Skip to main content
SpringerLink
Log in

Quasi-Interval Bipartite Consensus Problems on Discrete-Time Signed Networks

  • Conference paper
  • First Online:
Book cover Proceedings of 2018 Chinese Intelligent Systems Conference

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 528))

  • 948 Accesses

Abstract

In this paper, discrete-time signed networks with cooperative and antagonistic interactions are considered in the presence of time-varying topologies. A separation approach is proposed such that the cooperations and antagonisms can be clearly distinguished. It is shown that given the repeated joint strong connectivity, signed networks can achieve bipartite consensus (respectively, stability) if and only if the repeated joint structural balance (respectively, unbalance) are ensured. Furthermore, when only joint spanning tree condition is satisfied, quasi-interval bipartite consensus (respectively, stability) holds if and only if the repeated joint structural balance (respectively, unbalance) can be guaranteed for the signed digraphs formed by only these joint root nodes. The simulation tests are included to verify the effectiveness of our obtained results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. L. Jure, H. Daniel, K. Jon, Signed networks in social media, in Proceedings of the 28th International Conference on Human Factors in Computing Systems, Atlanta, GA, USA, April 2010, pp. 1361–1370

    Google Scholar 

  2. A. Daron, O. Asuman, Opinion dynamics and learning in social networks. Dyn. Games Appl. 1(1), 3–49 (2011)

    Article  MathSciNet  Google Scholar 

  3. A.V. Proskurnikov, A. Matveev, M. Cao, Opinion dynamics in social networks with hostile camps: consensus vs. polarization. IEEE Trans. Autom. Control 61(6), 1524–1536 (2016)

    Article  MathSciNet  Google Scholar 

  4. M.E. Valcher, P. Misra, On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Syst. Control Lett. 66(66), 94–103 (2014)

    Article  MathSciNet  Google Scholar 

  5. J. Hu, W. Zheng, Bipartite consensus for multi-agent systems on directed signed networks, in Proceeding of the 52nd IEEE Conference on Decision and Control (Florence, Italy, 2013), pp. 3452–3456

    Google Scholar 

  6. H. Zhang, J. Chen, Bipartite consensus of multiagent systems over signed graphs: state feedback and output feedback control approaches. Int. J. Robust Nonlinear Control 27(1), 3–14 (2017)

    Article  Google Scholar 

  7. W. Ren, R.W. Beard, Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)

    Article  Google Scholar 

  8. R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)

    Article  Google Scholar 

  9. W. Ren, R.W. Beard, Distributed consensus in multi-vehicle cooperative control. Commun. Control Eng. 27(2), 71–82 (2008)

    MATH  Google Scholar 

  10. W. Xia, M. Cao, K.H. Johansson, Structural balance and opinion separation in trust-mistrust social networks. IEEE Trans. Control Netw. Syst. 3(1), 46–56 (2015)

    Article  MathSciNet  Google Scholar 

  11. C. Altafini, Consensus problems on networks with antagonistic interactions. IEEE Trans. Autom. Control 58(4), 935–946 (2013)

    Article  MathSciNet  Google Scholar 

  12. D. Meng, M. Du, Y. Jia, Interval bipartite consensus of networked agents associated with signed digraphs. IEEE Trans. Autom. Control 61(12), 3755–3770 (2016)

    Article  MathSciNet  Google Scholar 

  13. Z. Meng, G. Shi, K.H. Johansson, M. Cao, Y. Hong, Behaviors of networks with antagonistic interactions and switching topologies. Automatica 73, 110–116 (2016)

    Article  MathSciNet  Google Scholar 

  14. J. Liu, X. Chen, T. Basar, M.A. Belabbas, Exponential convergence of the discrete and continuous-time Altafini’s models. IEEE Trans. Autom. Control 62(12), 6168–6182 (2017)

    Article  MathSciNet  Google Scholar 

  15. J.M. Hendrickx, A lifting approach to models of opinion dynamics with antagonisms, in Proceedings of the IEEE Conference on Decision and Control (Los Angeles, CA, USA, 2014), pp. 2118–2123

    Google Scholar 

  16. D. Meng, Convergence analysis of directed signed networks via an M-matrix approach. Int. J. Control, https://doi.org/10.1080/00207179.2017.1294263

  17. D. Cartwright, F. Harary, Structural balance: a generalization of Heider’s theory. Psychol. Rev. 63(5), 9–25 (1977)

    Google Scholar 

  18. R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, 1985)

    Google Scholar 

  19. D. Meng, Z. Meng, Y. Hong, A state transition matrix-based approach to separation of cooperations and antagonisms in opinion dynamics. arXiv:1705.04430

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (61873013, 61473010, 61473015, 61520106010), in part by the Beijing Natural Science Foundation (4162036), and in part by the Fundamental Research Funds for the Central Universities.

Author information

Authors and Affiliations

  1. The Seventh Research Division, Beihang University (BUAA), Beijing, China

    Jianqiang Liang & Deyuan Meng

  2. School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China

    Jianqiang Liang & Deyuan Meng

Authors
  1. Jianqiang Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Deyuan Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deyuan Meng .

Editor information

Editors and Affiliations

  1. Beihang University, Beijing, China

    Yingmin Jia

  2. Beijing University of Posts and Telecommunications, Beijing, China

    Junping Du

  3. University of Science and Technology Beijing, Beijing, China

    Weicun Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Liang, J., Meng, D. (2019). Quasi-Interval Bipartite Consensus Problems on Discrete-Time Signed Networks. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2018 Chinese Intelligent Systems Conference. Lecture Notes in Electrical Engineering, vol 528. Springer, Singapore. https://doi.org/10.1007/978-981-13-2288-4_2

Download citation

Publish with us

Policies and ethics

Search

Navigation