JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2023 Vol.24 No.6 P.906-915

http://doi.org/10.1631/FITEE.2200618

Controllability of Boolean control networks with multiple time delays in both states and controls

Author(s): Yifeng LI, Lan WANG
Affiliation(s): National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing 401331, China; more
Corresponding email(s): liyifeng@cqnu.edu.cn, wanglan202212@126.com
Key Words: Boolean control networks, Semi-tensor product of matrices, Controllability, Time delay

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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.

状态和控制均具有多时滞的布尔控制网络可控性

李一峰¹，王兰²
¹重庆师范大学重庆国家应用数学中心，中国重庆市，401331
²南京师范大学数学科学学院数学系，中国南京市，210023
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。

关键词：布尔控制网络；矩阵半张量积；能控性；时滞

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