Improved Multiple-State Observer Design for Boolean Control Networks

  • Junqi YangEmail author
  • Lizhi Cui
  • Yantao Chen
  • Zihan Gao
  • Wei Qian
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 480)


This paper tries to deal with the issue of state estimation for Boolean control networks (BCNs), and a kind of improved multiple-state observer is proposed. The improved multiple-state observer can be described by means of a specific BCN that overcomes the difficulty of the existing multiple-state observer, where it is difficult to find a general expression for the observer matrix. Next, based on the states that can possibly generate the output and the ones that are observed by the designed observer in current time step, an adaptive algorithm which finishes the design of multiple-state observer is provided to update the observer states, and the purpose of state estimation for BCN is achieved. Finally, an example is given to illustrate the proposed methods.


Boolean control networks Multiple-state observer State estimation Observer design 



This work was supported by National Nature Science Foundation of China (grant nos. 61403129, 61573129). This work was also supported by the Programme of Key Young Teacher of Henan Province Higher University (grant no. 2015GGJS-064), the Doctoral Fund Program of Henan Polytechnic University (grant no. B2015-30), innovation Scientists and Technicians Troop Construction Projects of Henan Polytechnic University and Henan Province (grant nos. T2017-1 and CXTD2016054), and the Science and Technology Innovation Talents Project of Henan Province (grant no. 164100510004).


  1. 1.
    Kauffman, S.A.: Metabolic stability and epigenesist in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cheng, D., Qi, H.: A linear representation of dynamics of Boolean control networks. IEEE Trans. Automat. Control 55(10), 2251–2258 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cheng, D., Qi, H., Li, Z.: Analysis and Control of Boolean Networks. Springer-verlag, London, U.K. (2011)CrossRefGoogle Scholar
  4. 4.
    Li, H., Wang, Y., Liu, Z.: Stability analysis for switched Boolean networks under arbitrary switching. Signals 59(7), 1978–1982 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Li, R., Yang, M., Chu, T.: State feedback stabilization for Boolean control networks. IEEE Trans. Automat. Control 58(7), 1853–1857 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhong, J., Ho, D.W.C., Lu, J., Xu, W.: Global robust stability and stabilization of Boolean network with disturbances. Automatica 84, 142–148 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cheng, D., Qi, H.: Controllability and observability of Boolean control networks. Automatica 45(7), 1659–1667 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cheng, D.: Disturbance decoupling of Boolean control networks. IEEE Trans. Automat. Control 56(1), 2–10 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Liu, Y., Li, B., Lou, J.: Disturbance decoupling of singular Boolean control networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 13(6), 1194–1200 (2016)CrossRefGoogle Scholar
  10. 10.
    Fornasini, E., Valcher, M.E.: Optimal control of Boolean control networks. IEEE Trans. Automat. Control 59(5), 1258–1270 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Li, F., Lu, X., Yu, Z.: Optimal control algorithms for switched Boolean network. J. Franklin Inst. 351(6), 3490–3501 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Cheng, D., Zhao, Y., Xu, T.: Receding horizon based feedback optimization for mix-valued logical networks. IEEE Trans. Automat. Control 60(12), 3361–3365 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Zhang, Z., Leifeld, T., Zhang, P.: Finite horizon tracking control of Boolean control networks. IEEE Trans. Automat. 63(6), 1798–1805 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Fornasini, E., Valcher, M.E.: Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans. Automat. Control 58(6), 1390–1401 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhang, Z., Leifeld, T., Zhang, P.: Observer design for Boolean control networks. In: IEEE 55th Conference on Decision and Control (CDC), pp. 6272–6277. IEEE, Las Vegas, USA (2016)Google Scholar
  16. 16.
    Zhang, Z., Leifeld, T., Zhang, P.: Unknown input decoupling and estimation in observer design for Boolean control networks. IFAC PapersOnLine 50(1), 2917–2922 (2017)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Junqi Yang
    • 1
    Email author
  • Lizhi Cui
    • 1
  • Yantao Chen
    • 1
  • Zihan Gao
    • 1
  • Wei Qian
    • 1
  1. 1.College of Electrical Engineering and AutomationHenan Polytechnic UniversityJiaozuoPeople’s Republic of China

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