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

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.