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Convergence speed of a fractional order consensus algorithm over undirected scale‐free networks
Author(s) -
Sun Wei,
Li Yan,
Li Changpin,
Chen YangQuan
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.390
Subject(s) - convergence (economics) , consensus , inverse , order (exchange) , computer science , scale (ratio) , property (philosophy) , mathematics , protocol (science) , scale free network , algorithm , mathematical optimization , complex network , topology (electrical circuits) , multi agent system , artificial intelligence , medicine , philosophy , physics , geometry , alternative medicine , finance , epistemology , quantum mechanics , pathology , combinatorics , economics , economic growth , world wide web
cale‐free networks have been rediscovered universally in natural and man‐made systems, and the consensus protocols have been tremendously studied over the last decade. Motivated by the fractional‐order dynamics of bacteria colonies, a fractional‐order protocol is employed to achieve the consensus over scale‐free networks. The most remarkable property of scale‐free networks lies in the inverse power‐law degree distributions. The present work concerns the convergence speed with different fractional orders corresponding to different power‐law parameters. The analytic solutions of consensus protocols are given and its property is discussed, explaining the quick convergence speed in the early stage of the consensus process, and the slower performance later. Inspired by such behavior, a switching order consensus protocol is proposed, which efficiently increases the convergence speed and ensures the exponential convergence as time tends to infinity. The disagreement of the system during the consensus procedure is investigated. Theoretic analysis and simulations demonstrate that, for certain scale‐free networks, an optimal order exists so that the fractional‐order consensus algorithm can minimize the disagreement or its integral.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society