Robustness of First- and Second-Order Consensus Algorithms for a Noisy Scale-Free Small-World Koch Network
In this brief, we study first- and second-order consensus algorithms for the scale-free small-world Koch network, where vertices are subject to white noise. We focus on three cases of consensus schemes: (1) first-order leaderless algorithm; (2) first-order algorithm with a single leader; and (3) sec...
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Veröffentlicht in: | IEEE transactions on control systems technology 2017-01, Vol.25 (1), p.342-350 |
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description | In this brief, we study first- and second-order consensus algorithms for the scale-free small-world Koch network, where vertices are subject to white noise. We focus on three cases of consensus schemes: (1) first-order leaderless algorithm; (2) first-order algorithm with a single leader; and (3) second-order leaderless algorithm. We are concerned with the coherence of the Koch network in the H 2 norm, which captures the level of agreement of vertices in face of stochastic disturbances. Based on the particular network construction, we derive explicit expressions of the coherence for all the three consensus algorithms, as well as their dependence on the network size. Particularly, for the first-order leader-follower model, we show that coherence relies on the shortest-path distance between the leader and the largest-degree vertices, as well as the degree of the leader. The asymptotic behaviors for coherence of the three consensus algorithms in Koch network behave differently from those associated with other networks lacking scale-free small-world features, indicating significant influences of the scale-free small-world topology on the performance of the consensus algorithms in noisy environments. |
doi_str_mv | 10.1109/TCST.2016.2550582 |
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We focus on three cases of consensus schemes: (1) first-order leaderless algorithm; (2) first-order algorithm with a single leader; and (3) second-order leaderless algorithm. We are concerned with the coherence of the Koch network in the H 2 norm, which captures the level of agreement of vertices in face of stochastic disturbances. Based on the particular network construction, we derive explicit expressions of the coherence for all the three consensus algorithms, as well as their dependence on the network size. Particularly, for the first-order leader-follower model, we show that coherence relies on the shortest-path distance between the leader and the largest-degree vertices, as well as the degree of the leader. 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We focus on three cases of consensus schemes: (1) first-order leaderless algorithm; (2) first-order algorithm with a single leader; and (3) second-order leaderless algorithm. We are concerned with the coherence of the Koch network in the H 2 norm, which captures the level of agreement of vertices in face of stochastic disturbances. Based on the particular network construction, we derive explicit expressions of the coherence for all the three consensus algorithms, as well as their dependence on the network size. Particularly, for the first-order leader-follower model, we show that coherence relies on the shortest-path distance between the leader and the largest-degree vertices, as well as the degree of the leader. The asymptotic behaviors for coherence of the three consensus algorithms in Koch network behave differently from those associated with other networks lacking scale-free small-world features, indicating significant influences of the scale-free small-world topology on the performance of the consensus algorithms in noisy environments.</description><subject>Algorithms</subject><subject>Coherence</subject><subject>Distributed average consensus</subject><subject>Eigenvalues and eigenfunctions</subject><subject>First order algorithms</subject><subject>graph algorithm</subject><subject>Heuristic algorithms</subject><subject>Laplace equations</subject><subject>Network topology</subject><subject>noise</subject><subject>Noise measurement</subject><subject>Robustness</subject><subject>scale-free network</subject><subject>Shortest-path problems</subject><subject>small-world network</subject><subject>White noise</subject><issn>1063-6536</issn><issn>1558-0865</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kFFLwzAUhYMoOKc_QHwJ-JyZmzRp-ziKU3FsYCc-hqy9dZ1dM5MW2b-3Y-LTPQ_fORc-Qm6BTwB4-rDK8tVEcNAToRRXiTgjI1AqYTzR6nzIXEumldSX5CqELecQKRGPyPbNrfvQtRgCdRWd1T50jNq2pDkWri3Z0pfoaebagG3oA502n87X3WYXaOU8tXTh6nCgeWEbZDOPSPOdbRr24XxT0ldXbOgCux_nv67JRWWbgDd_d0zeZ4-r7JnNl08v2XTOChlBx1AkOtax1bIorUTOuSwlVkqqNFUihVTrdWo11wK1tAlGcVVgHGEJPLGpBjkm96fdvXffPYbObF3v2-GlgURxIQGkGCg4UYV3IXiszN7XO-sPBrg5KjVHpeao1PwpHTp3p06NiP98HGkNgstf9BxxYQ</recordid><startdate>201701</startdate><enddate>201701</enddate><creator>Yi, Yuhao</creator><creator>Zhang, Zhongzhi</creator><creator>Shan, Liren</creator><creator>Chen, Guanrong</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-1260-2079</orcidid></search><sort><creationdate>201701</creationdate><title>Robustness of First- and Second-Order Consensus Algorithms for a Noisy Scale-Free Small-World Koch Network</title><author>Yi, Yuhao ; Zhang, Zhongzhi ; Shan, Liren ; Chen, Guanrong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c341t-e286767a63cda3e0003d3ef535995291966b9a6062e63a8e47fce74ed108a9613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algorithms</topic><topic>Coherence</topic><topic>Distributed average consensus</topic><topic>Eigenvalues and eigenfunctions</topic><topic>First order algorithms</topic><topic>graph algorithm</topic><topic>Heuristic algorithms</topic><topic>Laplace equations</topic><topic>Network topology</topic><topic>noise</topic><topic>Noise measurement</topic><topic>Robustness</topic><topic>scale-free network</topic><topic>Shortest-path problems</topic><topic>small-world network</topic><topic>White noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yi, Yuhao</creatorcontrib><creatorcontrib>Zhang, Zhongzhi</creatorcontrib><creatorcontrib>Shan, Liren</creatorcontrib><creatorcontrib>Chen, Guanrong</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on control systems technology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Yi, Yuhao</au><au>Zhang, Zhongzhi</au><au>Shan, Liren</au><au>Chen, Guanrong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robustness of First- and Second-Order Consensus Algorithms for a Noisy Scale-Free Small-World Koch Network</atitle><jtitle>IEEE transactions on control systems technology</jtitle><stitle>TCST</stitle><date>2017-01</date><risdate>2017</risdate><volume>25</volume><issue>1</issue><spage>342</spage><epage>350</epage><pages>342-350</pages><issn>1063-6536</issn><eissn>1558-0865</eissn><coden>IETTE2</coden><abstract>In this brief, we study first- and second-order consensus algorithms for the scale-free small-world Koch network, where vertices are subject to white noise. We focus on three cases of consensus schemes: (1) first-order leaderless algorithm; (2) first-order algorithm with a single leader; and (3) second-order leaderless algorithm. We are concerned with the coherence of the Koch network in the H 2 norm, which captures the level of agreement of vertices in face of stochastic disturbances. Based on the particular network construction, we derive explicit expressions of the coherence for all the three consensus algorithms, as well as their dependence on the network size. Particularly, for the first-order leader-follower model, we show that coherence relies on the shortest-path distance between the leader and the largest-degree vertices, as well as the degree of the leader. 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subjects | Algorithms Coherence Distributed average consensus Eigenvalues and eigenfunctions First order algorithms graph algorithm Heuristic algorithms Laplace equations Network topology noise Noise measurement Robustness scale-free network Shortest-path problems small-world network White noise |
title | Robustness of First- and Second-Order Consensus Algorithms for a Noisy Scale-Free Small-World Koch Network |
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