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The set stabilization problem for Markovian jump Boolean control networks: An average optimal control approach

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  • Zhu, Sanmei
  • Feng, Jun-e

Abstract

In this paper, the authors address the set stabilization problem for Markovian jump Boolean control networks (MJBCNs) by state feedback control. Based on the semi-tensor product, a necessary and sufficient condition for the set stabilization of MJBCNs is put forward via optimal control approach. Moreover, a policy iterative algorithm is deduced for designing the state feedback control. Finally, the proposed method and results are supported by the example of an apoptosis network.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321001818
    DOI: 10.1016/j.amc.2021.126133
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    References listed on IDEAS

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    1. Zhong, Jie & Liu, Yang & Kou, Kit Ian & Sun, Liangjie & Cao, Jinde, 2019. "On the ensemble controllability of Boolean control networks using STP method," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 51-62.
    2. 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.
    3. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    4. Li, Haitao & Xu, Xiaojing & Ding, Xueying, 2019. "Finite-time stability analysis of stochastic switched boolean networks with impulsive effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 557-565.
    5. Li, Xiaodi & Shen, Jianhua & Akca, Haydar & Rakkiyappan, R., 2015. "LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 798-804.
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    Cited by:

    1. Li, Xi & Liu, Yang & Lou, Jungang & Lu, Jianquan, 2023. "Robust minimal strong reconstructibility problem of Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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