Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Observability of Boolean networks via STP and graph methods

Observability of Boolean networks via STP and graph methods

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

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)
      • 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.
    2. 2)
      • 21. Li, R., Yang, M., Chu, T.: ‘State feedback stabilization for Boolean control networks’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 18531857.
    3. 3)
      • 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.
    4. 4)
      • 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.
    5. 5)
      • 36. Layek, R., Datta, A.: ‘Fault detection and intervention in biological feedback’, J. Biol. Syst., 2013, 20, (4), pp. 441453.
    6. 6)
      • 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.
    7. 7)
      • 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.
    8. 8)
      • 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.
    9. 9)
      • 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.
    10. 10)
      • 2. Davidson, E.H., Bolouri, H.: ‘A genomic regulatory network for development’, Science, 2002, 295, (5560), p. 1669.
    11. 11)
      • 8. Li, R., Yang, M., Chu, T.: ‘Observability conditions of Boolean control networks’, Int. J. Robust Nonlinear Control, 2014, 24, (17), pp. 27112723.
    12. 12)
      • 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.
    13. 13)
      • 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.
    14. 14)
      • 20. Zhang, H., Wang, X., Lin, X.: ‘Synchronization of asynchronous switched Boolean network’, IEEE/ACM Trans. Comput. Biol. Bioinf., 2015, 12, (6), pp. 14491456.
    15. 15)
      • 7. Zhu, Q., Liu, Y., Lu, J., et al: ‘Observability of Boolean control networks’, Sci. China Inf. Sci., 2018, 61, (9), p. 092201.
    16. 16)
      • 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.
    17. 17)
      • 37. Laschov, D., Margaliot, M., Even, G.: ‘Observability of Boolean networks: a graph-theoretic approach’, Automatica, 2013, 49, (8), pp. 23512362.
    18. 18)
      • 38. Cheng, D., Qi, H.: ‘Controllability and observability of Boolean control networks’, Automatica, 2009, 45, (7), pp. 16591667.
    19. 19)
      • 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.
    20. 20)
      • 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.
    21. 21)
      • 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.
    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)
      • 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.
    24. 24)
      • 25. Fornasini, E., Valcher, M.E.: ‘Fault detection analysis of Boolean control networks’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 27342739.
    25. 25)
      • 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.
    26. 26)
      • 34. Lopez, I., Gamez, M., Carreno, R.: ‘Observability in dynamic evolutionary models’, BioSystems, 2004, 58, pp. 99109.
    27. 27)
      • 24. Li, H., Xie, L., Wang, Y.: ‘On robust control invariance of Boolean control networks’, Automatica, 2016, 68, pp. 392396.
    28. 28)
      • 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.
    29. 29)
      • 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.
    30. 30)
      • 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.
    31. 31)
      • 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.
    32. 32)
      • 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.
    33. 33)
      • 35. Garcia, M.R., Vilas, C., Banga, J.R., et al: ‘Exponential observers for distributed tubular (bio) reactors’, AlChE J., 2008, 54, pp. 29432956.
    34. 34)
      • 18. Liu, Y., Li, B., Chen, H., et al: ‘Function perturbations on singular Boolean networks’, Automatica, 2017, 84, pp. 3642.
    35. 35)
      • 10. Laschov, D., Margaliot, M.: ‘Controllability of Boolean control networks via the perron–frobenius theory’, Automatica, 2012, 48, (6), pp. 12181223.
    36. 36)
      • 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.
    37. 37)
      • 1. Kauffman, S.A.: ‘Metabolic stability and epigenesis in randomly constructed genetic nets’, J. Theor. Biol., 1969, 22, (3), pp. 437467.
    38. 38)
      • 39. Fornasini, E., Valcher, M.E.: ‘Observability, reconstructibility and state observers of Boolean control networks’, IEEE Trans. Autom. Control, 2013, 58, (6), pp. 13901401.
    39. 39)
      • 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).
    40. 40)
      • 31. Liang, J., Chen, H., Lam, J.: ‘An improved criterion for controllability of Boolean control networks’, Automatica, 2017, 62, (11), pp. 60126018.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2018.5279
Loading

Related content

content/journals/10.1049/iet-cta.2018.5279
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address