Skip to main content
Top

2016 | OriginalPaper | Chapter

13. Design and Analysis of Reset Strategy for Consensus in Networks with Cluster Pattern

Authors : Marcos Cesar Bragagnolo, Irinel-Constantin Morărescu, Jamal Daafouz, Pierre Riedinger

Published in: Delays and Networked Control Systems

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter addresses the problem of consensus in networks partitioned in several disconnected clusters. Each cluster is represented by a fixed, directed, and strongly connected graphs. In order to enforce the consensus, we assume that each cluster poses a leader that can reset its state by taking into account other leaders state. First, we characterize the consensus value of this model. Second, we provide sufficient condition in LMI form for the stability of the consensus. Finally, we perform a decay rate analysis and design the interaction network of the leaders which allows to reach a prescribed consensus value.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference R. Hegselmann, U. Krause: Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artif. Soc. Soc. Simul. 5(3) (2002) R. Hegselmann, U. Krause: Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artif. Soc. Soc. Simul. 5(3) (2002)
2.
go back to reference O. Ratmann, C. Wiuf, J.W. Pinney, From evidence to inference: probing the evolution of protein interaction networks. HFSP J. 3(5), 290–306 (2009)CrossRef O. Ratmann, C. Wiuf, J.W. Pinney, From evidence to inference: probing the evolution of protein interaction networks. HFSP J. 3(5), 290–306 (2009)CrossRef
3.
go back to reference D. Gfeller, P. De Los, Rios: spectral coarse graining and synchronization in oscillator networks. Phys. Rev. Lett. 100, 174104 (2008)CrossRef D. Gfeller, P. De Los, Rios: spectral coarse graining and synchronization in oscillator networks. Phys. Rev. Lett. 100, 174104 (2008)CrossRef
4.
go back to reference V.D. Blondel, J.-L. Guillaume, R. Lambiotte, E. Lefebvre, Fast unfolding of communities in large networks. J Stat. Mech: Theory Exp. P10008(10) (2008) V.D. Blondel, J.-L. Guillaume, R. Lambiotte, E. Lefebvre, Fast unfolding of communities in large networks. J Stat. Mech: Theory Exp. P10008(10) (2008)
5.
go back to reference S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)MathSciNetCrossRef S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)MathSciNetCrossRef
7.
go back to reference I.-C. Morărescu, A. Girard, Opinion dynamics with decaying confidence: application to community detection in graphs. IEEE Trans. Autom. Control 56(8), 1862–1873 (2011)MathSciNetCrossRef I.-C. Morărescu, A. Girard, Opinion dynamics with decaying confidence: application to community detection in graphs. IEEE Trans. Autom. Control 56(8), 1862–1873 (2011)MathSciNetCrossRef
8.
go back to reference M.E.J. Newman, Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA 103(23), 8577–8582 (2006)CrossRef M.E.J. Newman, Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA 103(23), 8577–8582 (2006)CrossRef
9.
go back to reference M.E.J. Newman, M. Girvan, Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004) M.E.J. Newman, M. Girvan, Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)
10.
go back to reference A. Jadbabaie, J. Lin, A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)MathSciNetCrossRef A. Jadbabaie, J. Lin, A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)MathSciNetCrossRef
11.
go back to reference L. Moreau, Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)MathSciNetCrossRef L. Moreau, Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)MathSciNetCrossRef
12.
go back to reference I.-C. Morărescu, S.-I. Niculescu, A. Girard, Consensus with constrained convergence rate and time-delays. in IFAC Worksop on Time-Delay Systems (TDS) (2010) I.-C. Morărescu, S.-I. Niculescu, A. Girard, Consensus with constrained convergence rate and time-delays. in IFAC Worksop on Time-Delay Systems (TDS) (2010)
13.
go back to reference R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRef R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRef
14.
go back to reference R. Olfati-Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetCrossRef R. Olfati-Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetCrossRef
15.
go back to reference W. Ren, R.W. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)MathSciNetCrossRef W. Ren, R.W. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)MathSciNetCrossRef
