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Graph-balancing algorithms for average consensus over directed networks. (English) Zbl 1333.93006

Summary: Consensus strategies find extensive applications in coordination of robot groups and decision-making of agents. Since balanced graph plays an important role in the average consensus problem and many other coordination problems for directed communication networks, this work explores the conditions and algorithms for the digraph balancing problem. Based on the analysis of graph cycles, we prove that a digraph can be balanced if and only if the null space of its incidence matrix contains positive vectors. Then, based on this result and the corresponding analysis, two weight balance algorithms have been proposed, and the conditions for obtaining a unique balanced solution and a set of analytical results on weight balance problems have been introduced. Then, we point out the relationship between the weight balance problem and the features of the corresponding underlying Markov chain. Finally, two numerical examples are presented to verify the proposed algorithms.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
94C15 Applications of graph theory to circuits and networks
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[1] DOI: 10.1007/978-1-4612-0619-4 · doi:10.1007/978-1-4612-0619-4
[2] DOI: 10.1016/j.automatica.2014.01.003 · Zbl 1298.93019 · doi:10.1016/j.automatica.2014.01.003
[3] DOI: 10.1109/TAC.2012.2219953 · Zbl 1369.93021 · doi:10.1109/TAC.2012.2219953
[4] DOI: 10.1016/j.automatica.2012.11.010 · Zbl 1258.93004 · doi:10.1016/j.automatica.2012.11.010
[5] DOI: 10.1016/j.automatica.2013.02.030 · Zbl 1319.93006 · doi:10.1016/j.automatica.2013.02.030
[6] DOI: 10.1109/TAC.2015.2405294 · Zbl 1360.93277 · doi:10.1109/TAC.2015.2405294
[7] DOI: 10.1137/070679132 · Zbl 1201.93102 · doi:10.1137/070679132
[8] DOI: 10.3166/EJC.18.539-557 · Zbl 1291.93290 · doi:10.3166/EJC.18.539-557
[9] DOI: 10.1007/978-1-4613-0163-9 · doi:10.1007/978-1-4613-0163-9
[10] DOI: 10.1307/mmj/1028989917 · Zbl 0056.42103 · doi:10.1307/mmj/1028989917
[11] DOI: 10.1287/opre.18.1.87 · Zbl 0193.24702 · doi:10.1287/opre.18.1.87
[12] DOI: 10.1109/TAC.2003.812781 · Zbl 1364.93514 · doi:10.1109/TAC.2003.812781
[13] DOI: 10.1109/TSP.2009.2014812 · Zbl 1391.94268 · doi:10.1109/TSP.2009.2014812
[14] DOI: 10.1109/TAC.2007.902752 · Zbl 1366.93503 · doi:10.1109/TAC.2007.902752
[15] DOI: 10.1016/j.automatica.2013.07.016 · Zbl 1315.93005 · doi:10.1016/j.automatica.2013.07.016
[16] DOI: 10.1109/JPROC.2006.887293 · Zbl 1376.68138 · doi:10.1109/JPROC.2006.887293
[17] DOI: 10.1109/TAC.2004.834113 · Zbl 1365.93301 · doi:10.1109/TAC.2004.834113
[18] DOI: 10.1080/00207721003802271 · Zbl 1260.93003 · doi:10.1080/00207721003802271
[19] DOI: 10.1109/TFUZZ.2010.2052259 · doi:10.1109/TFUZZ.2010.2052259
[20] DOI: 10.1109/TFUZZ.2009.2017378 · doi:10.1109/TFUZZ.2009.2017378
[21] DOI: 10.1109/TAC.2005.846556 · Zbl 1365.93302 · doi:10.1109/TAC.2005.846556
[22] DOI: 10.1109/TAC.2011.2169618 · Zbl 1369.93051 · doi:10.1109/TAC.2011.2169618
[23] DOI: 10.1080/00207721.2011.618641 · Zbl 1276.93008 · doi:10.1080/00207721.2011.618641
[24] DOI: 10.1109/TAC.2008.929381 · Zbl 1367.93255 · doi:10.1109/TAC.2008.929381
[25] DOI: 10.1016/j.sysconle.2004.02.022 · Zbl 1157.90347 · doi:10.1016/j.sysconle.2004.02.022
[26] DOI: 10.1016/j.neucom.2011.09.009 · Zbl 06017376 · doi:10.1016/j.neucom.2011.09.009
[27] DOI: 10.1109/TCYB.2013.2242197 · doi:10.1109/TCYB.2013.2242197
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