Abstract
In this paper, the problem of controllability of Boolean control networks (BCNs) with multiple time delays in both states and controls is investigated. First, the controllability problem of BCNs with multiple time delays in controls is considered. For this controllability problem, a controllability matrix is constructed by defining a new product of matrices, based on which a necessary and sufficient controllability condition is obtained. Then, the controllability of BCNs with multiple time delays in states is studied by giving a necessary and sufficient condition. Subsequently, based on these results, a controllability matrix for BCNs with multiple time delays in both states and controls is proposed that provides a concise controllability condition. Finally, two examples are given to illustrate the main results.
摘要
本文研究状态和控制均具有多时滞的布尔控制网络可控性问题. 首先, 考虑控制具有多时滞的布尔控制网络可控性问题. 对于该问题, 本文通过定义一个新的矩阵乘积构建系统的可控性矩阵, 基于该矩阵, 得到一个系统可控的充分必要条件. 其次, 研究状态具有多时滞的布尔控制网络可控性问题, 提出一个状态具有多时滞的布尔控制网络可控的充分必要条件. 然后, 提出一个状态和控制均具有多时滞的布尔控制网络可控性矩阵, 利用该矩阵, 提供一个简洁的可控性条件. 最后, 给出2个例子说明得到的理论结果.
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The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Yifeng LI designed the research and drafted the paper. Lan WANG helped organize the paper. Yifeng LI and Lan WANG revised and finalized the paper.
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Yifeng LI and Lan WANG declare that they have no conflict of interest.
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Project supported by the Natural Science Foundation of Chongqing, China (No. CSTB2022NSCQ-MSX2869), the Science and Technology Research Program of Chongqing Municipal Education Commission, China (No. KJQN202200524), the Research Project of National Center for Applied Mathematics in Chongqing, China (No. ncamc2022-msxm05), and the Program of Chongqing Normal University, China (No. 21XLB045)
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Li, Y., Wang, L. Controllability of Boolean control networks with multiple time delays in both states and controls. Front Inform Technol Electron Eng 24, 906–915 (2023). https://doi.org/10.1631/FITEE.2200618
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DOI: https://doi.org/10.1631/FITEE.2200618