Pinning Control Design for Stabilization of Boolean Networks From Constructed Boolean Control Networks

  • Rongjian Liu
  • Jianquan LuEmail author
  • Jie Zhong
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)


In this work, we study the pinning control design for stabilization of Boolean netowrks (BNs) from constructed Boolean control networks (BCNs). Based on the algebraic model of BNs, for a given matrix set, not only feasible pinning controllers can be obtained but also the solution for the pinning controllers is unique. Thus, we can design the pinning controllers for BNs from the aspect of BCNs.


Boolean networks Boolean control networks Pinning control Semi-tensor product of matrices 



This work was supported by the National Natural Science Foundation of China under Grant No. 61573102, the Natural Science Foundation of Jiangsu Province of China under Grant no. BK20170019, Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002, and China Postdoctoral Science Foundation under Grant No. 2014M560377 and 2015T80483, Jiangsu Province Six Talent Peaks Project under Grant 2015-ZNDW-002, and the Fundamental Research Funds for the Central Universities under Grant No. 2242017K41045.


  1. 1.
    Akutsu, T., Hayashida, M., Ching, W.K., Ng, M.K.: Control of Boolean networks: hardness results and algorithms for tree structured networks. J. Theor. Biol. 244(4), 670–679 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bof, N., Fornasini, E., Valcher, M.E.: Output feedback stabilization of Boolean control networks. Automatica 57, 21–28 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cheng, D., Qi, H.: A linear representation of dynamics of Boolean networks. IEEE Trans. Autom. Control 55(10), 2251–2258 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chen, H., Liang, J., Huang, T., Cao, J.: Synchronization of arbitrarily switched Boolean networks. IEEE Trans. Neural Netw. Learn. Syst. 28(3), 612–619 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chen, H., Liang, J., Wang, Z.: Pinning controllability of autonomous Boolean control networks. Sci. China Inf. Sci. 59(7), 070107 (2016)CrossRefGoogle Scholar
  6. 6.
    Guo, X., Lu, J., Alsaedi, A., Alsaadi, F.E.: Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays. Phys. A Stat. Mech. Appl. 495, 488–497 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Guo, Y., Wang, P., Gui, W., Yang, C.: Set stability and set stabilization of Boolean control networks based on invariant subsets. Automatica 61, 106–112 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Laschov, D., Margaliot, M.: Controllability of Boolean control networks via the Perron-Frobenius theory. Automatica 48(6), 1218–1223 (2012)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Li, F.: Pinning control design for the stabilization of Boolean networks. IEEE Trans. Neural Netw. Learn. Syst. 27(7), 1585–1590 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Li, H., Wang, Y.: Output feedback stabilization control design for Boolean control networks. Automatica 49(12), 3641–3645 (2013)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lu, J., Zhong, J., Huang, C., Cao, J.: On pinning controllability of Boolean control networks. IEEE Trans. Autom. Control 61(6), 1658–1663 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Li, R., Yang, M., Chu, T.: State feedback stabilization for Boolean control networks. IEEE Trans. Autom. Control 58(7), 1853–1857 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu, R., Lu, J., Lou, J., Alsaedi, A., Alsaadi, F.E.: Set stabilization of Boolean networks under pinning control strategy. Neurocomputing 260, 142–148 (2017)CrossRefGoogle Scholar
  15. 15.
    Liu, X., Chen, T.: Finite-time and fixed-time cluster synchronization with or without pinning control. IEEE Trans. Cybern. 48(1), 240–252 (2018)CrossRefGoogle Scholar
  16. 16.
    Li, H., Wang, Y.: Further results on feedback stabilization control design of Boolean control networks. Automatica 83, 303–308 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Liu, R., Lu, J., Liu, Y., Cao, J., Wu, Z.: Delayed feedback control for stabilization of Boolean control networks with state delay. IEEE Trans. Neural Netw. Learn. Syst. 29(7), 3283–3288 (2018)MathSciNetGoogle Scholar
  18. 18.
    Meng, L., Liu, M., Feng, G.: Stability and \( l_1 \) gain analysis of Boolean networks with markovian jump parameters. IEEE Trans. Autom. Control 62(8), 4222–4228 (2017)CrossRefGoogle Scholar
  19. 19.
    Meng, M., Feng, J.E.: Optimal control problem of singular Boolean control networks. Int. J. Control. Autom. Syst. 13(2), 266–273 (2015)CrossRefGoogle Scholar
  20. 20.
    Wang, L.P., Pichler, E.E., Ross, J.: Oscillations and chaos in neural networks: an exactly solvable mode. Proc. Natl. Acad. Sci. 87(23), 9467–9471 (1990)CrossRefGoogle Scholar
  21. 21.
    Xiao, Y., Dougherty, E.R.: The impact of function perturbations in Boolean networks. Bioinformatics 23(10), 1265–1273 (2007)CrossRefGoogle Scholar
  22. 22.
    Zhang, H., Wang, X., Lin, X.: Synchronization of Boolean networks with different update schemes. IEEE/ACM Trans. Comput. Biol. Bioinform. 11(5), 965–972 (2014)CrossRefGoogle Scholar
  23. 23.
    Zhang, K., Zhang, L., Xie, L.: Invertibility and nonsingularity of Boolean control networks. Automatica 60, 155–164 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zou, Y., Zhu, J.: System decomposition with respect to inputs for Boolean control networks. Automatica 50(4), 1304–1309 (2014)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Cyber Science and EngineeringSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.School of MathematicsSoutheast UniversityNanjingPeople’s Republic of China
  3. 3.Department of MathematicsCity University of Hong KongKowloonHong Kong

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