Hierarchical clustering of dynamical networks using a saddle-point analysis

IEEE Transactions on Automatic Control

Volumn 58, Issue 1, 2013, Pages 113-124

  Bürger, Mathias ^a   Zelazo, Daniel ^b   Allgöwer, Frank ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Cluster synchronization; dynamical networks; saddle point optimization

Indexed keywords

ASYMPTOTIC BEHAVIORS; BISECTION PROBLEMS; CLUSTER SYNCHRONIZATION; DYNAMIC NETWORK; DYNAMICAL NETWORKS; HETEROGENEOUS DYNAMICS; HIER-ARCHICAL CLUSTERING; HIERARCHICAL CLUSTERING ANALYSIS; INITIAL CONDITIONS; INTERACTION RULES; NETWORK NODE; NETWORK PARTITIONING; SADDLE POINT; SADDLE POINT PROBLEMS; SATURATION LEVELS; THEORETICAL RESULT; UNDERLYING GRAPHS;

DYNAMICS;

SYNCHRONIZATION;

EID: 84871799989     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2206695     Document Type: Article

References (29)

1. M. Escalona-Morán, M. Cosenza, P. Guillén, and P. Coutin, "Synchronization and clustering in electroencephalographic signals," Chaos, Solitons & Fractals, vol. 31, no. 4, pp. 820-825, 2007. (Pubitemid 44247656)
2. D. Lazer, A. Pentland, L. Adamic, S. Aral, and A.-L. Barabasi, "Computational social science," Science, vol. 323, no. 5915, pp. 721-723, 2009.
3. W. Lu, B. Liu, and T. Chen, "Cluster synchronization in networks of coupled nonidentical dynamical systems," Chaos, vol. 20, p. 013120, 2010.
4. M. Mesbahi andM. Egerstedt, Graph TheoreticMethods inMultiagent Networks. Princeton, NJ: Princton Univ. Press, 2010.
5. 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)
6. P. DeLellis, M. di Bernardo, and G. Russo, "On QUAD, lipschitz, and contracting vector fields for consensus and synchronization of networks," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 58, no. 3, pp. 576-573, Mar. 2011.
7. W. Wu, W. Zhou, and T. Chen, "Cluster synchronization of linearly coupled complex networks under pinning control," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 56, no. 4, pp. 829-839, Apr. 2009.
8. Z. Ma, Z. Liu, and G. Zhang, "A newmethod to realize cluster synchronization in connected chaotic networks," Chaos, vol. 16, p. 023103, 2006.
9. W. Xia and M. Cao, "Clustering in diffusively coupled networks," Automatica, vol. 47, pp. 2395-2405, 2011.
10. V. Blondel, J. M. Hendrickx, and J. N. Tsitsiklis, "On krauses multi-agent consensus model with state-dependent connectivity," IEEE Trans. Autom. Control, vol. 54, no. 11, pp. 2586-2597, Nov. 2009.
11. F. De Smet and D. Aeyels, "Clustering in a network of non-identical and mutually interacting agents," in Proc. Roy. Soc. A, 2009, vol. 465, pp. 745-768.
12. D. Aeyels and F. De Smet, "Cluster formation in a time-varying multiagent system," Automatica, vol. 47, no. 11, pp. 2481-2487, 2011.
13. S. Fortunato, "Community detection in graphs," Phys. Rep., vol. 486, pp. 75-174, 2010.
14. A. Pinar, Y. Fogel, and B. Lesieutre, "The inhibiting bisection problem," Lawrence Berkeley National Laboratory, Berkeley, CA, 2006. [Online]. Available: http://escholarship. org/uc/item/0gt129fs, Tech. Rep.
15. C. Ford and D. Fulkerson, "Maximal flow through a network," Can. J. Math., vol. 8, pp. 399-404, 1956.
16. C. Godsil and G. Royle, Algebraic Graph Theory. New York: Springer, 2001.
17. D. Helbing, "Traffic and related self-driven many-particle systems," Rev. Mod. Phys., vol. 73, pp. 1067-1141, Dec. 2001. (Pubitemid 33395907)
18. A. Bergen and D. Hill, "A structure preserving model for power system stability analysis," IEEE Trans. Power App. Syst., vol. PAS-100, no. 1, pp. 25-35, Jan. 1981. (Pubitemid 11497664)
19. D. Zelazo and M. Mesbahi, "Edge agreement: Graph-theoretic performance bounds and passivity analysis," IEEE Trans. Autom. Control, vol. 56, no. 3, pp. 544-555, Mar. 2011.
20. R. T. Rockafellar, Network Flows and Monotropic Optimization. Belmont, MA: Athena Scientific, 1998.
21. D. Bertsekas, "Min common/max crossing duality: A geometric view of conjugacy in convex optimization," Lab. Inf. Dec. Syst., Tech. Rep. LIDS-P-2796, 2009, MIT.
22. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U. K. : Cambridge Univ. Press, 2003.
23. A. Nedic and A. Ozdaglar, "Subgradient methods for saddle-point problems," J. Optimiz. Theory Appl., pp. 205-228, 2009.
24. R. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1997.
25. H. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall, 2002.
26. G. Strang, "Duality in the classroom," Amer. Math. Monthly, vol. 91, pp. 250-254, 1984.
27. B. Lesieutre, S. Roy, and A. Pinar, "Power system extreme event screening using graph partitioning," in Proc. 38th North Amer. Power Symp., 2006, pp. 503-510.
28. A. Aroposthatis, S. Sastry, and P. Varaiya, "Analysis of power-flow equation," Int. J. Elect. Power Energy Syst., vol. 3, no. 3, pp. 115-126, 1981. (Pubitemid 12521147)
29. E. Bompard, D. Wu, and F. Xue, "The concept of betweenness in the analysis of power grid vulnerability," in Proc. Complexity Eng, Rome, Italy, 2010, pp. 52-54.