摘要
布尔网络作为研究基因调控网络的一种重要模型,近年来引起了国内外很多学者的广泛关注.本文利用代数状态空间表示方法,研究具有切换概率分布的概率布尔网络的依分布稳定和镇定问题.首先,回顾针对切换布尔网络稳定性分析的现有的研究结果.其次,给出具有切换概率分布的概率布尔网络依分布稳定的定义,并利用矩阵的半张量积建立具有切换概率分布的概率布尔网络的代数表示.再次,基于该代数表示,建立具有切换概率分布的概率布尔网络的依分布稳定的充分必要条件.最后,给出具有切换概率分布的概率布尔控制网络镇定问题可解的充要条件,并给出相应的控制设计方法.
As an important model for studying gene regulatory networks, Boolean networks have attracted extensive attention from many scholars in the past few decades. Using the algebraic state space representation method, this paper investigates the stability and stabilization in distribution of probabilistic Boolean networks(PBNs) with switching probability distribution(SPD). Firstly, the existing results on the stability of switched Boolean networks are briefly reviewed.Secondly, the definition of stability in distribution of PBNs with SPD is given, and based on the semi-tensor product of the matrices, PBNs with SPD can be converted into the algebraic representation. Thirdly, based on the algebraic representation,a necessary and sufficient condition is presented for the stability in distribution of PBNs with SPD. Finally, a necessary and sufficient condition is presented for the stabilization in distribution of PBNs with SPD, and the corresponding control design method is given.
作者
李雅璐
李海涛
丁雪莹
LI Ya-lu;LI Hai-tao;DING Xue-ying(School of Mathematics and Statistics,Shandong Normal University,Jinan Shandong 250014,China)
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2019年第11期1896-1904,共9页
Control Theory & Applications
基金
国家自然科学基金项目(61873150)
山东省自然科学杰出青年基金项目(JQ201613)
泰山学者青年专家项目资助~~
关键词
概率布尔网络
切换概率分布
稳定
镇定
矩阵半张量积
probabilistic boolean network
switching probability distribution
stability
stabilization
semi-tensor product of matrices
