Skip to main content
SpringerLink
Log in

Reaching Consensus in a Variable-Topology Multiagent System under Additive Random Noise

  • Large Scale Systems Control
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A discrete-time multiagent system with a fixed set of elements (particles) is studied. Particles synchronize with each other in accordance with a family of communication graphs. At each time instant (step), the system is described by a vector that updates iteratively: the state of each agent is linearly determined by the states of its neighbors and also by an additive random noise component; in addition, links between particles change over time. Thus, the system’s evolution can be modeled by an iterative process in which the state vector is multiplied by a certain stochastic matrix and added to a random vector. The goal of this paper is to analyze an index measuring the system’s closeness to a consensus. Some constraints on the family of communication graphs that are sufficient for obtaining an upper bound on this index are established. Also, a modified model in which the upper bound is satisfied under slightly weakened conditions on communication graphs is presented.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agaev, R.P, The Region of Convergence of a Differential Model of Consensus, Upravlen. Bol’sh. Sist., 2012, no. 36, pp. 81–92.

    Google Scholar 

  2. Agaev, R.P. and Chebotarev, P.Yu, On the Asymptotic Formula of Consensus Protocols, Upravlen. Bol’sh. Sist., 2013, no. 43, pp. 55–77.

    Google Scholar 

  3. Agaev, R.P. and Chebotarev, P.Yu, Convergence and Stability in Consensus and Coordination Problems: A Survey of Basic Results, Upravlen. Bol’sh. Sist., 2010, no. 30.1, pp. 470–505.

    Google Scholar 

  4. Amelina, N.O. and Fradkov, A.L, Approximate Consensus in the Dynamic Stochastic Network with Incomplete Information and Measurement Delays, Autom. Remote Control, 2012, vol. 73, no. 11, pp. 1765–1783.

    Article  MathSciNet  Google Scholar 

  5. Gantmakher, F., The Theory of Matrices, New York: Chelsea, 1959.

    Google Scholar 

  6. Horn, R.A. and Johnson, C.R., Matrix Analysis, New York: Cambridge Univ. Press, 2013.

    MATH  Google Scholar 

  7. Jadbabaie, A., Lin, J., and Morse, A.S, Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules, IEEE Trans. Autom. Control, 2003, vol. 48, no. 6, pp. 988–1001.

    Article  MathSciNet  Google Scholar 

  8. Jadbabaie, A. and Olshevsky, A, Combinatorial Bounds and Scaling Laws for Noise Amplification in Networks, Eur. Control Conf. (ECC-2013), Zürich, Switzerland, 2013, pp. 596–601.

    Chapter  Google Scholar 

  9. Manita, A. and Manita, L, Distributed Time Synchronization Algorithms and Opinion Dynamics, J. Physics: Conf. Series, 2018, vol. 955, no. 1, pp. 012–038.

    Google Scholar 

  10. Manita, A. and Manita, L, Stochastic Time Synchronization Models Based on Agreement Algorithms, in Analytical and Computational Methods in Probability Theory, New York: Springer, 2017, pp. 361–375.

    Chapter  Google Scholar 

  11. Moreau, L, Stability of Multiagent Systems with Time-Dependent Communication Links, IEEE Trans. Autom. Control, 2005, vol. 50, no. 2, pp. 169–182.

    Article  MathSciNet  Google Scholar 

  12. Olfati-Saber, R., Fax, J.A., and Murray, R.M, Consensus and Cooperation in Networked Multi-Agent Systems, Proc. IEEE, 2007, vol. 95, no. 1, pp. 215–223.

    Article  Google Scholar 

  13. Shi, G. and Johansson, K.H, The Role of Persistent Graphs in the Agreement Seeking of Social Networks, IEEE J. Select. Areas Communicat., Supplement, 2013, vol. 31, no. 9, pp. 595–606.

    Article  Google Scholar 

  14. Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I., and Shochet, O, Novel Type of Phase Transition in a System of Self-Driven Particles, Phys. Rev. Lett., 1995, vol. 75, no. 6, pp. 1226–1229.

    Article  MathSciNet  Google Scholar 

  15. Wu, C.W, Algebraic Connectivity of Directed Graphs, Lin. Multil. Algebra, 2005, vol. 53.3, pp. 203–223.

    Article  MathSciNet  Google Scholar 

  16. Young, G.F., Scardovi, L., and Leonard, N.E, Rearranging Trees for Robust Consensus, 50th IEEE Conf. on Decision and Control and Eur. Control Conf. (CDC-ECC), Orlando, December 12–15, 2011, pp. 1000–1005.

    Chapter  Google Scholar 

  17. Young, G.F., Scardovi, L., and Leonard, N.E, Robustness of Noisy Consensus Dynamics with Directed Communication, Am. Control Conf., Marriott Waterfront, Baltimore, 2010, pp. 6312–6317.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    S. I. Sheipak

Authors
  1. S. I. Sheipak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. I. Sheipak.

Additional information

Russian Text © The Author(s), 2018, published in Upravlenie Bol’shimi Sistemami, 2018, No. 74, pp. 23–41.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheipak, S.I. Reaching Consensus in a Variable-Topology Multiagent System under Additive Random Noise. Autom Remote Control 81, 911–921 (2020). https://doi.org/10.1134/S0005117920050100

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117920050100

Keywords

Search

Navigation