Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Averaging Algorithms and Consensus

Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_214

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.

Keywords

Cooperative control Coordination Distributed control Multi-agent systems Networked systems 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Agaev R, Chebotarev P (2000) The matrix of maximum out forests of a digraph and its applications. Autom Remote Control 61(9):1424–1450MathSciNetGoogle Scholar
  2. Agaev R, Chebotarev P (2005) On the spectra of nonsymmetric Laplacian matrices. Linear Algebra Appl 399:157–178MathSciNetGoogle Scholar
  3. Bai H, Arcak M, Wen J (2011a) Cooperative control design: a systematic, passivity-based approach. Springer, New YorkGoogle Scholar
  4. 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 1500–1505Google Scholar
  5. Bullo F, Cortes J, Martinez S (2009) Distributed control of robotic networks. Princeton University Press, PrincetonGoogle Scholar
  6. 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):3169–3174MathSciNetGoogle Scholar
  7. Cortes J (2008) Discontinuous dynamical systems. IEEE Control Syst Mag 28(3):36–73MathSciNetGoogle Scholar
  8. Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001MathSciNetGoogle Scholar
  9. 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):213–224MathSciNetGoogle Scholar
  10. Mesbahi M, Egerstedt M (2010) Graph theoretic methods for multiagent networks. Princeton University Press, PrincetonGoogle Scholar
  11. Moreau L (2005) Stability of multi-agent systems with time-dependent communication links. IEEE Trans Autom Control 50(2):169–182MathSciNetGoogle Scholar
  12. Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233Google Scholar
  13. Qu Z (2009) Cooperative control of dynamical systems: applications to autonomous vehicles. Springer, LondonGoogle Scholar
  14. Ren W, Beard RW (2008) Distributed consensus in multi-vehicle cooperative control. Springer, LondonGoogle Scholar
  15. Ren W, Cao Y (2011) Distributed coordination of multi-agent networks. Springer, LondonGoogle Scholar
  16. Spanos DP, Murray RM (2005) Distributed sensor fusion using dynamic consensus. In: Proceedings of the IFAC world congress, PragueGoogle Scholar
  17. Tsitsiklis JN, Bertsekas DP, Athans M (1986) Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans Autom Control 31(9):803–812MathSciNetGoogle Scholar
  18. Yang P, Freeman RA, Lynch KM (2008) Multi-agent coordination by decentralized estimation and control. IEEE Trans Autom Control 53(11):2480–2496MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Wei Ren
    • 1
  1. 1.Department of Electrical Engineering, University of CaliforniaRiversideUSA