引用本文:刘洋,刘泽娇,卢剑权.状态翻转控制下布尔控制网络的可镇定性和Q学习算法(英文)[J].控制理论与应用,2021,38(11):1743~1753.[点击复制]
LIU Yang,LIU Ze-jiao,LU Jian-quan.State-flipped control and Q-learning algorithm for the stabilization of Boolean control networks[J].Control Theory and Technology,2021,38(11):1743~1753.[点击复制]
状态翻转控制下布尔控制网络的可镇定性和Q学习算法(英文)
State-flipped control and Q-learning algorithm for the stabilization of Boolean control networks
摘要点击 1368  全文点击 408  投稿时间：2021-08-25  修订日期：2021-12-01
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DOI编号  10.7641/CTA.2021.10795
  2021,38(11):1743-1753
中文关键词  布尔控制网络  半张量积  状态翻转控制  全局镇定性  Q学习算法
英文关键词  Boolean control networks  semi-tensor product  state-flippped control  global stabilization  Q-learning algorithm
基金项目  Supported by the National Natural Science Foundation of China (62173308, 61973078) and the Natural Science Foundation of Zhejiang Province of China (LR20F030001, LD19A010001).
作者单位E-mail
刘洋* 浙江师范大学 liuyang@zjnu.edu.cn 
刘泽娇 浙江师范大学  
卢剑权 东南大学  
中文摘要
      在给定一个子集的条件下, 本文研究了在状态翻转控制下布尔控制网络的全局镇定问题. 对于节点集的给定子 集, 状态翻转控制可以将某些节点的值从1 (或0)变成0 (或1). 将翻转控制作为控制之一, 本文研究了状态翻转控制下的 布尔控制网络. 将控制输入和状态翻转控制结合, 提出了联合控制对和状态翻转转移矩阵的概念. 接着给出了状态翻转 控制下布尔控制网络全局稳定的充要条件. 镇定核是最小基数的翻转集合, 本文提出了一种寻找镇定核的算法. 利用可 达集的概念, 给出了一种判断全局镇定和寻找联合控制对序列的方法. 此外, 如果系统是一个大型网络, 则可以利用一 种名为Q学习算法的无模型强化学习方法寻找联合控制对序列. 最后给出了一个数值例子来说明本文的理论结果.
英文摘要
      In this paper, the global stabilization of Boolean control networks under state-flipped control with respect to a given subset is addressed. For a given subset of the set of the nodes, the state-flipped control can change the values of some nodes from 1 or 0 to 0 or 1. Considering the flips as controls, Boolean networks under state-flipped control are studied. Combining control inputs with state-flipped controls, the concepts of joint control pair and the state-flipped-transition matrix are proposed. A necessary and sufficient condition is provided to check whether a Boolean control network under state-flipped control can be globally stabilized. An algorithm is developed to find the stabilizing kernel, which is the flip set with the minimal cardinal number. By using the reachable set, another method is provided for global stabilization and joint control pair sequences. Besides, if the system is a large scale network, a model-free reinforcement learning method called Q-learning algorithm, is used for the joint control pair sequences. A numerical example is given to illustrate the theoretical results.