree (< 12 connections) graphs, where the first semi-analytical method is less effective.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Sep 2021 11:08 |
Last Modified: | 16 Sep 2021 05:10 |
Status: | Published |
Publisher: | IEEE (Institute of Electrical and Electronics Engineers) |
Refereed: | Yes |
Identification Number: | 10.1109/CDC.2016.7798378 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:178190 |