状态翻转控制下布尔控制网络的可镇定性和Q学习算法  

State-flipped control and Q-learning algorithm for the stabilization of Boolean control networks

作　　者：刘洋 刘泽娇[1,3] 卢剑权 LIU Yang;LIU Ze-jiao;LU Jian-quan(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua Zhejiang 321004,China;College of Mathematical Medicine,Zhejiang Normal University,Jinhua Zhejiang 321004,China;Jinhua Intelligent Manufacturing Research Institute,Jinhua Zhejiang 321032,China;School of Mathematics,Southeast University,Nanjing Jiangsu 210096,China)

机构地区：[1]浙江师范大学数学与计算机科学学院,浙江金华321004 [2]浙江师范大学数理医学院,浙江金华321004 [3]金华市智能制造研究院,浙江金华321032 [4]东南大学数学学院,江苏南京210096

出　　处：《控制理论与应用》2021年第11期1743-1753,共11页Control Theory & Applications

基　　金：Supported by the National Natural Science Foundation of China(62173308,61973078);the Natural Science Foundation of Zhejiang Province of China(LR20F030001,LD19A010001)。

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.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.

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 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]