References

• 1. 1)
     • 15. Zhao, Y., Cheng, D.: ‘On controllability and stabilizability of probabilistic Boolean control networks’, Sci. China Inf. Sci., 2013, 57, (1), pp. 1–14.
  2. 2)
     • 2. Kauffman, S.A.: ‘The origins of order: self organization and selection in evolution’ (Oxford University Press, 1993).
  3. 3)
     • 28. Laschov, D., Margaliot, M.: ‘A maximum principle for single-input Boolean control networks’, IEEE Trans. Autom. Control, 2011, 56, (4), pp. 913–917.
  4. 4)
     • 5. Albert, R., Barabási, A.-L.: ‘Dynamics of complex systems: scaling laws for the period of Boolean networks’, Phys. Rev. Lett., 2000, 84, (24), pp. 5660–5663.
  5. 5)
     • 12. Cheng, D., Qi, H.: ‘Controllability and observability of Boolean control networks’, Automatica, 2009, 45, (7), pp. 1659–1667.
  6. 6)
     • 8. Shmulevich, I., Dougherty, E.R., Kim, S., et al: ‘Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2002, 18, (2), pp. 261–274.
  7. 7)
     • 13. Laschov, D., Margaliot, M.: ‘Controllability of Boolean control networks via the Perron–Frobenius theory’, Automatica, 2012, 48, (6), pp. 1218–1223.
  8. 8)
     • 36. Li, H., Wang, Y.: ‘Controllability and stabilization of Boolean control networks with state and input constraints’. 32nd Chinese Control Conf. (CCC), 2013, pp. 447–452.
  9. 9)
     • 20. Cheng, D., Zhao, Y.: ‘Identification of Boolean control networks’, Automatica, 2011, 47, (4), pp. 702–710.
  10. 10)
      • 24. Cheng, D.: ‘On finite potential games’, Automatica, 2014, 50, (7), pp. 1793–1801.
  11. 11)
      • 4. Akutsu, T., Miyano, S., Kuhara, S., et al: ‘Identification of genetic networks from a small number of gene expression patterns under the Boolean network model’. Pacific Symp. Biocomputing, 1999, vol. 4, pp. 17–28.
  12. 12)
      • 39. Chen, H., Li, X., Sun, J.: ‘Stabilization, controllability and optimal control of Boolean networks with impulsive effects and state constraints’, IEEE Trans. Autom. Control, 2015, 60, (3), pp. 806–811.
  13. 13)
      • 22. Cheng, D.: ‘Disturbance decoupling of Boolean control networks’, IEEE Trans. Autom. Control, 2011, 56, (1), pp. 2–10.
  14. 14)
      • 14. Li, F., Sun, J.: ‘Controllability of Boolean control networks with time delays in states’, Automatica, 2011, 47, (3), pp. 603–607.
  15. 15)
      • 7. Heidel, J., Maloney, J., Farrow, C., et al: ‘Finding cycles in synchronous Boolean networks with applications to biochemical systems’, Int. J. Bifurcation Chaos, 2003, 13, (3), pp. 535–552.
  16. 16)
      • 1. Kauffman, S.A.: ‘Metabolic stability and epigenesis in randomly constructed genetic nets’, J. Theor. Biol., 1969, 22, (3), pp. 437–467.
  17. 17)
      • 16. Cheng, D., Qi, H., Li, Z., et al: ‘Stability and stabilization of Boolean networks’, Int. J. Robust Nonlinear Control, 2011, 21, (2), pp. 134–156.
  18. 18)
      • 19. Qi, H., Cheng, D., Hu, X.: ‘Stabilization of random Boolean networks’. Eighth World Congress on Intelligent Control and Automation (WCICA), 2010, pp. 1968–1973.
  19. 19)
      • 3. Akutsu, T., Hayashida, M., Ching, W.-K., et al: ‘Control of Boolean networks: hardness results and algorithms for tree structured networks’, J. Theor. Biol., 2007, 244, (4), pp. 670–679.
  20. 20)
      • 6. Aldana, M.: ‘Boolean dynamics of networks with scale-free topology’, Phys. D, Nonlinear Phenom., 2003, 185, (1), pp. 45–66.
  21. 21)
      • 30. Li, Z., Cheng, D.: ‘Algebraic approach to dynamics of multivalued networks’, Int. J. Bifurcation Chaos, 2010, 20, (3), pp. 561–582.
  22. 22)
      • 21. Guo, Y., Wang, P., Gui, W., et al: ‘Set stability and set stabilization of Boolean control networks based on invariant subsets’, Automatica, 2015, 61, pp. 106–112.
  23. 23)
      • 31. Wang, Y., Zhang, C., Liu, Z.: ‘A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems’, Automatica, 2012, 48, (7), pp. 1227–1236.
  24. 24)
      • 26. Cheng, D., Qi, H.: ‘State–space analysis of Boolean networks’, IEEE Trans. Neural Netw., 2010, 21, (4), pp. 584–594.
  25. 25)
      • 38. Li, Z., Song, J.: ‘Controllability of Boolean control networks avoiding states set’, Sci. China Inf. Sci., 2014, 57, (3), pp. 1–13.
  26. 26)
      • 37. Li, H., Wang, Y.: ‘Controllability analysis and control design for switched Boolean networks with state and input constraints’, SIAM J. Control Optim., 2015, 53, (5), pp. 2955–2979.
  27. 27)
      • 40. Guo, Y.: ‘Controllability of Boolean control networks with state-dependent constraints’, Sci. China Inf. Sci., 2016, 59, (3), pp. 1–14.
  28. 28)
      • 33. Xu, X., Hong, Y.: ‘Solvability and control design for synchronization of Boolean networks’, J. Syst. Sci. Complex., 2013, 26, (6), pp. 871–885.
  29. 29)
      • 17. Li, H., Wang, Y.: ‘Output feedback stabilization control design for Boolean control networks’, Automatica, 2013, 49, (12), pp. 3641–3645.
  30. 30)
      • 29. Li, F., Sun, J., Wu, Q.: ‘Observability of Boolean control networks with state time delays’, IEEE Trans. Neural Netw., 2011, 22, (6), pp. 948–954.
  31. 31)
      • 32. Wu, Y., Kumar, M., Shen, T.: ‘A stochastic logical system approach to model and optimal control of cyclic variation of residual gas fraction in combustion engines’, Appl. Therm. Eng., 2016, 93, pp. 251–259.
  32. 32)
      • 23. Cheng, D.: ‘Input-state approach to Boolean networks’, IEEE Trans. Neural Netw., 2009, 20, (3), pp. 512–521.
  33. 33)
      • 27. Cheng, D., Qi, H., Li, Z.: ‘Model construction of Boolean network via observed data’, IEEE Trans. Neural Netw., 2011, 22, (4), pp. 525–536.
  34. 34)
      • 18. Li, H., Wang, Y., Liu, Z.: ‘Stability analysis for switched Boolean networks under arbitrary switching signals’, IEEE Trans. Autom. Control, 2014, 59, (7), pp. 1978–1982.
  35. 35)
      • 34. Zhao, Y., Li, Z., Cheng, D.: ‘Optimal control of logical control networks’, IEEE Trans. Autom. Control, 2011, 56, (8), pp. 1766–1776.
  36. 36)
      • 35. Zhao, Y., Qi, H., Cheng, D.: ‘Input-state incidence matrix of Boolean control networks and its applications’, Syst. Control Lett., 2010, 59, (12), pp. 767–774.
  37. 37)
      • 9. Shmulevich, I., Dougherty, E.R., Zhang, W.: ‘From Boolean to probabilistic Boolean networks as models of genetic regulatory networks’, Proc. IEEE, 2002, 90, (11), pp. 1778–1792.
  38. 38)
      • 25. Cheng, D., Feng, J.-e., Lv, H.: ‘Solving fuzzy relational equations via semitensor product’, IEEE Trans. Fuzzy Syst., 2012, 20, (2), pp. 390–396.
  39. 39)
      • 11. Cheng, D., Qi, H., Li, Z.: ‘Analysis and control of Boolean networks: a semi-tensor product approach’ (Springer, 2011).
  40. 40)
      • 10. Cheng, D., Qi, H.: ‘A linear representation of dynamics of Boolean networks’, IEEE Trans. Autom. Control, 2010, 55, (10), pp. 2251–2258.