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A minimum-time control for Boolean control networks with impulsive disturbances

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  • Chen, Hongwei
  • Wu, Bo
  • Lu, Jianquan

Abstract

This paper investigates a Mayer-type optimal control and minimum-time control of a Boolean control network (BCN) with impulsive disturbances. Using the semi-tensor product, the BCN with impulsive disturbances is converted into algebraic discrete-time impulsive dynamic systems, and several necessary conditions for optimality are derived. Then we consider the problem of steering a BCN with impulsive disturbances from a given initial state to a desired state in minimal time. And a necessary condition, stated in the form of maximum principle, is obtained for a control to be time-optimal. It shows that the impulsive disturbances play an important role in the optimal control problem for BCNs. At last, a biological example is given to illustrate the effectiveness and advantage of the obtained results.

Suggested Citation

  • Chen, Hongwei & Wu, Bo & Lu, Jianquan, 2016. "A minimum-time control for Boolean control networks with impulsive disturbances," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 477-483.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:477-483
    DOI: 10.1016/j.amc.2015.09.075
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    References listed on IDEAS

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    1. Zang, Hong & Zhang, Tonghua & Zhang, Yanduo, 2015. "Bifurcation analysis of a mathematical model for genetic regulatory network with time delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 204-226.
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    Cited by:

    1. 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.
    2. Qilong Sun & Haitao Li, 2022. "Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, October.
    3. Xiangshan Kong & Qilong Sun & Haitao Li, 2022. "Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    4. Zou, Yunlei & Zhu, Jiandong, 2016. "Reachability of higher-order logical control networks via matrix method," Applied Mathematics and Computation, Elsevier, vol. 287, pages 50-59.
    5. 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.
    6. Gao, Bo & Deng, Zheng-hong & Zhao, Da-wei & Song, Qun, 2017. "State analysis of Boolean control networks with impulsive and uncertain disturbances," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 187-192.

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