Stochastic approximation for consensus seeking: Mean square and almost sure convergence

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 306-311

  Huang, Minyi ^a   Manton, Jonathan H ^b  

^a CARLETON UNIVERSITY   (Canada)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; MEAN SQUARE ERROR;

NOISY MEASUREMENTS; STOCHASTIC APPROXIMATION; STOCHASTIC CONSENSUS PROBLEMS;

STOCHASTIC CONTROL SYSTEMS;

EID: 52449093845     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434630     Document Type: Conference Paper

References (32)

1. R. W. Beard and V. Stepanyan. Synchronization of information in distributed multiple vehicle coordination control. Proc. IEEE CDC Conf., Maui, Hawaii, pp. 2029-2034, Dec. 2003.
2. V. D. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis. Convergence in multiagent coordination, consensus, and nocking. Proc. 44th IEEE CDC-ECC'05, Seville, Spain, pp. 2996-3001, Dec. 2005.
3. V. Borkar and P. Varaiya. Asymptotic agreement in distributed estimation. IEEE Trans. Automat. Control, vol. 27, pp. 650-655, June 1982.
4. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah. Randomized gossip algorithms. IEEE Trans. Inf. Theory, vol. 52, pp. 2508-2530, June 2006.
5. S. Chatterjee and E. Seneta. Towards consensus: some convergence theorems on repeated averaging. J. Appl. Probab., vol. 14, pp. 89-97, 1977.
6. Y. S. Chow and H. Teicher. Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York, 1978.
7. J. Cortes, S. Martinez, and F. Bullo. Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans. Automat. Control, vol. 51, no. 8, pp. 1289-1298, Aug. 2006.
8. J. P. Desai, V. Kumar, and J. P. Ostrowski. Control of changes in formation for a team of mobile robots. Proc. IEEE Int. Conf. on Robotics and Automat., Detroit, Michigan, pp. 1556-1561, May 1999.
9. M. J. Fischer. The consensus problem in unreliable distributed systems (a brief survey). In Foundations of Computation Theory, M. Karpinsky Ed., Lecture Notes in Computer Science, vol. 158, pp. 127-140, Springer-Verlag, 1983.
10. M. H. de Groot. Reaching a consensus. J. Amer. Statist. Assoc., vol. 69, pp. 118-121, 1974.
11. M. Huang and J. H. Manton. Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior. Submitted for journal publication, Oct. 2006.
12. M. Huang and J. H. Manton. Stochastic double array analysis and convergence of consensus algorithms with noisy measurements. Proc. American Control Conference, New York, pp. 705-710, July 2007.
13. M. Huang and J. H. Manton. Stochastic Lyapunov analysis for consensus algorithms with noisy measurements. Proc. American Control Conference, New York, pp. 1419-1424, July 2007.
14. A. Jadbabaie, J. Lin, and A. S. Morse. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Contr., vol. 48, no. 6, pp. 988-1000, June 2003.
15. Y. Liu and Y. R. Yang. Reputation propagation and aggreement in wireless ad hoc networks. Proc. IEEE Wireless Commun. Network Conf., 2003.
16. N. Lynch. Distributed Algorithms. Morgan Kaufmann, San Matero, CA, 1996.
17. J. A. Marshall and M. E. Broucke. On invariance of cyclic group symmetries in multiagent formations. Proc. IEEE CDC-ECC'05, Seville, Spain, pp. 746-751, Dec. 2005.
18. B. Mohar. The Laplacian spectrum of graphs. In Graph Theory, Combinatorics, and Applications, vol. 2, pp. 871-898, Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk Eds., Wiley, 1991.
19. R. Olfati-Saber. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Automat. Contr., vol. 51, pp. 401-420, Mar. 2006.
20. R. Olfati-Saber and R. M. Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Contr., vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
21. R. Olfati-Saber, J. A. Fax, and R. M. Murray. Consensus and cooperation in networked multi-agent systems. IEEE Proc., vol. 95, pp. 215-233, Jan. 2007.
22. W. Ren, R. W. Beard, and D. B. Kingston. Multi-agent Kalman consensus with relative uncertainty. Proc. American Control Conf., Portland, OR, pp. 1865-1870, June 2005.
23. W. Ren, R. W. Beard, and E. M. Atkins. A survey of consensus problems in multi-agent coordination. Proc. American Control Conference, Portland, OR, pp. 1859-1864, June 2005.
24. E. Seneta. Non-negative Matrices and Markov Chains. 2nd ed., Springer-Verlag, New York, 1981.
25. H. G. Tanner, G. J. Pappas, and V Kumar. Input-to-state stability on formation graphs. Proc. IEEE Decision Contr. Conf, Las Vegas, NV, pp. 2439-2444, 2002.
26. H. Teicher. Almost certain convergence in double arrays. Z. Wahrscheinlichkeitstheorie verw. Gebiete, vol. 69, pp. 331-345, 1985.
27. J. N. Tsitsiklis and M. Athans. Convergence and asymptotic agreement in distributed decision problems. IEEE Trans. Automat. Control, vol. 29, no. 1, pp. 42-50, Jan. 1984.
28. J. N. Tsitsiklis, D. P. Bertsekas, and M. Athans. Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans. Automat. Contr., vol. 31, no. 9, pp. 803-812, 1986.
29. P. K. Visscher. How self-organization evolves. Nature, vol. 421, pp. 799-800, Feb. 2003.
30. R. L. Winkler. The consensus of subjective probability distributions. Management Science, vol. 15, B61-B75, 1968.
31. L. Xiao and S. Boyd. Fast linear iterations for distributed averaging, Systems and Control Letters, vol. 53, pp. 65-78, 2004.
32. L. Xiao, S. Boyd, and S.-J. Kim. Distributed average consensus with least-mean-square deviation. Journal of Parallel and Distributed Computing, vol. 67, pp. 33-46, 2007.