Advertisement

Robustness of Network Controllability Against Cascading Failure

  • Lv-lin HouEmail author
  • Yan-dong Xiao
  • Liang Lu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11936)

Abstract

Controllability of networks widely existing in real-life systems have been a critical and attractive research subject for both network science and control systems communities. Research in network controllability has mostly focused on the effects of the network structure on its controllability, and some studies have begun to investigate the controllability robustness of complex networks. Cascading failure is common phenomenon in many infrastructure networks, which largely affect normal operation of networks, and sometimes even lead to collapse, resulting in considerable economic losses. The robustness of network controllability against the cascading failure is studied by a linear load-capacity model with a breakdown probability in this paper. The controllability of canonical model networks under different node attack strategies is investigated, random failure and malicious attack. It is shown by numerical simulations that the tolerant parameter of load-capacity model has an important role in the emergence of cascading failure, independent to the types of network. The networks with moderate average degree are more vulnerable to the cascading failure while these with high average degree are very robust. In particular, betweenness attack strategy is more harmful to the network controllability than degree attack one, especially for the scale-free networks.

Keywords

Controllability Robustness Cascading failure Complex networks 

References

  1. 1.
    Liu, Y.Y., Slotine, J.J., Barabási, A.L.: Controllability of complex networks. Nature 473(7346), 167–173 (2011)CrossRefGoogle Scholar
  2. 2.
    Yuan, Z., Zhao, C., Di, Z.: Exact controllability of complex networks. Nat. Commun. 63–73 (2013)Google Scholar
  3. 3.
    Jia, T., Pósfai, M.: Connecting core percolation and controllability of complex networks. Sci. Rep. 4, 5379 (2014)Google Scholar
  4. 4.
    Liu, Y.Y., Barabási, A.L.: Control principles of complex systems. Rev. Mod. Phys. 88(3), 035006 (2016)CrossRefGoogle Scholar
  5. 5.
    Menichetti, G., Dall’Asta, L., Bianconi, G.: Network controllability is determined by the density of low in-degree and out-degree nodes. Phys. Rev. Lett. 113, 078701 (2014)CrossRefGoogle Scholar
  6. 6.
    Chen, G.R., Lou, Y., Wang, L.: A comparative robustness study on controllability of complex networks. IEEE Trans. Circ. Syst. 66(5), 828–832 (2019)Google Scholar
  7. 7.
    Lu, Z.-M., Li, X.-F.: Attack vulnerability of network controllability. PLoS ONE 11(9), e0162289 (2016)CrossRefGoogle Scholar
  8. 8.
    Wang, B., Gao, L., Gao, Y., Deng, Y.: Maintain the structural controllability under malicious attacks on directed networks. EPL (Europhys. Lett.) 101, 58003 (2013)CrossRefGoogle Scholar
  9. 9.
    Xiao, Y.-D., Lao, S.-Y., Hou, L.-L., Bai, L.: Optimization of robustness of network controllability against malicious attacks. Chin. Phys. B 121(11), 678–686 (2014)Google Scholar
  10. 10.
    Wang, W.-X., Ni, X., Lai, Y.-C., Grebogi, C.: Optimizing controllability of complex networks by minimum Structural perturbations. Phys. Rev. E 85, 026115 (2012)CrossRefGoogle Scholar
  11. 11.
    Hou, L.-L., Lao, S.-Y, Liu, G., Bai, L.: Controllability and Directionality in Complex Networks. Chin. Phys. Lett. 29, 108901 (2012)CrossRefGoogle Scholar
  12. 12.
    Xiao, Y.-D., Lao, S.-Y., Hou, L.-L., Bai, L.: Edge orientation for optimizing controllability of complex networks. Phys. Rev. E 90, 042804 (2014)CrossRefGoogle Scholar
  13. 13.
    Liang, M., Jin, S.-Q., Wang, D.-J., Zou, X.-F.: Optimization of controllability and robustness of complex networks by edge directionality. Eur. Phys. J. B 89, 186 (2016)CrossRefGoogle Scholar
  14. 14.
    Ruths, J., Ruths, D.: Robustness of network controllability under edge removal. In: Ghoshal, G., Poncela-Casasnovas, J., Tolksdorf, R. (eds.) Complex Networks IV. SCI, vol. 476, pp. 185–193. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36844-8_18CrossRefzbMATHGoogle Scholar
  15. 15.
    Pu, C.-L., Pei, W.-J., Michaelson, A.: Robustness analysis of network controllability. Phys. A: Stat. Mech. Appl. 391(18), 4420–4425 (2012)CrossRefGoogle Scholar
  16. 16.
    Wang, L., Fu, Y.-B., Chen, M.Z.-Q., Yang, X.-H.: Controllability robustness for scale-free networks based on nonlinear load-capacity. Neurocomputing 251, 99–105 (2017)CrossRefGoogle Scholar
  17. 17.
    Nie, S., Wang, X., Zhang, H., Li, Q., Wang, B.: Robustness of controllability for networks based on edge-attack. PLoS ONE 9(2), e89066 (2014)CrossRefGoogle Scholar
  18. 18.
    Sold, R.V., Rosas-Casals, M., Corominas-Murtre, B., Valverde, S.: Robustness of the European power grids under intentional attack. Phys. Rev. E 77(2), 026102 (2008)Google Scholar
  19. 19.
    Barabási, A.L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Phys. A: Stat. Mech. Appl. 272(1), 173–187 (1999)CrossRefGoogle Scholar
  20. 20.
    Erdős, P., Rényi, A.: On random graphs. Publicationes Mathematicae Debrecen 6, 290–297 (1959)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Goh, K.I., Kahng, B., Kim, D.: Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87, 287701 (2001)CrossRefGoogle Scholar
  24. 24.
    Kalman, R.E.: Mathematical description of linear dynamical systems, J. Soc. Ind. Appl. Math. Series A: Control 1(2), 152–192 (1963)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Lin, C.T.: Structural controllability. IEEE Trans. Autom. Control 19(3), 201–208 (1974)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Hopcroft, J.E., Karp, R.M.: An n^5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2(4), 225–231 (1973)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Motter, A.E., Lai, Y.-C.: Cascade-based attacks on complex networks. Phys. Rev. E 66(6), 065102 (2002)CrossRefGoogle Scholar
  28. 28.
    Motter, A.E.: Cascade control and defense in complex networks. Phys. Rev. E 93(9), 098701 (2004)Google Scholar
  29. 29.
    Dou, B.-L., Wang, X.-G., Zhang, S.-Y.: Robustness of networks against cascading failures. Phys. A: Stat. Mech. Appl. 389(11), 2310–2317 (2010)CrossRefGoogle Scholar
  30. 30.
    Wang, J.-W., Rong, L.-L.: A model for cascading failures in scale-free networks with a breakdown probability. Phys. A 388, 1289–1298 (2009)CrossRefGoogle Scholar
  31. 31.
    Liu, J., Xiong, Q.Y., Shi, X., Wang, K., Shi, W.R.: Robustness of complex networks with an improved breakdown probability against cascading failures. Phys. A 456, 302–309 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Academy of Joint LogisticsNational Defense UniversityBeijingPeople’s Republic of China
  2. 2.Science and Technology on Information Systems Engineering LaboratoryNational University of Defense TechnologyChangshaPeople’s Republic of China

Personalised recommendations