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A Survey on Distributed Estimation and Control Applications Using Linear Consensus Algorithms

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Networked Control Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 406))

Abstract

In this chapter we present a popular class of distributed algorithms, known as linear consensus algorithms, which have the ability to compute the global average of local quantities. These algorithms are particularly suitable in the context of multi-agent systems and networked control systems, i.e. control systems that are physically distributed and cooperate by exchanging information through a communication network. We present the main results available in the literature about the analysis and design of linear consensus algorithms,for both synchronous and asynchronous implementations. We then show that many control, optimization and estimation problems such as least squares, sensor calibration, vehicle coordination and Kalman filtering can be cast as the computation of some sort of averages, therefore being suitable for consensus algorithms. We finally conclude by presenting very recent studies about the performance of many of these control and estimation problems, which give rise to novel metrics for the consensus algorithms. These indexes of performance are rather different from more traditional metrics like the rate of convergence and have fundamental consequences on the design of consensus algorithms.

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References

  1. Alighanbari, M., How, J.P.: An unbiased Kalman consensus algorithm. In: Proceedings of IEEE American Control Conference, ACC 2006 (2006)

    Google Scholar 

  2. Angeli, D., Bliman, P.-A.: Tight estimates for non-stationary consensus with fixed underlying spanning tree. In: Proceedings of 17th IFAC World Congress, IFAC 2008 (2008)

    Google Scholar 

  3. Aysal, T.C., Yildiz, M.E., Sarwate, A.D., Scaglione, A.: Broadcast gossip algorithms for consensus. IEEE Transactions on Signal Processing 57(7), 2748–2761 (2009)

    Article  MathSciNet  Google Scholar 

  4. Bamieh, B., Jovanovic, M., Mitra, P., Patterson, S.: Coherence in large-scale networks: Dimension dependent limitations of local feedback. In: IEEE Trans. Aut. Cont. (to appear, 2010)

    Google Scholar 

  5. Barooah, P.: Estimation and Control with Relative Measurements: Algorithms and Scaling Laws. PhD thesis, University of California, Santa Barbara (2007)

    Google Scholar 

  6. Bauso, D., Giarré, L., Pesenti, R.: Nonlinear protocols for optimal distributed consensus in networks of dynamic agents. Systems and Control Letters 55, 918–928 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bliman, P.A., Ferrari-Trecate, G.: Average consensus problems in networks of agents with delayed communications. In: Proceedings of 44th IEEE Conference on Decision and Control, CDC 2005, vol. 44(8), pp. 1985–1995 (2008)

    Google Scholar 

  8. Blondel, V.D., Hendrickx, J.M., Olshevsky, A., Tsitsiklis, J.N.: Convergence in multiagent coordination, consensus, and flocking. In: Proceedings of 44th IEEE Conference on Decision and Control (CDC 2005) and European Control Conference (ECC 2005), pp. 2996–3000 (December 2005)

    Google Scholar 

  9. Bolognani, S., Del Favero, S., Schenato, L., Varagnolo, D.: Consensus-based distributed sensor calibration and least-square parameter identification in WSNs. International Journal of Robust and Nonlinear Control 20(2), 176–193 (2010)

    Article  MathSciNet  Google Scholar 

  10. Boyd, S., Diaconis, P., Parrilo, P., Xiao, L.: Symmetry analysis of reversible Markov chains. Internet Mathematics 2, 31–71 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms. IEEE Transactions on Information Theory/ACM Transactions on Networking 52(6), 2508–2530 (2006)

    MathSciNet  Google Scholar 

  12. Bullo, F., Cortés, J., Martínez, S.: Distributed Control of Robotic Networks. Applied Mathematics Series. Princeton University Press, Princeton (2009)

    MATH  Google Scholar 

  13. Cao, M., Morse, A.S., Anderson, B.D.O.: Reaching a consensus in a dynamically changing environment– a graphical approach. SIAM Journal on Control and Optimization 47(2), 575–600 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Carli, R., Chiuso, A., Schenato, L., Zampieri, S.: Distributed Kalman filtering based on consensus strategies. IEEE Journal on Selected Areas in Communications 26(4), 622–633 (2008)

    Article  Google Scholar 

  15. Carli, R., Chiuso, A., Zampieri, S., Schenato, L.: A PI consensus controller for networked clocks synchronization. In: IFAC World Congress on Automatic Control, IFAC 2008 (2008)

    Google Scholar 

  16. Carli, R., Como, G., Frasca, P., Garin, F.: Average consensus on digital noisy networks. In: Proc. of 1st IFAC Workshop on Estimation and Control of Networked Systems (NecSys 2009), September 24-26, 2009, pp. 36–41 (2009)

    Google Scholar 

  17. Carli, R., Fagnani, F., Speranzon, A., Zampieri, S.: Communication constraints in the average consensus problem. Automatica 44(3), 671–684 (2008)

