Skip to main content

Advertisement

Springer Nature Link
Log in

Controllability of Boolean control networks avoiding states set

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this paper, using semi-tensor product and the vector form of Boolean logical variables, the Boolean control network (BCN) is expressed as a bilinear discrete time system about state and control variables. Based on the algebraic form, the reachability and controllability avoiding undesirable states set are discussed. The reachability and controllability discussed here are under certain constraint and the definitions of reachability and controllability avoiding undesirable states set have practical meaning. Also, the necessary and sufficient conditions for reachability and controllability are given. At last, the control sequence that steers one state to another is constructed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22: 437–467

    Article  MathSciNet  Google Scholar 

  2. Huang S, Ingber I. Shape-dependent control of cell growth, differentiation, and apotosis: Switching between attractors in cell regulatory networks. Exp Cell Res, 2000, 261: 91–103

    Article  Google Scholar 

  3. Huang S. Regulation of cellular states in mammalian cells from a genomewide view. In: Collado-Vodes J, Hofestadt R, eds. Gene Regulation and Metabolism. Cambridge: MIT Press, 2002. 181–220

    Google Scholar 

  4. Farrow C, Heidel J, Maloney H, et al. Scalar equations for synchronous Boolean networks with biological applications. IEEE Trans Neural Networks, 2004, 15: 348–354

    Article  Google Scholar 

  5. Datta A, Choudhary A, Bittner M L, et al. Ecternal control in markovion genetic regulatory networks. Mach Learn, 2003, 52: 169–191

    Article  MATH  Google Scholar 

  6. Datta A, Choudhary A, Bittner M L, et al. External control in markovion genetic regulatory networks: the imperfect information case. Bioinformatics, 2004, 20: 924–930

    Article  Google Scholar 

  7. Pal R, Ivanov I, Datta A, et al. Generating Boolean networks with a prescribed attractor structure. Syst Biol, 2005, 21: 4021–4025

    Google Scholar 

  8. Pal R, Datta A, Bitter M L, et al. Intervention in context-sensitive probabilistic Boolean networks. Syst Biol, 2005, 21: 1211–1218

    Google Scholar 

  9. Pal R, Datta A, Dougherty E R. Optimal infinite-horizon control for probabilistic Boolean networks. IEEE Trans Signal Process, 2006, 54: 2375–2387

    Article  Google Scholar 

  10. Datta A, Pal R, Choudhary A, et al. Control approaches for probabilistic gene regulatory networks. IEEE Signal Process Mag, 2007, 24: 54–63

    Article  Google Scholar 

  11. Akutsu T, Hayashida M, Ching W, et al. Control of Boolean networks: hardness results and algorithms for tree structured networks. J Theor Biol, 2007, 244: 670–679

    Article  MathSciNet  Google Scholar 

  12. Cheng D. Semi-tensor Product of Matrices-Theory and Applications. Beijing: Science Press, 2007

    Google Scholar 

  13. Cheng D, Qi H. Controllability and observability of Boolean control networks. Automatica, 2009, 45: 1659–1667

    Article  MATH  MathSciNet  Google Scholar 

  14. Cheng D, Qi H. A linear representation of dynamics of Boolean networks. IEEE Trans Autom Control, 2010, 55: 2251–2258

    Article  MathSciNet  Google Scholar 

  15. Cheng D, Qi H, Zhao Y. On Boolean control networks-an algebraic approach. In: Proceedings of the 18th IFAC World Congress, Milano, 2011. 8366–8377

    Google Scholar 

  16. Cheng D, Qi H, Li Z. Analysis and Control of Boolean Networks: A Semi-tensor Product Approach. London: Springer-Verlag, 2011

    Book  Google Scholar 

  17. Zhao Y, Qi H, Cheng D. Input-state incidence matrix of Boolean control networks and its applications. Syst Control Lett, 2010, 59: 767–774

    Article  MATH  MathSciNet  Google Scholar 

  18. Cheng D. Semi-tensor product of matrices and its applications-A survey. In: the International Congress of Chinese Mathematicians, Hangzhou, 2007. 641–668

    Google Scholar 

  19. Magnus J, Neudecker H. Matrix Differential Calculus with Applications in Statistics and Econometrics. John Wiley and Sons, 1999

    Google Scholar 

  20. Fanti M, Maione B, Turchiano B. Controllability of linear single-input positive discrete-time systems. Int J Control, 1989, 50: 2523–2542

    Article  MATH  MathSciNet  Google Scholar 

  21. Caccetta L, Rumchev V G. A survey of reachability and controllability for positive linear systems. Ann Oper Res, 2000, 98: 101–122

    Article  MATH  MathSciNet  Google Scholar 

  22. Rumchev V G, James D J G. Controllability of positive linear discrete-time systems. Int J Control, 1989, 50: 845–857

    Article  MATH  MathSciNet  Google Scholar 

  23. Laschov D, Margaliot M. Controllability of Boolean control networks via Perron-Frobenius theory. Automatica, 2012, 48: 1218–1223

    Article  MATH  MathSciNet  Google Scholar 

  24. Robert F. Discrete Iterations, A Metric Study. Translated by Rokne J. Berlin: Springer-Verlag, 1986

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450002, China

    ZhiQiang Li & JinLi Song

Authors
  1. ZhiQiang Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. JinLi Song
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to ZhiQiang Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Z., Song, J. Controllability of Boolean control networks avoiding states set. Sci. China Inf. Sci. 57, 1–13 (2014). https://doi.org/10.1007/s11432-013-4839-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-013-4839-0

Keywords