Edge agreement: Graph-theoretic performance bounds and passivity analysis

IEEE Transactions on Automatic Control

Volumn 56, Issue 3, 2011, Pages 544-555

  Zelazo, Daniel ^a   Mesbahi, Mehran ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Agreement protocol; consensus; networked dynamic systems; passivity

Indexed keywords

AGREEMENT PROBLEMS; AGREEMENT PROTOCOL; CONSENSUS; CONSENSUS ALGORITHMS; GRAPH LAPLACIAN; GRAPH-THEORETIC; LAPLACIANS; NETWORKED DYNAMIC SYSTEMS; NONLINEAR EXTENSION; OPTIMAL SENSOR PLACEMENT; PASSIVITY; PERFORMANCE BOUNDS; SPANNING TREE; SUBGRAPHS;

GRAPH THEORY; PASSIVATION;

LAPLACE TRANSFORMS;

EID: 79952587406     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2056730     Document Type: Article

References (33)

1. M. Arcak, "Passivity as a design tool for group coordination", IEEE Trans. Autom. Control, vol. 52, no. 8, pp. 1380-1390, Aug. 2007. (Pubitemid 47321551)
2. B. Bamieh, F. Paganini, and M. Dahleh, "Distributed control of spatially-invariant systems", IEEE Trans. Autom. Control, vol. 47, no. 7, pp. 1091-1107, Jul. 2002.
3. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation. Englewood Cliffs, NJ: Prentice-Hall, 1989.
4. B-D Chen and S. Lall, "Dissipation inequalities for distributed systems on graphs", in Proc. IEEE Conf. Decision Control, Dec. 2003, pp. 3084-3090.
5. J. Cortes and F. Bullo, "Coordination and geometric optimization via distributed dynamical systems", SIAM J. Control Optim., vol. 45, no. 5, pp. 1543-1574, 2005.
6. R. D'Andrea and G. E. Dullerud, "Distributed control design for spatially interconnected systems", IEEE Trans. Autom. Control, vol. 48, no. 9, pp. 1478-1495, Sep. 2003.
7. G. E. Dullerud and F. Paganini, A Course in Robust Control Theory. New York: Springer, 2005.
8. D. V. Dimarogonas and K. H. Johansson, "On the stability of distancebased formation control", in Proc. IEEE Conf. Decision Control, Dec. 2008, pp. 1200-1205.
9. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations", IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1465-1476, Sep. 2004.
10. M. Fiedler, "Algebraic connectivity of graphs", Czechoslovak Math. J., vol. 23, no. 98, pp. 298-305, 1973.
11. C. Godsil and G. Royle, Algebraic Graph Theory. New York: Springer, 2001.
12. I. Gutman, "The star is the tree with greatest greatest Laplacian eigenvalue", Kragujevac J. Math., vol. 24, pp. 61-65, 2002.
13. Y. Hatano and M. Mesbahi, "Agreement over random networks", IEEE Trans. Autom. Control, vol. 50, no. 11, pp. 1867-1872, Nov. 2005. (Pubitemid 41748891)
14. R. A. Horn and C. Johnson, Matrix Analysis. Cambridge, U. K.: Cambridge Univ. Press, 1985.
15. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules", IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988-1001, Jun. 2003.
16. H. K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice Hall, 2001.
17. B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms. New York: Springer, 2007.
18. ∞ consensus control in directed networks of agents with time-delaty", Syst. Control Lett., vol. 57, pp. 643-653, 2007.
19. M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks. Princeton, NJ: Princeton Univ. Press, 2010.
20. M. Mesbahi and F. Y. Hadaegh, "Formation flying control of multiple spacecraft via graphs, matrix inequalities, and switching", AIAA J. Guid., Control, Dyn., vol. 24, no. 2, pp. 369-377, 2001. (Pubitemid 32286584)
21. L. Moreau, "Stability of multiagent systems with time-dependent communication links", IEEE Trans. Autom. Control, vol. 50, no. 2, pp. 169-182, Feb. 2005. (Pubitemid 40319348)
22. A. Muhammad and M. Egerstedt, "Control using higher order Laplacians in network topologies", in Proc. Math. Theory Netw. Syst., Jul. 2006, pp. 1024-1038.
23. R. Olfati-Saber, J. A. Fax, and R. M. Murray, "Consensus and cooperation in networked multi-agent systems", Proc. IEEE, vol. 95, no. 1, pp. 215-233, Jan. 2007.
24. R. Olfati-Saber and R. M. Murray, "Consensus problems innetworks of agents with switching topology and time-delays", IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
25. M. Petrovic and I. Gutman, "The path is the tree with smallest greatest Laplacian eigenvalue", Kragujevac J. Math., vol. 24, pp. 67-70, 2002.
26. A. Rahmani, M. Ji, M. Mesbahi, and M. Egerstedt, "Controllability of multi-agent systems from a graph theoretic perspective", SIAM J. Control Optim., vol. 48, no. 1, pp. 162-186, 2009.
27. W. Ren and R. W. Beard, Distributed Consensus in Multi-Vehicle Cooperative Control. London, U. K.: Springer-Verlag, 2008.
28. W. Ren, R. W. Beard, and E. M. Atkins, "A survey of consensus problems in multi-agent coordination", in Proc. Amer. Control Conf., Jun. 2005, vol. 3, pp. 1859-1864. (Pubitemid 41189135)
29. J. Sandhu, M. Mesbahi, and T. Tsukamaki, "Cuts and flows in relative sensing and control of spatially distributed systems", in Proc. Amer. Control Conf., Jun. 2005, pp. 73-78. (Pubitemid 41189351)
30. J. Sandhu, M. Mesbahi, and T. Tsukamaki, "Relative sensing networks: Observability, estimation, and the control structure", in Proc. IEEE Conf. Decision Control, Dec. 2005, pp. 6400-6405.
31. A. Tahbaz-Salehi and A. Jadbabaie, "Distributed coverage verifcation in sensor networks without location information", in Proc. 47th IEEE Conf. Decision Control, Dec. 2008, pp. 4170-4176.
32. L. Xiao, S. Boyd, and S. Lall, "A scheme for robust distributed sensor fusion based on average consensus", in Proc. 4h Int. Symp. Inform. Processing Sensor Networks, Apr. 2005, pp. 64-70.
33. D. Zelazo, A. Rahmani, and M. Mesbahi, "Agreement via the edge Laplacian", in Proc. IEEE Conf. Decision Control, Dec. 2007, pp. 2309-2314. (Pubitemid 351277499)