Advertisement

Efficient Quantization in the Average Consensus Problem

  • Ruggero Carli
  • Sandro Zampieri
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 353)

Abstract

In the average consensus a set of linear systems has to be driven to the same final state which corresponds to the average of their initial states. This mathematical problem can be seen as the simplest example of coordination task and in fact it can be used to model both the control of multiple autonomous vehicles which all have to be driven to the centroid of the initial positions, and to model the decentralized estimation of a quantity from multiple measure coming from distributed sensors. In general we can expect that the performance of a consensus strategy will be strongly related to the amount of information the agents exchange each other. This contribution presents a consensus strategy in which the exchanged data are symbols and not real numbers. This is based on a logarithmic quantizer based state estimator. The stability of this technique is then analyzed.

Keywords

Distributed Estimations Quantization Distributed Algorithms Consensus Multiagent Systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mazo M., Speranzon A, Johansson K H, Hu X (2004) Multi-robot tracking of a moving object using directional sensors, Proceedings of 2004 International Conference on Robotics and Automation (ICRA)Google Scholar
  2. 2.
    Fax J A, Murray R M (2004) Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control, 49: 1465–1476CrossRefMathSciNetGoogle Scholar
  3. 3.
    Olfati-Saber R, Murray R M (2004) Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49:1520–1533CrossRefMathSciNetGoogle Scholar
  4. 4.
    Olfati-Saber R (2005) Distributed Kalman filter with embedded consensus filters, Proceedings of 44th IEEE Conference on Decision and Control-European Control Conference, 8179–8184Google Scholar
  5. 5.
    Carli R, Fagnani F, Speranzon A, Zampieri S (2006) Communication constraints in coordinated consensus problem, Proceedings of 2006 American Control ConferenceGoogle Scholar
  6. 6.
    Cortes J, Martinez S, Bullo F (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions, IEEE Transactions on Automatic Control, 51: 1289:1298CrossRefMathSciNetGoogle Scholar
  7. 7.
    Jadbabaie A, Lin J, Morse A S (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48:988–1001CrossRefMathSciNetGoogle Scholar
  8. 8.
    D’Andrea R, Dullerud G E, Distributed control design for spatially interconnected systems, IEEE Transactions on Automatic Control, 48:1478–1495Google Scholar
  9. 9.
    Marodi M, D’Ovidio F, Vicksek T (2002) Synchronization of oscillators with long range interaction: Phase transition and anomalous finite size effects, Phisical Review E, 66Google Scholar
  10. 10.
    Strogatz S H (2000) From Kuramoto to Crawford: exploring the onset of synchronization of in populations of coupled oscillators, Phisical D: Nonlinear Phenomena, 143:1–20zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hatano Y, Meshabi M (2004) Agreement of random networks, Proceedings of 43rd IEEE Conference on Decision and ControlGoogle Scholar
  12. 12.
    Carli R, Fagnani F, Speranzon A, Zampieri S (2006) Communication constraints in coordinated consensus problem, Proocedings of the 2006 American Control ConferenceGoogle Scholar
  13. 13.
    Tanner H G, Jadbabaie A, Pappas G J (2003) Stable flocking of mobile agents, part i: fixed topology, Proocedings of the 42th IEEE Conference on Decision and ControlGoogle Scholar
  14. 14.
    Tanner H G, Jadbabaie A, Pappas G J (2003) Stable flocking of mobile agents, part ii: dynamic topology. Proocedings of the 42th IEEE Conference on Decision and ControlGoogle Scholar
  15. 15.
    Beard R W, Lawton J, Hadaegh F Y (2001) A coordination architecture for spacecraft formation control, IEEE Transactions on Control Systems Technology, 9:777–790CrossRefGoogle Scholar
  16. 16.
    Bhatta P., Leonard N E (2002) Stabilization and coordination of underwater gliders, Proceedings of 41th IEEE Conference on Decision and ControlGoogle Scholar
  17. 17.
    Elia M, Mitter S J (2001) Stabilization of linear systems with limited information, IEEE Transactions on Automatic and Control, 46:1384–1400zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Carli R, Fagnani F, Speranzon A, Zampieri S (2005) Communication constraints in the state agreement problem, In Technical Report N.32, Politecnico di Torino, Submitted to AutomaticaGoogle Scholar
  19. 19.
    Carli R, Fagnani F, Zampieri S (2006) On the state agreement with quantized information, Proceedings of 17th International Symposium on Mathematical Theory of Networks and SystemsGoogle Scholar
  20. 20.
    Kashyap A, Basar T, Srikant R (2006), Consensus with quantized information updates, Proceedings of 45th IEEE Conference on Decision and ControlGoogle Scholar
  21. 21.
    Nair G, Fagnani F, Zampieri S, Evans R (2006) Feedback control under data rate constraints: an overview, Proceedings of 45th IEEE Conference on Decision and ControlGoogle Scholar
  22. 22.
    Blanchini F, Miani S (2003) Stabilization of LPV systems: state feedback, state estimation and duality, SIAM Journal on Control and Optimization, 32:76–97CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ruggero Carli
    • 1
  • Sandro Zampieri
    • 1
  1. 1.Department of Information EngineeringUniversità di PadovaItaly

Personalised recommendations