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概率布尔网络的牵制鲁棒镇定

沈宇桐, 徐勇   

  1. 河北工业大学理学院, 天津 300401
  • 收稿日期:2021-09-01 修回日期:2021-12-07 出版日期:2022-06-25 发布日期:2022-07-29
  • 基金资助:
    河北省自然科学基金项目(G2019202350)资助课题.

沈宇桐, 徐勇. 概率布尔网络的牵制鲁棒镇定[J]. 系统科学与数学, 2022, 42(6): 1454-1466.

SHEN Yutong, XU Yong. Pinning Robust Stabilization of Probabilistic Boolean Networks[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(6): 1454-1466.

Pinning Robust Stabilization of Probabilistic Boolean Networks

SHEN Yutong, XU Yong   

  1. School of Science, Hebei University of Technology, Tianjin 300401
  • Received:2021-09-01 Revised:2021-12-07 Online:2022-06-25 Published:2022-07-29
文章研究概率布尔网络通过牵制控制器依概率1实现鲁棒镇定的问题.首先,利用矩阵的半张量积,给出带有干扰的概率布尔网络在牵制控制下的代数表示,通过牵制反馈控制器,改变了状态概率转移矩阵的列,得到了可在任意干扰下依概率1实现鲁棒镇定的概率布尔网络.其次,根据状态概率转移矩阵列的变化,确定牵制节点集,验证了牵制反馈矩阵的可解性并提出牵制控制器的设计算法.最后,给出实例说明结果的有效性.
In this paper, the problem of probabilistic Boolean networks which achieve robust stabilization with probability 1 under pinning control is studied. Firstly, by using semi-tensor product of matrices, the algebraic expression of probabilistic Boolean networks with interference is proposed under pinning control. By pinning state-feedback controllers, the columns of the state probability transition matrices are changed, and a new probabilistic Boolean network which can achieve robust stabilization with probability 1 is obtained under any interference. Secondly, the pinning nodes set is determined according to the change of the state probability transition matrices. In addition, the solvability of the pinning state-feedback matrices is verified and an algorithm for designing pinning controllers is proposed. Finally, an example is given to illustrate the effectiveness of the results.

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