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Efficient Restoration of Structural Controllability Under Malicious Edge Attacks for Complex Networks

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Part of the Lecture Notes in Networks and Systems book series (LNNS,volume 449)


In recent years, protecting large-scale complex networks, such as electric power grids and their monitoring systems, has become a critical part of cutting-edge research. Adversaries often attempt to intercept and hack these systems by interfering with intermediate nodes or preventing controllers and physical systems from receiving actuator signals and industrial sensor measurements. The present work concentrates primarily on the structural controllability of such systems, as this topic has recently received significant interest through the equivalent problem of the power dominating set within the field of electrical power and network control. Nonetheless, it is well established that these problems are NP-hard with low approximation. Developing strategies that can restore a network’s performance is critical given their importance for a wide range of networks, particularly power networks. Thus, this paper focuses on regaining the structural controllability for Erdős-Rényi random directed networks following attacks on edges. Furthermore, these strategies will be evaluated using Matlab simulations to examine their applicability in real-world contexts.

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  • DOI: 10.1007/978-3-030-99584-3_14
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    The full code is available in [16].

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    The full code is available upon request from the author.


  1. Lin, C.-T.: Structural controllability. IEEE Trans. Autom. Control 19(3), 201–208 (1974)

    MathSciNet  CrossRef  Google Scholar 

  2. Liu, Y.-Y., Slotine, J.-J., Barabási, A.-L.: Controllability of complex networks. Nature 473(7346), 167–173 (2011)

    CrossRef  Google Scholar 

  3. Kalman, R.E.: Mathematical description of linear dynamical systems. J. Soc. Ind. Appl. Math. Series Control 1(3), 152–192 (1963)

    MathSciNet  CrossRef  Google Scholar 

  4. Haynes, T.W., Hedetniemi, S.M., Hedetniemi, S.T., Henning, M.A.: Domination in graphs applied to electric power networks. SIAM J. Discrete Mathematics 15(4), 519–529 (2002)

    MathSciNet  CrossRef  Google Scholar 

  5. Kneis, J., Mölle, D., Richter, S., Rossmanith, P.: Parameterized power domination complexity. Inf. Process. Lett. 98(4), 145–149 (2006)

    MathSciNet  CrossRef  Google Scholar 

  6. Zhao, M., Shan, E., Kang, L.: Power domination in the generalized petersen graphs. Discussiones Mathematicae: Graph Theory 40(3), 695–712 (2020)

    MathSciNet  CrossRef  Google Scholar 

  7. Hedetniemi, S.T., McRae, A.A., Mohan, R.: Algorithms and complexity of power domination in graphs. In: Haynes, T.W., Hedetniemi, S.T., Henning, M.A. (eds.) Structures of Domination in Graphs. DM, vol. 66, pp. 461–484. Springer, Cham (2021).

    CrossRef  MATH  Google Scholar 

  8. Sudakov, B., Vu, V.H.: Local resilience of graphs. Random Struct. Algorithms 33(4), 409433 (2008)

    MathSciNet  CrossRef  Google Scholar 

  9. Alwasel, B., Wolthusen, S.D.: Recovering structural controllability on Erdős-Rényi graphs in the presence of compromised nodes. In: Rome, E., Theocharidou, M., Wolthusen, S. (eds.) CRITIS 2015. LNCS, vol. 9578, pp. 105–119. Springer, Cham (2016).

    CrossRef  Google Scholar 

  10. Lou, Y., Wang, L., Chen, G.: Toward stronger robustness of network controllability: a snapback network model. IEEE Trans. Circ. Syst. I: Regular Papers 65(9), 2983–2991 (2018)

    MathSciNet  MATH  Google Scholar 

  11. Li, X., Zhang, Z., Liu, J., Gai, K.: A new complex network robustness attack algorithm. In: Proceedings of the ACM international Symposium on Blockchain and Secure Critical Infrastructure, pp. 13–17 (2019)

    Google Scholar 

  12. Chen, G., Lou, Y., Wang, L.: A comparative study on controllability robustness of complex networks. IEEE Trans. Circ. Syst. II: Express Briefs 66(5), 828–832 (2019)

    Google Scholar 

  13. Alwasel, B.: Recovery of structural controllability into critical infrastructures under malicious attacks. Int. J. Adv. Comput. Sci. Appl. 11(4), 723–728 (2020)

    Google Scholar 

  14. Lou, Y., He, Y., Wang, L., Chen, G.: Predicting network controllability robustness: a convolutional neural network approach. IEEE Trans. Cybern. (2020)

    Google Scholar 

  15. Alwasel, B.: Robustness analysis of structural controllability for directed networks against single edge attacks. Int. J. Innovative Technol. Expl. Eng. 9(8), 944–951 (2020)

    Google Scholar 

  16. Alwasel, B.: Simulating robustness of structural controllability for directed networks under multi-round edge strategies. IEEE Access 9, 84688–84699 (2021)

    CrossRef  Google Scholar 

  17. Ramos, G., Silvestre, D., Silvestre, C.: The robust minimal controllability and observability problem. Int. J. Robust Nonlinear Control 31(10), 5033–5044 (2021)

    MathSciNet  CrossRef  Google Scholar 

  18. Zhao, J., Sun, S., Shen, H., Xia, C.: An effective network repair strategy against both random and malicious edge attacks. In: 40th Chinese Control Conference, pp. 8628–8633, IEEE (2021)

    Google Scholar 

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Correspondence to Bader Alwasel .

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Alwasel, B. (2022). Efficient Restoration of Structural Controllability Under Malicious Edge Attacks for Complex Networks. In: Barolli, L., Hussain, F., Enokido, T. (eds) Advanced Information Networking and Applications. AINA 2022. Lecture Notes in Networks and Systems, vol 449. Springer, Cham.

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