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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Vydané v:	IEEE transactions on control systems technology Ročník 25; číslo 1; s. 342 - 350
Hlavní autori:	Yi, Yuhao, Zhang, Zhongzhi, Shan, Liren, Chen, Guanrong
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.01.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
ISSN:	1063-6536, 1558-0865
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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. 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.
AbstractList	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. 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 [Formula Omitted] 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.
Author	Guanrong Chen Zhongzhi Zhang Yuhao Yi Liren Shan
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Cites_doi	10.1109/CDC.2008.4739314 10.1109/TIT.2013.2243816 10.1103/PhysRevE.79.061113 10.1109/CDC.2013.6761082 10.1016/0743-7315(89)90021-X 10.1088/1751-8113/47/3/035003 10.1109/TCST.2015.2388732 10.1002/qua.560500102 10.1109/ECC.2015.7330605 10.1126/science.286.5439.509 10.1137/S003614450342480 10.1109/TAC.2012.2202052 10.1109/TCNS.2014.2357552 10.1109/TCST.2014.2317793 10.1109/TAC.2013.2281473 10.1016/j.tcs.2010.11.036 10.1073/pnas.252631999 10.1109/TCST.2013.2256787 10.1109/TAC.2005.864190 10.1109/CDC.2011.6161307 10.1109/TAC.2014.2314223 10.1016/S0167-8191(99)00018-6 10.1088/1751-8113/45/2/025102 10.2307/2285509 10.1109/ACC.2014.6859421 10.1109/ACC.2010.5531506 10.1093/comjnl/bxv014 10.1016/j.jpdc.2006.08.010 10.1090/gsm/056 10.1109/TAC.2007.895897 10.1016/j.dam.2014.01.015 10.1038/35065725 10.1109/CDC.2010.5718151 10.1016/j.tcs.2014.12.024 10.1038/30918 10.1109/CDC.2012.6425812 10.1109/TSP.2010.2077282 10.1007/s002240000092 10.1038/35019019 10.1038/nature06940 10.1109/JPROC.2006.887293 10.1109/TAC.2004.834433 10.1109/CDC.2011.6161507 10.1109/ACC.2012.6315183 10.1103/PhysRevLett.86.3200 10.1109/TC.2006.25
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References	ref13 ref34 ref12 ref37 ref15 ref14 ref31 ref30 ref33 ref11 ref32 ref10 xiao (ref18) 2007; 67 ref1 ref39 ref17 ref38 ref16 ref19 lynch (ref2) 1996 watts (ref36) 1998; 393 barabási (ref35) 1999; 286 ref46 ref24 ref45 ref23 ref48 ref26 ref47 ref25 ref20 ref42 ref41 ref22 ref44 ref21 wang (ref43) 2008 ref28 ref27 ref29 ref8 ref7 cybenko (ref3) 1989; 7 ref9 ref4 ref6 ref5 ref40
References_xml	– ident: ref19 doi: 10.1109/CDC.2008.4739314 – ident: ref22 doi: 10.1109/TIT.2013.2243816 – ident: ref44 doi: 10.1103/PhysRevE.79.061113 – ident: ref32 doi: 10.1109/CDC.2013.6761082 – volume: 7 start-page: 279 year: 1989 ident: ref3 article-title: Dynamic load balancing for distributed memory multiprocessors publication-title: J Parallel Distrib Comput doi: 10.1016/0743-7315(89)90021-X – ident: ref46 doi: 10.1088/1751-8113/47/3/035003 – ident: ref12 doi: 10.1109/TCST.2015.2388732 – ident: ref45 doi: 10.1002/qua.560500102 – ident: ref30 doi: 10.1109/ECC.2015.7330605 – start-page: 748 year: 2008 ident: ref43 article-title: Consensus on scale-free network publication-title: Proc Amer Control Conf – volume: 286 start-page: 509 year: 1999 ident: ref35 article-title: Emergence of scaling in random networks publication-title: Science doi: 10.1126/science.286.5439.509 – ident: ref34 doi: 10.1137/S003614450342480 – ident: ref16 doi: 10.1109/TAC.2012.2202052 – ident: ref17 doi: 10.1109/TCNS.2014.2357552 – ident: ref11 doi: 10.1109/TCST.2014.2317793 – ident: ref28 doi: 10.1109/TAC.2013.2281473 – ident: ref25 doi: 10.1016/j.tcs.2010.11.036 – ident: ref37 doi: 10.1073/pnas.252631999 – ident: ref10 doi: 10.1109/TCST.2013.2256787 – ident: ref8 doi: 10.1109/TAC.2005.864190 – ident: ref15 doi: 10.1109/CDC.2011.6161307 – ident: ref29 doi: 10.1109/TAC.2014.2314223 – ident: ref5 doi: 10.1016/S0167-8191(99)00018-6 – ident: ref47 doi: 10.1088/1751-8113/45/2/025102 – ident: ref1 doi: 10.2307/2285509 – ident: ref24 doi: 10.1109/ACC.2014.6859421 – ident: ref20 doi: 10.1109/ACC.2010.5531506 – ident: ref23 doi: 10.1093/comjnl/bxv014 – volume: 67 start-page: 33 year: 2007 ident: ref18 article-title: Distributed average consensus with least-mean-square deviation publication-title: J Parallel Distrib Comput doi: 10.1016/j.jpdc.2006.08.010 – ident: ref48 doi: 10.1090/gsm/056 – ident: ref9 doi: 10.1109/TAC.2007.895897 – ident: ref38 doi: 10.1016/j.dam.2014.01.015 – ident: ref33 doi: 10.1038/35065725 – ident: ref14 doi: 10.1109/CDC.2010.5718151 – ident: ref39 doi: 10.1016/j.tcs.2014.12.024 – volume: 393 start-page: 440 year: 1998 ident: ref36 article-title: Collective dynamics of 'small-world' networks publication-title: Nature doi: 10.1038/30918 – ident: ref31 doi: 10.1109/CDC.2012.6425812 – ident: ref21 doi: 10.1109/TSP.2010.2077282 – ident: ref4 doi: 10.1007/s002240000092 – ident: ref40 doi: 10.1038/35019019 – ident: ref42 doi: 10.1038/nature06940 – ident: ref13 doi: 10.1109/JPROC.2006.887293 – ident: ref6 doi: 10.1109/TAC.2004.834433 – year: 1996 ident: ref2 publication-title: Distributed Algorithms – ident: ref26 doi: 10.1109/CDC.2011.6161507 – ident: ref27 doi: 10.1109/ACC.2012.6315183 – ident: ref41 doi: 10.1103/PhysRevLett.86.3200 – ident: ref7 doi: 10.1109/TC.2006.25
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SubjectTerms	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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