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The equivalence issue of two kinds of controllers in Boolean control networks

Author

Listed:
  • Li, Meilin
  • Lu, Jianquan
  • Lou, Jungang
  • Liu, Yang
  • Alsaadi, Fuad E.

Abstract

In this paper, the equivalence issue between state feedback controller and free sequence controller in Boolean control network (BCN) is investigated. Based on the algebraic representation of Boolean networks, we prove that a Boolean control network can be stabilized to a cycle or a fixed point via free sequence controller if and only if there is a state feedback controller which can derive the Boolean control network to the cycle or the fixed point. Then, two algorithms are provided to find the state feedback controller. After that, we prove that a BCN can be globally controllable by free sequence controller, while the BCN is not necessarily globally controllable by state feedback controller. At last, an example is given to illustrate the results.

Suggested Citation

  • Li, Meilin & Lu, Jianquan & Lou, Jungang & Liu, Yang & Alsaadi, Fuad E., 2018. "The equivalence issue of two kinds of controllers in Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 633-640.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:633-640
    DOI: 10.1016/j.amc.2017.11.011
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    References listed on IDEAS

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    1. Fangfei Li, 2016. "Feedback control design for the complete synchronisation of two coupled Boolean networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 2996-3003, September.
    2. Wang, Liqing & Liu, Yang & Wu, Zhengguang & Alsaadi, Fuad E., 2018. "Strategy optimization for static games based on STP method," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 390-399.
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    Cited by:

    1. Mao, Ying & Wang, Liqing & Liu, Yang & Lu, Jianquan & Wang, Zhen, 2018. "Stabilization of evolutionary networked games with length-r information," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 442-451.
    2. Zhu, Sanmei & Feng, Jun-e, 2021. "The set stabilization problem for Markovian jump Boolean control networks: An average optimal control approach," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    3. Tong, Liyun & Liu, Yang & Lou, Jungang & Lu, Jianquan & Alsaadi, Fuad E., 2018. "Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 263-275.
    4. Yu, Yongyuan & Meng, Min & Feng, Jun-e & Gao, Yan, 2019. "An adjoint network approach to design stabilizable switching signals of switched Boolean networks," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 12-22.

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