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Agreement over noisy networks

Agreement over noisy networks

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  • Author(s): A.K. Das 1 ; Y. Hatano 2 ; M. Mesbahi 3
    • View affiliations
    • Affiliations: 1: Applied Physics Laboratory, University of Washington, Seattle, USA
      2: Department of Mechanical Engineering, University of Washington, Seattle, USA
      3: Department of Aeronautics and Astronautics, University of Washington, Seattle, USA
  • Source: Volume 4, Issue 11, November 2010, p. 2416 – 2426
    DOI:  10.1049/iet-cta.2009.0394 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

The authors consider the agreement problem over noisy communication networks. This problem is analysed via a blend of ideas from stochastic stability (supermartingales) and algebraic graph theory (spectra of graph Laplacians). In this venue, the authors show that the noisy agreement protocol has a guaranteed probabilistic convergence, provided that an embedded step size meets a graph theoretic constraint. The authors then proceed to define a pertinent graph parameter and point out the ramifications of having noisy information exchange links in networks that can be modelled as random and random geometric graphs.

Inspec keywords: telecommunication links; graph theory; convergence; stability; protocols; probability; stochastic processes; telecommunication networks

Other keywords: noisy information exchange link; stochastic stability; noisy communication network; algebraic graph theory; noisy agreement protocol; graph Laplacians; agreement problem; random geometric graph; supermartingales; probabilistic convergence

Subjects: Protocols; Combinatorial mathematics; Other topics in statistics; Telecommunication applications

References

    1. 1)
      • D. Bertsekas , J. Tsitsiklis . (1999) Parallel and distributed computation.
    2. 2)
      • Das, A.K., Mesbahi, M.: `Distributed linear parameter estimation in sensor networks based on dynamic consensus algorithm', Proc. IEEE SECON, 2006, Reston, Virginia.
    3. 3)
      • B. Bollobás . (2001) Random graphs.
    4. 4)
      • T.K. Philips , S.S. Panwar , A.N. Tantawi . Connectivity properties of a packet radio network model. IEEE Trans. Inf. Theory , 1044 - 1047
    5. 5)
      • A.N. Shiryayev . (1984) Probability.
    6. 6)
      • R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control , 49 , 1520 - 1533
    7. 7)
      • W.B. Davenport . (1987) Probability and random processes.
    8. 8)
      • A. Ramamoorthy , J. Shi , R.D. Wesel . On the capacity of network coding for random networks. IEEE Trans. Inf. Theory , 51 , 2878 - 2885
    9. 9)
      • A. Jadbabaie , J. Lin , A.S. Morse . Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control , 48 , 988 - 1001
    10. 10)
      • Olshevsky, A., Tsitsiklis, J.N.: `Convergence rates in distributed consensus and averaging', IEEE Conf. on Decision Control, 2006, San Diego, California.
    11. 11)
      • R.S. Bucy . Stability and positive supermartingales. J. Differ. Equ. , 1 , 151 - 155
    12. 12)
      • P. Gupta , P.R. Kumar , W.H. Fleming , W.M. McEneaney , G. Yin , Q. Zhang . (1999) Critical power for asymptotic connectivity in wireless networks, Stochastic analysis, control, optimization and applications.
    13. 13)
      • H. Kushner . (1967) Stochastic stability and control.
    14. 14)
      • T. Vicsek , A. Czirok , E.B. Jacob , I. Cohen , O. Schochet . Novel type of phase transitions in a system of self-driven particles. Phys. Rev. Lett. , 1226 - 1229
    15. 15)
      • M. Penrose . (2003) Random geometric graphs.
    16. 16)
      • Zhang, H., Hou, J.C.: `Capacity of wireless ad-hoc networks under ultra wide band with power constraint', Proc. IEEE INFOCOM, 2005, Miami, Florida.
    17. 17)
      • N. Biggs . (1993) Algebraic graph theory.
    18. 18)
      • Y. Hatano , M. Mesbahi . Agreement over random networks. IEEE Trans. Autom. Control , 50 , 1867 - 1872
    19. 19)
      • Li, X.-Y., Wan, P.-J., Wang, Y.: `Fault tolerant deployment and topology control in wireless networks', Proc. MobiHoc, 2003, Annapolis, Maryland.
    20. 20)
      • L. Moreau . Stability of multiagent systems with time-dependent communication links. IEEE Trans. Autom. Control , 50 , 169 - 182
    21. 21)
      • F. Xue , P.R. Kumar . The number of neighbors needed for connectivity of wireless networks. Wirel. Netw. , 169 - 181
    22. 22)
      • B.T. Polyak . (1987) Introduction to optimization.
    23. 23)
      • J.A. Fax , R.M. Murray . Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control , 49 , 1465 - 1476
    24. 24)
      • J. Cortes , S. Martinez , F. Bullo . Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans. Autom. Control , 8 , 1289 - 1298
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