New Internal Model Average Consensus Estimators with Light Communication Load

  • Juwon Lee
  • Juhoon Back
Regular Papers Control Theory and Applications


The dynamic average consensus problem for a group of agents is considered. Each agent in the group is supposed to estimate the average of inputs applied to all agents and the estimation should be done in a distributed way. By reinterpreting the proportional integral type estimator, a new structure for the average estimator which can embed the internal model of inputs is proposed and conditions which result in the zero estimation error in the steady state are derived. We present constructive design procedures for the cases of constant inputs and time-varying inputs employing the root locus for the former and LQR-based design for the latter. The theory is validated through numerical simulations.


Consensus distributed system multi-agent network system state estimation 


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  1. [1]
    A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 998–1001, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J. A. Fax and R. M. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465–1476, 2004.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    F. Bullo, J. Cortés, and S. Martínez, Distributed Control of Robotic Networks, Princeton Univ., Princeton, NJ, 2009.CrossRefzbMATHGoogle Scholar
  5. [5]
    M. Mesbahi and M. Egerstedt, Graph Theoretic Methods for Multiagent Networks, Princeton Univ., NJ, 2010.CrossRefzbMATHGoogle Scholar
  6. [6]
    W. Ren and Y. Cao, Distributed Coordination of Multi-Agent Networks, Springer-Verlag, London, U.K., 2011.CrossRefzbMATHGoogle Scholar
  7. [7]
    W. Ren, R. W. Beard, and E. M. Atkins, “Information consensus in multivehicle cooperative control: Collective group behavior through local interaction,” IEEE Control Syst. Mag., vol. 27, no. 2, pp. 71–82, 2007.CrossRefGoogle Scholar
  8. [8]
    Y. Cao, W. Yu, W. Ren, and G. Chen, “An overview of recent progress in the study of distributed multi-agent coordination,” IEEE Trans. on Industrial Informatics, Special Issue on Advances in Theories and Industrial Applications of Networked Control Systems, vol. 9, no. 1, pp. 427–438, 2013.Google Scholar
  9. [9]
    D. Subhro and J. M. Moura, “Distributed Kalman filtering with dynamic observations consensus,” IEEE Transactions on Signal Processing, vol. 63, no. 17, pp. 4458–4473, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Q. Zhirong, X. Lihua, and Y. Hong, “Quantized leaderless and leader-following consensus of high-order multi-agent systems with limited data rate,” IEEE Transactions on Automatic Control, vol. 61, no. 9, pp. 2432–2447, 2016.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J. Cortés, “Distirbuted kriged kalman filter for spatial estimation,” IEEE Transactions on Automatic Control, vol. 54, no. 12, pp. 2816–2827, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    K. M. Lynch, I. B. Schwartz, P. Yang, and R. A. Freeman, “Decentralized environment modeling by mobile sensor networks,” IEEE Transactions on Robotics, vol. 24, no. 3, pp. 710–724, 2008.CrossRefGoogle Scholar
  13. [13]
    A. Cherukuri and J. Cortés, “Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment,” Automatica, vol. 74, pp.183-193, 2016.Google Scholar
  14. [14]
    P. Yi, Y. Hong, and F. Liu, “Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems,” Automatica, vol. 74, pp. 259–269, 2016MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    S. S. Kia, “Distributed optimal in-network resource allocation algorithm design via a control theoretic approach,” Systems & Control Letters, vol. 107, pp. 49–57, 2017.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    D. P. Spanos, R. Olfati-Saber, and R. M. Murray, “Dynamic consensus for mobile networks,” IFAC World Congress, Prague, Czech Republic, 2005.Google Scholar
  17. [17]
    H. Bai, R. A. Freeman, and K. M. Lynch, “Robust dynamic average consensus of time-varying inputs,” Proc. of IEEE Conference on Decision and Control, pp. 3104–3109, Atlanta, GA, USA, 2010.Google Scholar
  18. [18]
    S. Nosrati, M. Shafiee, and M. B. Menhaj, “Dynamic average consensus via nonlinear protocols,” Automatica, vol. 48, no. 9, pp. 2262–2270, 2012.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M. Zhu and S. Martínez, “Discrete-time dynamic average consensus,” Automatica, vol. 46, no. 2, pp. 322–329, 2010.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    E. Montijano, J. I. Montijano, C. Sagüés, and S. Martínez, “Robust discrete time dynamic average consensus,” Automatica, vol. 50, no. 12, pp. 3131–3138, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    S. S. Kia, J. Cortés, and S. Martínez, “Dynamic average consensus under limited control authority and privacy requirements,” International Journal of Robust and Nonlinear Control, vol. 25, no. 13, pp. 1941–1966, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    S. S. Kia, B. V. Scoy, J. Cortés, R. A. Freeman, K. M. Lynch, and S. Martínez, “Tutorial on dynamic average consensus: the problem, its applications, and the algorithms,” arXiv preprint arXiv:1803.04628, 2018.Google Scholar
  23. [23]
    R. A. Freeman, P. Yang, and K. M. Lynch, “Stability and convergence properties of dynamic average consensus estimators,” Proc. of IEEE Confernce on Decision and Control, pp. 398–403, San Diego, USA, 2006.Google Scholar
  24. [24]
    B. A. Francis and W. M. Wonham, “The internal model principle of control theory,” Automatica, vol. 12, no. 5, pp. 457–465, 1976.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    C. T. Chen, Linear System Theory and Design, 4th edition, Oxford University Press, 2012.Google Scholar
  26. [26]
    S. E. Tuna, “LQR-based coupling gain for synchronization of linear systems,” IEEE, arXiv [Online]_Available: http: //, 2008.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of RoboticsKwangwoon UniversitySeoulKorea

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