随机状态触发脉冲布尔控制网络的渐近反馈能控性  

Asymptotical Feedback Controllability of Boolean Networks with State-dependent Random Impulses

作　　者：卢剑权 汪洋 丁雪莹 LU Jianquan;WANG Yang;DING Xueying(School of Mathematics,Southeast University,Nanjing 210096,China)

机构地区：[1]东南大学数学学院,江苏南京210096

出　　处：《聊城大学学报（自然科学版）》2023年第4期1-13,共13页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(61973078)资助。

摘　　要：基于矩阵半张量积方法,利用混杂指标模型,研究了随机状态触发脉冲布尔控制网络的渐近反馈能控性。首先针对这类网络提出了四种能控性定义,为避免Zeno现象,又给出了前向完备性的概念,并进一步推导了网络前向完备的充要条件。基于最大不变子集的性质,推导了随机状态触发脉冲布尔控制网络两个状态之间渐近反馈可达性的充要条件。通过引入可达性矩阵,进一步得到了网络特定状态渐近反馈可达性以及网络渐近反馈能控性的充要条件。最后,结合例子讨论了渐近反馈能控性与其它能控性之间的关系。Based on the semi-tensor product of matrices,the asymptotical feedback controllability(AFC)of state triggered random impulsive Boolean control networks(SRIBCNs)is studied by utilizing a hybrid index model.Firstly,four kinds of definitions of controllability are proposed for SRIBCNs.In order to avoid Zeno phenomenon,we give the concept of forward completeness and further derive a necessary and sufficient condition for the forward completeness of SRIBCNs.Based on the properties of the largest control invariant subset,a necessary and sufficient condition for the asymptotical feedback reachability(AFR)between two states of SRIBCN is derived.By introducing the reachability matrix,the necessary and sufficient conditions for the AFR of the specific state and the AFC of SRIBCN are obtained.Finally,the relationship between AFC and other controllability is discussed with examples.

关 键 词：布尔控制网络 混杂指标模型 随机脉冲 矩阵半张量积 状态反馈控制 渐近能控性 

分 类 号：O233[理学—运筹学与控制论]