    Article  MathSciNet  Google Scholar 

  18. Carli, R., Frasca, P., Fagnani, F., Zampieri, S.: Gossip consensus algorithms via quantized communication. Automatica 46, 70–80 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  19. Carli, R.: Some issues on the Average Consensus Problem. PhD thesis, Università di Padova, Italy (2008)

    Google Scholar 

  20. Carli, R., Garin, F., Zampieri, S.: Quadratic indices for the analysis of consensus algorithms. In: Proc. of the 4th Information Theory and Applications Workshop, La Jolla, CA, USA, pp. 96–104 (Feburary 2009)

    Google Scholar 

  21. Cortés, J.: Distributed algorithms for reaching consensus on general functions. Automatica 44, 726–737 (2008)

    Article  Google Scholar 

  22. Cortes, J., Martinez, S., Bullo, F.: Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Transactions on Automatic Control 51(8), 1289–1298 (2006)

    Article  MathSciNet  Google Scholar 

  23. Delvenne, J.-C., Carli, R., Zampieri, S.: Optimal strategies in the average consensus problem. In: Proc. of the IEEE Conference on Decision and Control 2007, pp. 2498–2503 (2007)

    Google Scholar 

  24. Delvenne, J.-C., Carli, R., Zampieri, S.: Optimal strategies in the average consensus problem. Systems and Control Letters 58, 759–765 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  25. Fagnani, F., Zampieri, S.: Asymmetric randomized gossip algorithms for consensus. In: Proceedings of 17th IFAC World Congress, IFAC 2008 (2008)

    Google Scholar 

  26. Fagnani, F., Zampieri, S.: Randomized consensus algorithms over large scale networks. IEEE Journal on Selected Areas in Communications 26(4), 634–649 (2008)

    Article  Google Scholar 

  27. Fagnani, F., Zampieri, S.: Average consensus with packet drop communication. SIAM Journal on Control and Optimization 48, 102–133 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  28. Fax, J.F., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control 49(9), 1465–1476 (2004)

    Article  MathSciNet  Google Scholar 

  29. Frasca, P., Carli, R., Fagnani, F., Zampieri, S.: Average consensus on networks with quantized communication. International Journal of Robust and Non-Linear Control 19(16), 1787–1816 (2009)

    Article  MathSciNet  Google Scholar 

  30. Frommer, A., Szyld, D.B.: On asynchronous iterations. Journal of Computation and Applied Mathematics 123, 201–216 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  31. Hatano, Y., Mesbahi, M.: Agreement over random networks. IEEE Transactions on Automatic Control 50(11), 1867–1872 (2005)

    Article  MathSciNet  Google Scholar 

  32. Huang, M., Manton, J.H.: Coordination and consensus of networked agents with noisy measurements: Stochastic algorithms and asymptotic behavior. SIAM Journal on Control and Optimization 48(1), 134–161 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  33. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  34. Kar, S., Moura, J.M.F., Ramanan, K.: Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication (submitted, 2008)

    Google Scholar 

  35. Kar, S., Moura, J.M.F.: Distributed consensus algorithms in sensor networks with imperfect communication: Link failures and channel noise. IEEE Transactions on Signal Processing 57(5), 355–369 (2009)

    Article  MathSciNet  Google Scholar 

  36. Kar, S., Moura, J.M.F.: Distributed consensus algorithms in sensor networks: Quantized data and random link failures. IEEE Transactions on Signal Processing 58(3), 1383–1400 (2010)

    Article  MathSciNet  Google Scholar 

  37. Kashyap, A., Başar, T., Srikant, R.: Quantized consensus. Automatica 43(7), 1192–1203 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  38. Lavaei, J., Murray, R.M.: On quantized consensus by means of gossip algorithm–Part I: Convergence proof. In: Proceedings of the American Control Conference, ACC 2009 (2009)

    Google Scholar 

  39. Minc, H.: Nonnegative matrices. John Wiley & Sons, Chichester (1988)

    MATH  Google Scholar 

  40. Moreau, L.: Stability of continuous-time distributed consensus algorithms. In: Proceedings of the 43rd IEEE Conference on Decision and Control (CDC 2004), vol. 4, pp. 3998–4003 (December 2004)

    Google Scholar 

  41. Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 50(2), 169–182 (2005)

    Article  MathSciNet  Google Scholar 

  42. Muthukrihnan, S., Ghosh, B., Schultz, M.H.: First and second order diffusive methods for rapid, coarse, distributed load balancing. Theory of Computing Systems 31, 331–354 (1998)

    Article  MathSciNet  Google Scholar 

  43. Nedić, A., Olshevsky, A., Ozdaglar, A., Tsitsiklis, J.N.: On distributed averaging algorithms and quantization effects. IEEE Transaction on Automatic Control 54(11), 2506–2517 (2009)

    Article  Google Scholar 

  44. Olfati-Saber, R.: Ultrafast consensus in small-world networks. In: Proceedings of the 2005 American Control Conference ACC 2005, vol. 4, pp. 2371–2378 (2005)

