Skip to main content
SpringerLink
Log in

Averaging Algorithms and Consensus

  • Reference work entry
  • First Online:
Encyclopedia of Systems and Control

  • 378 Accesses

Abstract

In this article, we overview averaging algorithms and consensus in the context of distributed coordination and control of networked systems. The two subjects are closely related but not identical. Distributed consensus means that a team of agents reaches an agreement on certain variables of interest by interacting with their neighbors. Distributed averaging aims at computing the average of certain variables of interest among multiple agents by local communication. Hence averaging can be treated as a special case of consensus – average consensus. For distributed consensus, we introduce distributed algorithms for agents with single-integrator, general linear, and nonlinear dynamics. For distributed averaging, we introduce static and dynamic averaging algorithms. The former is useful for computing the average of initial conditions (or constant signals), while the latter is useful for computing the average of time-varying signals. Future research directions are also discussed.

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 899.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
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

Bibliography

  • Agaev R, Chebotarev P (2000) The matrix of maximum out forests of a digraph and its applications. Autom Remote Control 61(9):1424–1450

    MathSciNet  Google Scholar 

  • Agaev R, Chebotarev P (2005) On the spectra of nonsymmetric Laplacian matrices. Linear Algebra Appl 399:157–178

    MathSciNet  Google Scholar 

  • Bai H, Arcak M, Wen J (2011a) Cooperative control design: a systematic, passivity-based approach. Springer, New York

    Google Scholar 

  • Bai H, Freeman RA, Lynch KM (2011b) Distributed Kalman filtering using the internal model average consensus estimator. In: Proceedings of the American control conference, San Francisco, pp 1500–1505

    Google Scholar 

  • Bullo F, Cortes J, Martinez S (2009) Distributed control of robotic networks. Princeton University Press, Princeton

    Google Scholar 

  • Chen F, Cao Y, Ren W (2012) Distributed average tracking of multiple time-varying reference signals with bounded derivatives. IEEE Trans Autom Control 57(12):3169–3174

    MathSciNet  Google Scholar 

  • Cortes J (2008) Discontinuous dynamical systems. IEEE Control Syst Mag 28(3):36–73

    MathSciNet  Google Scholar 

  • Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001

    MathSciNet  Google Scholar 

  • Li Z, Duan Z, Chen G, Huang L (2010) Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Trans Circuits Syst I Regul Pap 57(1):213–224

    MathSciNet  Google Scholar 

  • Mesbahi M, Egerstedt M (2010) Graph theoretic methods for multiagent networks. Princeton University Press, Princeton

    Google Scholar 

  • Moreau L (2005) Stability of multi-agent systems with time-dependent communication links. IEEE Trans Autom Control 50(2):169–182

    MathSciNet  Google Scholar 

  • Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233

    Google Scholar 

  • Qu Z (2009) Cooperative control of dynamical systems: applications to autonomous vehicles. Springer, London

    Google Scholar 

  • Ren W, Beard RW (2008) Distributed consensus in multi-vehicle cooperative control. Springer, London

    Google Scholar 

  • Ren W, Cao Y (2011) Distributed coordination of multi-agent networks. Springer, London

    Google Scholar 

  • Spanos DP, Murray RM (2005) Distributed sensor fusion using dynamic consensus. In: Proceedings of the IFAC world congress, Prague

    Google Scholar 

  • Tsitsiklis JN, Bertsekas DP, Athans M (1986) Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans Autom Control 31(9):803–812

    MathSciNet  Google Scholar 

  • Yang P, Freeman RA, Lynch KM (2008) Multi-agent coordination by decentralized estimation and control. IEEE Trans Autom Control 53(11):2480–2496

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, University of California, Riverside, CA, USA

    Wei Ren

Authors
  1. Wei Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mechanical Engineering, Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Honeywell Automation and Control Solutions, Golden Valley, MN, USA

    Tariq Samad

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag London

About this entry

Cite this entry

Ren, W. (2015). Averaging Algorithms and Consensus. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_214

Download citation

Publish with us

Policies and ethics

Search

Navigation