skip to main content
10.1145/1967701.1967742acmconferencesArticle/Chapter ViewAbstractPublication PagescpsweekConference Proceedingsconference-collections
research-article

Consensus in networked multi-agent systems with adversaries

Published:12 April 2011Publication History

ABSTRACT

In the past decade, numerous consensus protocols for networked multi-agent systems have been proposed. Although some forms of robustness of these algorithms have been studied, reaching consensus securely in networked multi-agent systems, in spite of intrusions caused by malicious agents, or adversaries, has been largely underexplored. In this work, we consider a general model for adversaries in Euclidean space and introduce a consensus problem for networked multi-agent systems similar to the Byzantine consensus problem in distributed computing. We present the Adversarially Robust Consensus Protocol (ARC-P), which combines ideas from consensus algorithms that are resilient to Byzantine faults and from linear consensus protocols used for control and coordination of dynamic agents. We show that ARC-P solves the consensus problem in complete networks whenever there are more cooperative agents than adversaries. Finally, we illustrate the resilience of ARC-P to adversaries through simulations and compare ARC-P with a linear consensus protocol for networked multi-agent systems.

References

  1. N. Agmon and D. Peleg. Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput., 36(1):56--82, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. F. Blanchini. Set invariance in control. Automatica, 35(11):1747--1767, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. F. Blanchini and S. Miani. Set-Theoretic Methods in Control. Birkhauser, Boston, Massachusetts, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Z. Bouzid, M. Gradinariu Potop-Butucaru, and S. Tixeuil. Byzantine convergence in robot networks: The price of asynchrony. In Int. Conf. on Principles of Distributed Systems, pages 54--70, December 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. M. H. DeGroot. Reaching a consensus. Journal of the American Statistical Association, 69(345):118--121, 1974.Google ScholarGoogle ScholarCross RefCross Ref
  6. D. Dolev, N. A. Lynch, S. S. Pinter, E. W. Stark, and W. E. Weihl. Reaching approximate agreement in the presence of faults. Journal of the ACM, 33(3):499--516, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. A. Fagiolini, F. Babboni, and A. Bicchi. Dynamic distributed intrusion detection for secure multi-robot systems. In Int. Conf. of Robotics and Aut., pages 2723--2728, May 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. A. Fagiolini, A. Bicchi, G. Dini, and I. Savino. Tolerating malicious monitors in detecting misbehaving robots. In IEEE Int. Workshop on Safety, Security, and Rescue Robotics, pages 108--114, October 2008.Google ScholarGoogle Scholar
  9. A. Fagiolini, M. Pellinacci, M. Valenti, G., G. Dini, and A. Bicchi. Consensus-based distributed intrusion detection for multi-robot systems. In Int. Conf. on Robotics and Aut., pages 120--127, May 2008.Google ScholarGoogle ScholarCross RefCross Ref
  10. J. A. Fax and R. M. Murray. Information flow and cooperative control of vehicle formations. IEEE Trans. on Aut. Control, 49(9):1465--1476, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  11. S. Gilbert, N. Lynch, S. Mitra, and T. Nolte. Self-stabilizing robot formations over unreliable networks. ACM Trans. Auton. Adapt. Syst., 4(3):1--29, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. V. Gupta, C. Langbort, and R. Murray. On the robustness of distributed algorithms. In IEEE Conf. on Decision and Control, December 2006.Google ScholarGoogle ScholarCross RefCross Ref
  13. P. Hovareshti, J. Baras, and V. Gupta. Average consensus over small world networks: A probabilistic framework. In IEEE Conf. on Decision and Control, December 2008.Google ScholarGoogle ScholarCross RefCross Ref
  14. M. Huang and J. Manton. Stochastic Lyapunov analysis for consensus algorithms with noisy measurements. In American Control Conf., July 2007.Google ScholarGoogle ScholarCross RefCross Ref
  15. Q. Hui, W. Haddad, and S. Bhat. On robust control algorithms for nonlinear network consensus protocols. Int. J. Robust Nonlinear Control, 20(3):269--284, 2010.Google ScholarGoogle ScholarCross RefCross Ref
  16. L. Lamport, R. Shostak, and M. Pease. The Byzantine generals problem. ACM Trans. Program. Lang. Syst., 4(2):382--401, 1982. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. D. Lee and M. Spong. Agreement with non-uniform information delays. In American Control Conf., pages 756--761, June 2006.Google ScholarGoogle Scholar
