引用本文:王彪,冯俊娥.关于布尔控制网络的能观性和能检性的研究现状[J].控制与决策,2020,35(9):2049-2058
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关于布尔控制网络的能观性和能检性的研究现状
王彪,冯俊娥
(山东大学数学学院,济南250100)
摘要:
布尔(控制)网络是模拟基因调控网络有效的数学模型.该模型将细胞内(或特定一个基因组内)基因与基因之间的相互作用关系量化,系统的状态和函数直接反应基因表达、复制、转录等生命活动,在新的数学工具矩阵半张量积的帮助下,取得了许多优秀成果.近些年,国内外病毒疫情频发,对全球各个方面造成巨大的冲击和损失,病毒检测技术是战“疫”中非常重要的一个环节.鉴于此,总结近年来矩阵半张量积在布尔(控制)网络的能观性和能检性方面取得的一些成果,以便更多学者关注这类问题和方法.首先回顾能观性和能检性的发展历程;然后,从理论角度分析并用网络图呈现4种能观性与3种能检性之间的关系,整理在布尔网络和布尔控制网络中相关的一些重要成果,包括状态反馈、输出反馈、含干扰、含切换等多种情形;最后通过简述能观性和能检性的应用现状展望其未来发展.
关键词:  布尔网络  布尔控制网络  能观性  能检性  能重构性
DOI:10.13195/j.kzyjc.2020.0308
分类号:TP273
基金项目:国家自然科学基金项目(61773371,61877036);山东省自然科学基金项目(ZR2019MF002).
Recent development on observability and detectability of Boolean control networks
WANG Biao,FENG Jun-e
(School of Mathematics,Shandong University,Ji'nan250100,China)
Abstract:
Boolean(control) network is an effective mathematical model of simulating gene regulation networks. By quantifying the interactions among genes within cells or a particular genome and related variables, the expression, replication, transcription and other activities of genes can be well reflected by a Boolean network model. Via a novel tool, semi-tensor product, a lot of excellent results on Boolean networks are obtained. In recent years, there have been frequent outbreaks of virus at home and abroad, causing great impact and loss to all aspects of the world. Virus detection technology plays a key role against virus diseases. In view of this, the paper mainly summarizes some recent achievements on observability and detectabitliy of Boolean control networks via semi-tensor product to attract more scholars' attention to such problems and methods. Firstly, the developments of observability and detectabitliy are reviewed. Then, from a theoretical point of view, the relationship among four types of observability and three types of detectability is shown by a network diagram. Moreover, some important works, including state feedback, output feedback, disturbance and so on, are introduced. Finally, following an overview of some applications of observability and detectability, future development is prospected.
Key words:  Boolean networks  Boolean control networks  observability  detectability  reconstructibility

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