Skip to main content
SpringerLink
Log in

Discrete-Time Dynamic Consensus on the Max Value

  • Conference paper
  • First Online:
15th European Workshop on Advanced Control and Diagnosis (ACD 2019) (ACD 2019 2018)

Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

Included in the following conference series:

Abstract

In this paper, we propose a novel consensus protocol for discrete-time multi-agent systems (MAS), which solves the dynamic consensus problem on the max value, the so-called dynamic max-consensus problem. In the dynamic max-consensus problem, the objective of each agent is to estimate the time-varying value of the maximum instantaneous value among the reference signals associated to the agents in the network, by exploiting only local interactions. The proposed interaction protocol enables the agents to solve this problem with an a priori bounded error, without exchange of input information among the agents. Furthermore, the proposed protocol can be tuned by means of a tuning parameter, enabling a trade-off between convergence time and steady-state error. We also provide a preliminary characterization of the maximum relative tracking error. Numerical simulations corroborate the theoretical analysis of the convergence properties of the proposed protocol.

This work was supported in part by the Italian Ministry of Research and Education (MIUR) with the grant “CoNetDomeSys”, code RBSI14OF6H, under call SIR 2014 and by Region Sardinia (RAS) with project MOSIMA, RASSR05871, FSC 2014-2020, Annualità 2017, Area Tematica 3, Linea d’Azione 3.1.

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 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
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

Notes

  1. 1.

    Note that by increasing the sampling frequency of the unknown reference exogenous signals their relative change in one iteration is reduced, thus for any signal with bounded relative change there exists a sampling frequency such that Assumption 22.1 is satisfied.

  2. 2.

    The round up function \(\lceil \cdot \rceil \) denotes the operation of rounding the argument to the first integer greater than or equal to the argument.

References

  1. Spanos, D.P., Olfati-Saber, R., Murray, R.M.: Dynamic consensus on mobile networks. In: IFAC World Congress, pp. 1–6 (2005)

    Google Scholar 

  2. Freeman, R.A., Yang, P., Lynch, K.M.: Stability and convergence properties of dynamic average consensus estimators. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 338–343 (2006)

    Google Scholar 

  3. Zhu, M., Martínez, S.: Discrete-time dynamic average consensus. Automatica 46(2), 322–329 (2010)

    Article  MathSciNet  Google Scholar 

  4. Montijano, E., Montijano, J.I., Sagüs, C., Martínez, S.: Robust discrete time dynamic average consensus. Automatica 50(12), 3131–3138 (2014)

    Article  MathSciNet  Google Scholar 

  5. Franceschelli, M., Gasparri, A.: Multi-stage discrete time and randomized dynamic average consensus. Automatica 99, 69–81 (2019)

    Article  MathSciNet  Google Scholar 

  6. Bai, H., Freeman, R.A., Lynch, K.M.: Robust dynamic average consensus of time-varying inputs. In: 49th IEEE Conference on Decision and Control, pp. 3104–3109 (2010)

    Google Scholar 

  7. Scoy, B.V., Freeman, R.A., Lynch, K.M.: A fast robust nonlinear dynamic average consensus estimator in discrete time. In: 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems NecSys 2015, vol. 48, no. 22, pp. 191–196 (2015)

    Google Scholar 

  8. Kia, S.S., Cortés, J., Martínez, S.: Dynamic average consensus under limited control authority and privacy requirements. Int. J. Robust Nonlinear Control. 25(13), 1941–1966 (2015)

    Article  MathSciNet  Google Scholar 

  9. Franceschelli, M., Frasca, P.: Proportional dynamic consensus in open multi-agent systems. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 900–905 (2018)

    Google Scholar 

  10. Dengchang, Z., Zhulin, A., Yongjun, X.: Time synchronization in wireless sensor networks using max and average consensus protocol. Int. J. Distrib. Sens. Netw. 2013, 03 (2013)

    Google Scholar 

  11. Petitti, A., Di Paola, D., Rizzo, A., Cicirelli, G.: Consensus-based distributed estimation for target tracking in heterogeneous sensor networks. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference, pp. 6648–6653 (2011)

    Google Scholar 

  12. Lucchese, R., Varagnolo, D., Delvenne, J., Hendrickx, J.: Network cardinality estimation using max consensus: the case of bernoulli trials. In: 2015 54th IEEE Conference on Decision and Control (CDC), pp. 895–901 (2015)

    Google Scholar 

  13. Borsche, T., Attia, S.A.: On leader election in multi-agent control systems. In: 2010 Chinese Control and Decision Conference, pp. 102–107 (2010)

    Google Scholar 

  14. Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  15. Nejad, B.M., Attia, S.A., Raisch, J.: Max-consensus in a max-plus algebraic setting: the case of fixed communication topologies. In: 2009 XXII International Symposium on Information, Communication and Automation Technologies, pp. 1–7 (2009)

    Google Scholar 

  16. Nejad, B.M., Attia, S.A., Raisch, J.: Max-consensus in a max-plus algebraic setting: the case of switching communication topologies. In: 10th IFAC Workshop on Discrete Event Systems IFAC Proceedings Volumes, vol. 43, no. 12, pp. 173–180 (2010)

    Google Scholar 

  17. Iutzeler, F., Ciblat, P., Jakubowicz, J.: Analysis of max-consensus algorithms in wireless channels. IEEE Trans. Signal Process. 60(11), 6103–6107 (2012)

    Article  MathSciNet  Google Scholar 

  18. Giannini, S., Petitti, A., Di Paola, D., Rizzo, A.: Asynchronous max-consensus protocol with time delays: convergence results and applications. IEEE Trans. Circuits Syst. I: Regul. Pap. 63(2), 256–264 (2016)

    Google Scholar 

  19. Zhang, S., Tepedelenlioǧlu, C., Banavar, M.K., Spanias, A.: Max consensus in sensor networks: non-linear bounded transmission and additive noise. IEEE Sens. J. 16(24), 9089–9098 (2016)

    Article  Google Scholar 

  20. Abdelrahim M., Hendrickx J.M., Heemels, M.H.W.P.: Max-consensus in open multi-agent systems with gossip interactions. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 4753–4758 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Cagliari, 09123, Cagliari, Italy

    Diego Deplano, Mauro Franceschelli & Alessandro Giua

Authors
  1. Diego Deplano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mauro Franceschelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alessandro Giua
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Diego Deplano .

Editor information

Editors and Affiliations

  1. Department of Electrical, Electronic and Information Engineering “G. Marconi”, Alma Mater Studiorum Università di Bologna, Bologna, Italy

    Elena Zattoni

  2. Department of Engineering, University of Ferrara, Ferrara, Italy

    Silvio Simani

  3. Department of Information Engineering, Polytechnic University of Marche, Ancona, Italy

    Giuseppe Conte

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Deplano, D., Franceschelli, M., Giua, A. (2022). Discrete-Time Dynamic Consensus on the Max Value. In: Zattoni, E., Simani, S., Conte, G. (eds) 15th European Workshop on Advanced Control and Diagnosis (ACD 2019). ACD 2019 2018. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-85318-1_22

Download citation

Publish with us

Policies and ethics

Search

Navigation