Kybernetika 54 no. 5, 1091-1104, 2018

Reconstructibility of Boolean control networks with time delays in states

Ping Sun, Lijun Zhang and Kuize ZhangDOI: 10.14736/kyb-2018-5-1091

Abstract:

This paper deals with the reconstructibility of Boolean control networks (BCNs) with time delays in states. First, a survey on the semi-tensor product, weighted pair graph, constructed forest and finite automata is given. Second, by using the weighted pair graph, constructed forest and finite automata, an algorithm is designed to judge whether a Boolean control network with time delays in states is reconstructable or not under a mild assumption. Third, an algorithm is proposed to determine the current state. Finally, an illustrative example is given to show the effectiveness of the proposed method.

Keywords:

Boolean control network, reconstructibility, semi-tensor product of matrices, weighted pair graph, finite automaton, formal language

Classification:

94C10, 03D05, 68Q45, 05C22

paper.pdf

References:

  1. T. Akutsu, M. Hayashida, W. Ching and M. K. Ng: Control of Boolean networks: Hardness results and algorithms for tree structured networks. J. Theoret. Biology 244 (2007), 670-679.   DOI:10.1016/j.jtbi.2006.09.023
  2. A. Bolotin: Constructibility of the universal wave function. Foundat. Physics 46 (2016), 1-16.   DOI:10.1007/s10701-016-0018-7
  3. D. Cheng: On semi-tensor product of matrices and its applications. Acta Math. Appl. Sinica 19 (2003), 219-228.   DOI:10.1007/s10255-003-0097-z
  4. D. Cheng: Input-state approach to Boolean networks. IEEE Trans. Neural Networks. 20 (2009), 512-521.   DOI:10.1109/tnn.2008.2011359
  5. D. Cheng and H. Qi: A linear representation of dynamics of Boolean networks. IEEE Trans. Automat. Control 55 (2010), 2251-2258.   DOI:10.1109/tac.2010.2043294
  6. D. Cheng, H. Qi and Z. Li: Realization of Boolean control networks. Automatica 46 (2010), 62-69.   DOI:10.1016/j.automatica.2009.10.036
  7. D. Cheng, H. Qi and Z. Li: Controllability and Observability of Boolean Control Networks. Springer-Verlag, London 2011.   CrossRef
  8. D. Cheng, H. Qi and Z. Li: Analysis and Control of Boolean Networks. Springer-Verlag, London 2011.   CrossRef
  9. C. Farrow et al.: Scalar equations for synchronous Boolean networks with biological applications. IEEE Trans. Neural Networks 15 (2004), 348-354.   DOI:10.1109/tnn.2004.824262
  10. E. Fornasini and M. E. Valcher: Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans. Automat. Control 58 (2013), 1390-1401.   DOI:10.1109/tac.2012.2231592
  11. E. Fornasini and M. E. Valcher: Fault detection analysis of Boolean control networks. IEEE Trans. Automat. Control 60 (2015), 2734-2739.   DOI:10.1109/tac.2015.2396646
  12. L. I. Haitao, G. Zhao, M. Meng and J. Feng: A survey on applications of semi-tensor product method in engineering. Science China (Inform. Sci.) 61 (2018), 1, 010202.   DOI:10.1007/s11432-017-9238-1
  13. M. Han, Y. Liu and Y. Tu: Controllability of Boolean control networks with time delays both in states and inputs. Neurocomputing 129 (2014), 467-475.   DOI:10.1016/j.neucom.2013.09.012
  14. T. Ideker, T. Galitski and L. Hood: A new approach to decoding life: systems biology. Ann. Rev. Genomics Hum. Genet. 2 (2001), 343-372.   DOI:10.1146/annurev.genom.2.1.343
  15. J. Kari: A Lecture Note on Automata and Formal Languages. http://users.utu.fi/jkari/automata/, 2016.   CrossRef
  16. S. A. Kauffman: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theoret. Biology 22 (1969), 437-467.   DOI:10.1016/0022-5193(69)90015-0
  17. H. K. Khalil: Nonlinear Systems. MacMillan, New York 1992.   CrossRef
  18. F. Li, J. Sun and Q. Wu: Observability of Boolean control networks with state time delays. IEEE Trans. Neural Networks 22 (2011), 948-954.   DOI:10.1109/tnn.2011.2126594
  19. F. Li, J. Sun and Q. Wu: Observability of Boolean control networks with state time delays. IEEE Trans. Neural Networks 22 (2011), 948-954.   DOI:10.1109/tnn.2011.2126594
  20. J. Lu, H. Li, Y. Liu and F. Li: Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Control Theory Appl. 11 (2017) 13, 2040-2047.   DOI:10.1049/iet-cta.2016.1659
  21. H. Sui: Regulation of Cellular states in mammalian cells from a genomewide view. In: Gene Regulations and Metabolism - Postgenomic Computational Approaches (J. Collado-Vides, ed.), MIT Press, MA 2002, pp. 181-220.   CrossRef
  22. A. Thomasian: Reconstruct versus read-modify writes in RAID. Inform. Process. Lett. 93 (2005), 163-168.   DOI:10.1016/j.ipl.2004.10.009
  23. A. Valmari: On constructibility and unconstructibility of LTS operators from other LTS operators. Acta Inform. 52 (2015), 207-234.   DOI:10.1007/s00236-015-0217-2
  24. K. Zhang and L. Zhang: Observability of Boolean control networks: a unified approach based on the theories of finite automata. IEEE Trans. Automat. Control 61 (2015), 6854-6861.   CrossRef
  25. L. Zhang and K. Zhang: Controllability and observability of Boolean control networks with time-variant delays in states. IEEE Trans. Neural Networks Learning Syst. 24 (2013), 1478-1484.   DOI:10.1109/tnnls.2013.2246187
  26. L. Zhang and K. Zhang: Controllability of time-variant Boolean control networks and its application to Boolean control networks with finite memories. Science China (Inform. Sci.) 56 (2013), 1-12.   DOI:10.1007/s11432-012-4651-2
  27. K. Zhang and L. Zhang: Controllability of probabilistic Boolean control networks with time-variant delays in states. Science China (Inform. Sci.) 59 (2016), 092204:1-092204:10.   DOI:10.1007/s11432-012-4651-2
  28. K. Zhang, L. Zhang and R. Su: A weighted pair graph representation for reconstructibility of Boolean control networks. SIAM J. Control Optim. 54 (2016), 3040-3060.   DOI:10.1137/140991285
  29. Y. Zhao, H. Qi and D. Cheng: Input-state incidence matrix of Boolean control networks and its applications. Systems Control Lett. 59 (2010), 767-774.   DOI:10.1016/j.sysconle.2010.09.002