16.
go back to reference A. Olshevsky, J.N. Tsitsiklis, Convergence speed in distributed consensus and averaging. SIAM J. Control Optim. 48(1), 33–55 (2009)MathSciNetCrossRefMATH A. Olshevsky, J.N. Tsitsiklis, Convergence speed in distributed consensus and averaging. SIAM J. Control Optim. 48(1), 33–55 (2009)MathSciNetCrossRefMATH
18.
go back to reference B. Touri, A. Nedic, On approximations and ergodicity classes in random chains. IEEE Trans. Autom. Control 57(11), 2718–2730 (2012)MathSciNetCrossRefMATH B. Touri, A. Nedic, On approximations and ergodicity classes in random chains. IEEE Trans. Autom. Control 57(11), 2718–2730 (2012)MathSciNetCrossRefMATH
19.
go back to reference M. Fiacchini, I.-C. Morărescu, Set theory based condition in LMI form for network topology preservation for decentralized control. in IEEE Conference on Decision and Control (CDC) (2012) M. Fiacchini, I.-C. Morărescu, Set theory based condition in LMI form for network topology preservation for decentralized control. in IEEE Conference on Decision and Control (CDC) (2012)
20.
go back to reference M.M. Zavlanos, G.J. Pappas, Distributed connectivity control of mobile networks. IEEE Trans. Robot. 24(6), 1416–1428 (2008)CrossRef M.M. Zavlanos, G.J. Pappas, Distributed connectivity control of mobile networks. IEEE Trans. Robot. 24(6), 1416–1428 (2008)CrossRef
21.
go back to reference B.D.O. Anderson, C. Yu, A.S. Morse, in Convergence of Periodic Gossiping Algorithms (Springer, 2010) B.D.O. Anderson, C. Yu, A.S. Morse, in Convergence of Periodic Gossiping Algorithms (Springer, 2010)
22.
go back to reference T.C. Aysal, M.E. Yildriz, A.D. Sarwate, A. Scaglione, Broadcast gossip algorithms for consensus. IEEE Trans. Sig. Process. 57, 2748–2761 (2009)MathSciNetCrossRef T.C. Aysal, M.E. Yildriz, A.D. Sarwate, A. Scaglione, Broadcast gossip algorithms for consensus. IEEE Trans. Sig. Process. 57, 2748–2761 (2009)MathSciNetCrossRef
23.
24.
go back to reference J. Liu, B.D.O. Anderson, M. Cao, A.S. Morse, Analysis of accelerated gossip algorithms. inIEEE Conference on Decision and Control (CDC) (2009) J. Liu, B.D.O. Anderson, M. Cao, A.S. Morse, Analysis of accelerated gossip algorithms. inIEEE Conference on Decision and Control (CDC) (2009)
25.
go back to reference M.C. Bragagnolo, I.C. Morărescu, J. Daafouz, P. Riedinger, LMI sufficient conditions for the consensus of linear agents with nearly-periodic resets. in IEEE American Control Conference (ACC) (2014) M.C. Bragagnolo, I.C. Morărescu, J. Daafouz, P. Riedinger, LMI sufficient conditions for the consensus of linear agents with nearly-periodic resets. in IEEE American Control Conference (ACC) (2014)
26.
go back to reference A. Banos, J. Carrasco, A. Barreiro, Reset times-dependent stability of reset control systems. IEEE Trans. Autom. Control 56(1), 217–223 (2011)MathSciNetCrossRef A. Banos, J. Carrasco, A. Barreiro, Reset times-dependent stability of reset control systems. IEEE Trans. Autom. Control 56(1), 217–223 (2011)MathSciNetCrossRef
27.
go back to reference O. Beker, C.V. Hollot, Y. Chait, Plant with an integrator: an example of reset control overcoming limitations of linear feedback. IEEE Trans. Autom. Control 46(11), 1797–1799 (2001)MathSciNetCrossRefMATH O. Beker, C.V. Hollot, Y. Chait, Plant with an integrator: an example of reset control overcoming limitations of linear feedback. IEEE Trans. Autom. Control 46(11), 1797–1799 (2001)MathSciNetCrossRefMATH
29.
go back to reference L. Hetel, J. Daafouz, S. Tarbouriech, C. Prieur, Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Anal: Hybrid Syst. 7, 4–15 (2013)MathSciNetMATH L. Hetel, J. Daafouz, S. Tarbouriech, C. Prieur, Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Anal: Hybrid Syst. 7, 4–15 (2013)MathSciNetMATH
30.
go back to reference T. Yucelen, W.M. Haddad, E.N. Johnson, Consensus protocols for networked multiagent systems with a uniformly continuous quasi-resetting architecture. in IEEE American Control Conference (ACC) (2013) T. Yucelen, W.M. Haddad, E.N. Johnson, Consensus protocols for networked multiagent systems with a uniformly continuous quasi-resetting architecture. in IEEE American Control Conference (ACC) (2013)
Metadata
Title
Design and Analysis of Reset Strategy for Consensus in Networks with Cluster Pattern
Authors
Marcos Cesar Bragagnolo
Irinel-Constantin Morărescu
Jamal Daafouz
Pierre Riedinger
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-32372-5_13