    Google Scholar 

  45. Olfati-Saber, R.: Algebraic connectivity ratio of ramanujan graphs. In: Proceedings of the 2007 American Control Conference (July 2007)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  47. Patterson, S., Bamieh, B., El-Abbadi, A.: Convergence rates of distributed average consensus with stochastic link failures. IEEE Transactions on Automatic Control (2009)

    Google Scholar 

  48. Penrose, M.: Random Geometric Graphs. Oxford University Press, Oxford (2003)

    Book  MATH  Google Scholar 

  49. Rajagopal, R., Wainwright, M.J.: Network-based consensus averaging with general noisy channels. Technical Report 751, Dept. of Statistics, UC Berkeley (2008)

    Google Scholar 

  50. Ren, W., Beard, R.W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control 50(5), 655–661 (2005)

    Article  MathSciNet  Google Scholar 

  51. Ren, W., Beard, R.W., Atkins, E.M.: Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine 27(2), 71–82 (2007)

    Article  Google Scholar 

  52. Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in multi-agent networked systems. Proceedings of IEEE 95(1), 215–233 (2007)

    Article  Google Scholar 

  53. Seneta, E.: Non-negative Matrices and Markov Chains. John Wiley & Sons, Inc., Springer (2006)

    Google Scholar 

  54. Seuret, A., Dimarogonas, D.V., Johansson, K.H.: Consensus under communication delays. In: Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, pp. 4922–4927 (December 2008)

    Google Scholar 

  55. Spanos, D.P., Olfati-Saber, R., Murray, R.M.: Distributed Kalman filtering in sensor networks with quantifiable performance. In: Proccedings of the Information Processing for Sensor Networks IPSN 2005, pp. 133–139 (2005)

    Google Scholar 

  56. Strikwerda, J.C.: A probabilistic analysis of asynchronous iteration. Journal of Linear Algebra and its Applications 349, 125–154 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  57. Tahbaz-Salehi, A., Jadbabaie, A.: Small world phenomenon, rapidly mixing Markov chains, and average consensus algorithms. In: Proceedings of IEEE Conference on Decision and Control, CDC 2007, pp. 276–281 (2007)

    Google Scholar 

  58. Tahbaz-Salehi, A., Jadbabaie, A.: Consensus over ergodic stationary graph processes. IEEE Transaction on Automatic Control 54(12) (2009)

    Google Scholar 

  59. Tanner, H., Jadbabaie, A., Pappas, G.J.: Flocking in fixed and switching networks. IEEE Transaction on Automatic Control 52(5), 863–868 (2007)

    Article  MathSciNet  Google Scholar 

  60. Tanner, H.G., Christodoulakis, D.K.: The stability of synchronization in local-interaction networks is robust with respect to time delays. In: Proceedings of the 44th IEEE Conference on Decision and Control, CDC 2005, pp. 4945–4950 (December 2005)

    Google Scholar 

  61. Tsitsiklis, J.N., Athans, M.: Convergence adn asymptotic agreement in distributed decision problems. IEEE Transactions on Automatic Control 29(1), 42–50 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  62. Xiao, F., Wang, L.: Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica 44(10), 2577–2582 (1998)

    Article  MathSciNet  Google Scholar 

  63. Xiao, L., Boyd, S.: Fast linear iterations for distributed averaging. Systems and Control Letters 53(1), 65–78 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  64. Xiao, L., Boyd, S., Kim, S.-J.: Distributed average consensus with least-mean-square deviation. Journal of Parallel and Distributed Computing 67(1), 33–46 (2007)

    Article  MATH  Google Scholar 

  65. Xiao, L., Boyd, S., Lall, S.: A scheme for robust distributed sensor fusion based on average consensus. In: Proceedings of the Information Processing for Sensor Networks, IPSN 2005, pp. 63–70 (2005)

    Google Scholar 

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Author information

Authors and Affiliations

  1. INRIA Grenoble Rhône-Alpes, France

    Federica Garin

  2. Department of Information Engineering, University of Padova, Italy

    Luca Schenato

Authors
  1. Federica Garin
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  2. Luca Schenato
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Editors and Affiliations

  1. Fac. Ingegneria, Dipto. Ingegneria, dell’Informazione, Università Siena, Via Roma 56, 53100, Siena, Italy

    Alberto Bemporad

  2. Dept. Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Maurice Heemels

  3. School of Electrical Engineering, Automatic Control Laboratory, Royal Institute of Technology (KTH), Osquldas väg 10, 100 44, Stockholm, Fl. 6, Sweden

    Mikael Johansson

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Garin, F., Schenato, L. (2010). A Survey on Distributed Estimation and Control Applications Using Linear Consensus Algorithms. In: Bemporad, A., Heemels, M., Johansson, M. (eds) Networked Control Systems. Lecture Notes in Control and Information Sciences, vol 406. Springer, London. https://doi.org/10.1007/978-0-85729-033-5_3

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  • DOI: https://doi.org/10.1007/978-0-85729-033-5_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-032-8

  • Online ISBN: 978-0-85729-033-5

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