  18. N. A. Lynch. Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco, California, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. M. Mesbahi and M. Egerstedt. Graph Theoretic Methods in Multiagent Networks. Princeton University Press, Princeton, New Jersey, 2010.Google ScholarGoogle Scholar
  20. R. Olfati-Saber. Ultrafast consensus in small-world networks. In American Control Conf., pages 2371--2378, June 2005.Google ScholarGoogle ScholarCross RefCross Ref
  21. R. Olfati-Saber, J. A. Fax, and R. M. Murray. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1):215--233, 2007.Google ScholarGoogle ScholarCross RefCross Ref
  22. R. Olfati-Saber, E. Franco, E. Frazzoli, and J. Shamma. Belief consensus and distributed hypothesis testing in sensor networks. In Networked Embedded Sensing and Control, volume 331 of Lecture Notes in Control and Information Sciences, pages 169--182. Springer Berlin / Heidelberg, 2006.Google ScholarGoogle Scholar
  23. R. Olfati-Saber and R. M. Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. on Aut. Control, 49(9):1520--1533, September 2004.Google ScholarGoogle ScholarCross RefCross Ref
  24. L. Pallottino, V. G. Scordio, E. Frazzoli, and A. Bicchi. Decentralized cooperative policy for conflict resolution in multi-vehicle systems. IEEE Trans. on Robotics, 23(6):1170--1183, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. F. Pasqualetti, A. Bicchi, and F. Bullo. Distributed intrusion detection for secure consensus computations. In IEEE Conf. on Decision and Control, pages 5594--5599, December 2007.Google ScholarGoogle ScholarCross RefCross Ref
  26. F. Pasqualetti, A. Bicchi, and F. Bullo. On the security of linear consensus networks. In IEEE Conf. on Decision and Control, December 2009.Google ScholarGoogle ScholarCross RefCross Ref
  27. F. Pasqualetti, R. Carli, A. Bicchi, and F. Bullo. Identifying cyber attacks via local model information. In IEEE Conf. on Decision and Control, December 2010.Google ScholarGoogle ScholarCross RefCross Ref
  28. M. Pease, R. Shostak, and L. Lamport. Reaching agreement in the presence of faults. J. ACM, 27(2):228--234, 1980. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. G. Prencipe. CORDA: Distributed coordination of a set of autonomous mobile robots. In Proc. 4th European Research Seminar on Advances in Distributed Systems, pages 185--190, May 2001.Google ScholarGoogle Scholar
  30. D. Spanos, R. Olfati-Saber, and R. Murray. Approximate distributed Kalman filtering in sensor networks with quantifiable performance. In 4th Int. Symp. on Information Processing in Sensor Networks, pages 133--139, April 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. S. Sundaram and C. Hadjicostis. Distributed function calculation via linear iterations in the presence of malicious agents; part II: Overcoming malicious behavior. In American Control Conf., pages 1356--1361, June 2008.Google ScholarGoogle ScholarCross RefCross Ref
  32. I. Suzuki and M. Yamashita. Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing, 28:1347--1363, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. H. Tanner, G. Pappas, and V. Kumar. Leader-to-formation stability. IEEE Trans. on Robotics and Automation, 20(3):443--455, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  34. S. Vanka, V. Gupta, and M. Haenggi. Power-delay analysis of consensus algorithms on wireless networks with interference. Int. J. Syst., Control Commun., 2(1/2/3):256--274, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. W. Wang and J.-J. Slotine. Contraction analysis of time-delayed communications and group cooperation. IEEE Trans. on Aut. Control, 51(4):712--717, April 2006.Google ScholarGoogle ScholarCross RefCross Ref
  36. L. Xiao, S. Boyd, and S. Lall. A scheme for robust distributed sensor fusion based on average consensus. In 4th Int. Symp. on Information Processing in Sensor Networks, pages 63--70, April 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Consensus in networked multi-agent systems with adversaries

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in
        • Published in

          cover image ACM Conferences
          HSCC '11: Proceedings of the 14th international conference on Hybrid systems: computation and control
          April 2011
          330 pages
          ISBN:9781450306294
          DOI:10.1145/1967701
          • General Chair:
          • Marco Caccamo,
          • Program Chairs:
          • Emilio Frazzoli,
          • Radu Grosu

          Copyright © 2011 ACM

          Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 12 April 2011

          Permissions

          Request permissions about this article.

          Request Permissions

          Check for updates

          Qualifiers

          • research-article

          Acceptance Rates

          Overall Acceptance Rate153of373submissions,41%

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader