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Observability of Boolean networks via STP and graph methods

Observability of Boolean networks via STP and graph methods

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This study addresses the observability of Boolean networks (BNs), using semi-tensor product (STP) of matrices. First, unobservable states can be divided into two types, and the first type of unobservable states can be easily determined by blocking idea. Second, it is found that all states reaching to observable states are observable. Based on subgraph of transition matrix and blocking idea, the second type of unobservable states can be also determined. Approaches are obtained to directly determine some observable or unobservable states. An algorithm is designed for determining the observability of BNs as well. Examples are given to illustrate the effectiveness of the given results.

References

    1. 1)
      • 1. Kauffman, S.A.: ‘Metabolic stability and epigenesis in randomly constructed genetic nets’, J. Theor. Biol., 1969, 22, (3), pp. 437467.
    2. 2)
      • 2. Davidson, E.H., Bolouri, H.: ‘A genomic regulatory network for development’, Science, 2002, 295, (5560), p. 1669.
    3. 3)
      • 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. 670679.
    4. 4)
      • 4. Heidel, J., Maloney, J., Farrow, C., et al: ‘Finding cycles in synchronous Boolean networks with applications to biochemical systems’, Int. J. Bifur. Chaos, 2003, 13, (03), pp. 535552.
    5. 5)
      • 5. Cheng, D., Qi, H., Li, Z.: ‘Analysis and control of Boolean networks: a semi-tensor product approach’ (Springer Science & Business Media, New York, 2010).
    6. 6)
      • 6. Cheng, D., Qi, H., Li, Z., et al: ‘Stability and stabilization of Boolean networks’, Int. J. Robust Nonlinear Control, 2011, 21, (2), pp. 134156.
    7. 7)
      • 7. Zhu, Q., Liu, Y., Lu, J., et al: ‘Observability of Boolean control networks’, Sci. China Inf. Sci., 2018, 61, (9), p. 092201.
    8. 8)
      • 8. Li, R., Yang, M., Chu, T.: ‘Observability conditions of Boolean control networks’, Int. J. Robust Nonlinear Control, 2014, 24, (17), pp. 27112723.
    9. 9)
      • 9. Zhang, K., Zhang, L., Xie, L.: ‘Finite automata approach to observability of switched Boolean control networks’, Nonlinear Anal., Hybrid Syst., 2016, 19, pp. 186197.
    10. 10)
      • 10. Laschov, D., Margaliot, M.: ‘Controllability of Boolean control networks via the perron–frobenius theory’, Automatica, 2012, 48, (6), pp. 12181223.
    11. 11)
      • 11. Liu, Y., Chen, H., Lu, J., et al: ‘Controllability of probabilistic Boolean control networks based on transition probability matrices’, Automatica, 2015, 52, pp. 340345.
    12. 12)
      • 12. Lu, J., Zhong, J., Ho, D.W.C., et al: ‘On controllability of delayed Boolean control networks’, SIAM J. Control Optim., 2016, 54, (2), pp. 475494.
    13. 13)
      • 13. Meng, M., Liu, L., Feng, G.: ‘Stability and l1 gain analysis of Boolean networks with markovian jump parameters’, IEEE Trans. Autom. Control, 2017, 62, (8), pp. 42224228.
    14. 14)
      • 14. Li, H., Wang, Y.: ‘Lyapunov-based stability and construction of lyapunov functions for Boolean networks’, SIAM J. Control Optim., 2017, 55, (6), pp. 34373457.
    15. 15)
      • 15. Tong, L., Liu, Y., Lou, J., et al: ‘Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks’, Appl. Math. Comput., 2018, 332, pp. 263275.
    16. 16)
      • 16. Mao, Y., Wang, L., Liu, Y., et al: ‘Stabilization of evolutionary networked games with length-r information’, Appl. Math. Comput., 2018, 337, pp. 442451.
    17. 17)
      • 17. Meng, M., Lam, J., Feng, J., et al: ‘Stability and guaranteed cost analysis of time-triggered Boolean networks’, IEEE Trans. Neural Netw. Learn. Syst., 2017, 29, (8), pp. 38933899.
    18. 18)
      • 18. Liu, Y., Li, B., Chen, H., et al: ‘Function perturbations on singular Boolean networks’, Automatica, 2017, 84, pp. 3642.
    19. 19)
      • 19. Zhang, H., Wang, X., Lin, X.: ‘Synchronization of Boolean networks with different update schemes’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2014, 11, (5), pp. 965972.
    20. 20)
      • 20. Zhang, H., Wang, X., Lin, X.: ‘Synchronization of asynchronous switched Boolean network’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2015, 12, (6), pp. 14491456.
    21. 21)
      • 21. Li, R., Yang, M., Chu, T.: ‘State feedback stabilization for Boolean control networks’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 18531857.
    22. 22)
      • 22. Zou, Y., Zhu, J., Liu, Y.: ‘State-feedback controller design for disturbance decoupling of Boolean control networks’, IET Control Theory Appl., 2017, 11, (18), pp. 32333239.
    23. 23)
      • 23. Li, M., Lu, J., Lou, J., et al: ‘The equivalence issue of two kinds of controllers in Boolean control networks’, Appl. Math. Comput., 2018, 321, pp. 633640.
    24. 24)
      • 24. Li, H., Xie, L., Wang, Y.: ‘On robust control invariance of Boolean control networks’, Automatica, 2016, 68, pp. 392396.
    25. 25)
      • 25. Fornasini, E., Valcher, M.E.: ‘Fault detection analysis of Boolean control networks’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 27342739.
    26. 26)
      • 26. Liu, Y., Li, B., Lu, J., et al: ‘Pinning control for the disturbance decoupling problem of Boolean networks’, IEEE Trans. Autom. Control, 2017, 62, (12), pp. 65956601.
    27. 27)
      • 27. Wu, Y., Shen, T.: ‘A finite convergence criterion for the discounted optimal control of stochastic logical networks’, IEEE Trans. Autom. Control, 2017, 63, pp. 262268.
    28. 28)
      • 28. Zhu, Q., Liu, Y., Lu, J., et al: ‘On the optimal control of Boolean control networks’, SIAM J. Control Optim., 2018, 56, pp. 13211341.
    29. 29)
      • 29. Wang, L., Liu, Y., Wu, Z., et al: ‘Strategy optimization for static games based on STP method’, Appl. Math. Comput., 2018, 316, pp. 390640.
    30. 30)
      • 30. Ideker, T., Galitski, T., Hood, L.: ‘A new approach to decoding life: systems biology’, Annu. Rev. Genomics Hum. Genet., 2001, 2, (1), pp. 343372.
    31. 31)
      • 31. Liang, J., Chen, H., Lam, J.: ‘An improved criterion for controllability of Boolean control networks’, Automatica, 2017, 62, (11), pp. 60126018.
    32. 32)
      • 32. Zhu, Q., Liu, Y., Lu, J., et al: ‘Further results on the controllabilty of Boolean control networks’, IEEE Trans. Autom. Control, 2018; DOI: 10.1109/TAC.2018.2830642.
    33. 33)
      • 33. Cobelli, C., Romaninjacur, G.: ‘Controllability, observability and structural identifiability of multi input and multi output biological compartmental systems’, IEEE Trans. Bio-Med. Eng., 1976, 23, (2), pp. 93100.
    34. 34)
      • 34. Lopez, I., Gamez, M., Carreno, R.: ‘Observability in dynamic evolutionary models’, BioSystems, 2004, 58, pp. 99109.
    35. 35)
      • 35. Garcia, M.R., Vilas, C., Banga, J.R., et al: ‘Exponential observers for distributed tubular (bio) reactors’, AlChE J., 2008, 54, pp. 29432956.
    36. 36)
      • 36. Layek, R., Datta, A.: ‘Fault detection and intervention in biological feedback’, J. Biol. Syst., 2013, 20, (4), pp. 441453.
    37. 37)
      • 37. Laschov, D., Margaliot, M., Even, G.: ‘Observability of Boolean networks: a graph-theoretic approach’, Automatica, 2013, 49, (8), pp. 23512362.
    38. 38)
      • 38. Cheng, D., Qi, H.: ‘Controllability and observability of Boolean control networks’, Automatica, 2009, 45, (7), pp. 16591667.
    39. 39)
      • 39. Fornasini, E., Valcher, M.E.: ‘Observability, reconstructibility and state observers of Boolean control networks’, IEEE Trans. Autom. Control, 2013, 58, (6), pp. 13901401.
    40. 40)
      • 40. Liu, R., Qian, C., Jin, Y.F.: ‘Observability and sensor allocation for Boolean networks’, IEEE American Control Conf. (ACC, 2017), Seattle, 2017, pp. 38803885.
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