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Bipartite Consensus Control for Coupled Harmonic Oscillators Using Sampled Data with Measurement Noise

  • Jun Liu
  • Hengyu LiEmail author
  • Jun Luo
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 582)

Abstract

This paper investigates the bipartite consensus issue of coupled harmonic oscillators by considering measurement noise under cooperation–competition network topology. By introducing the definition of bipartite consensus in mean square associate with networked harmonic oscillator systems, a bipartite consensus algorithms which only use sampled velocity data of agents in network are given. Finally, we present an example to illustrate the corresponding theoretical results.

Keywords

Harmonic oscillators Cooperation–competition network Measurement noise Bipartite consensus 

References

  1. 1.
    Ren, W., Cao, Y.: Distributed coordination of multi-agent networks: emergent problems, models, and issues. Springer, London (2011)CrossRefGoogle Scholar
  2. 2.
    Tuna, S.E.: Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks. Automatica 75, 236–243 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ren, W.: Synchronization of coupled harmonic oscillators with local interaction. Automatica 44(2), 3195–3200 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wei, B., Xiao, F.: Event-triggered control for synchronization of coupled harmonic oscillators. Syst. Control Lett. 97, 163–168 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhou, J., Zhang, H., Xiang, L., Wu, Q.: Synchronization of coupled harmonic oscillators with local instantaneous interaction. Automatica 48(8), 1715–1721 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhang, H., Zhou, J.: Synchronization of sampled-data coupled harmonic oscillators with control inputs missing. Syst. Control Lett. 61(12), 1277–1285 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, J., Feng, J., Xu, C., Chen, M.Z., Zhao, Y., Feng, J.: The synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise. Automatica 66, 155–162 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Wang, J., Feng, J., Xu, C., Zhao, Y.: Almost sure exponential synchronisation of networked harmonic oscillators via intermittent coupling subject to Markovian jumping. IET Control Theor. Appl. 12(11), 1658–1664 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Liu, J., Ji, J., Zhou, J., Xiang, L., Zhao, L.: Adaptive group consensus in uncertain networked EulerLagrange systems under directed topology. Nonlinear Dyn. 82(3), 1145–1157 (2015)CrossRefGoogle Scholar
  10. 10.
    Altafini, C.: Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Control 58(4), 935–946 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hu, J., Zheng, W.X.: Emergent collective behaviors on coopetition networks. Phys. Lett. A 378(26), 1787–1796 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hu, J., Geng, J., Zhu, H.: An observer-based consensus tracking control and application to event-triggered tracking. Commun. Nonlinear Sci. Numer. Simul. 20(2), 559–570 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wang, H., Yu, W., Wen, G., Chen, G.: Finite-time bipartite consensus for multi-agent systems on directed signed networks. IEEE Trans. Circ. Syst. I Reg. Pap. 65(12), 4336–4348 (2018)CrossRefGoogle Scholar
  14. 14.
    Xia, W., Cao, M., Johansson, K.H.: Structural balance and opinion separation in trustmistrust social networks. IEEE Trans. Control Netw. Syst. 3(1), 46–56 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Liu, J., Li, H., Luo, J.: Bipartite consensus control for coupled harmonic oscillators under a coopetitive network topology. IEEE Access 6, 3706–3714 (2018)CrossRefGoogle Scholar
  16. 16.
    Yang T.: Impulsive control theory, vol. 272. In: Lecture Notes in Control and Information Sciences. Springer (2001)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsJining UniversityQufuPeople’s Republic of China
  2. 2.School of Mechatronic Engineering and AutomationShanghai UniversityShanghaiPeople’s Republic of China

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