Invertibility and nonsingularity of Boolean control networks

doi:10.1016/j.automatica.2015.07.016

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	Invertibility and nonsingularity of Boolean control networks
	Zhang, Kuize 1,2; Zhang, Lijun 1,4; Xie, Lihua 3
	2015-10-01
发表期刊	AUTOMATICA
ISSN	0005-1098
卷号	60 页码:155-164
摘要	Invertibility is an interesting and classical control-theoretic problem. However, there has been no result for the invertibility of Boolean control networks (BCNs) so far. We first adopt the theory of symbolic dynamics to characterize it. First, it is shown that a BCN generates a continuous mapping from the space of input trajectories to the space of output trajectories. Based on it, the concepts of nonsingularity and invertibility of BCNs are first defined as the injectivity and bijectivity of the mapping, respectively. Second, combined symbolic dynamics with the semi-tensor product (STP) of matrices, an equivalent test criterion for invertibility is given; easily computable algorithms to construct the inverse BCN for an invertible BCN are presented; and it is proved that invertibility remains invariant under coordinate transformations. Third, an equivalent test criterion for nonsingularity is given via defining a novel directed graph that is called weighted pair graph. Lastly, as an application of invertibility to systems biology, we prove that the BCN model proposed in Faure et al. (2006) is not invertible, i.e., we prove that arbitrarily controlling mammalian cell cycles is unfeasible at the theoretical level. (C) 2015 Elsevier Ltd. All rights reserved.
关键词	Boolean control network Invertibility Nonsingularity Symbolic dynamics Weighted pair graph Semi-tensor product of matrices Control of the mammalian cell cycle
DOI	10.1016/j.automatica.2015.07.016
语种	英语
资助项目	Fundamental Research Funds for the Central Universities[HEUCFX41501] ; Key Laboratory of Systems and Control, Chinese Academy of Sciences ; National Natural Science Foundation of China[61174047] ; Program for New Century Excellent Talents in University of Ministry of Education of China ; Basic Research Foundation of Northwestern Polytechnical University[JC201230] ; Singapore-MIT Alliance for Science and Technology, National Research Foundation of Singapore[NRF2011NRF-CRP001-090] ; Singapore-MIT Alliance for Science and Technology, National Research Foundation of Singapore[NRF2013EWT-EIRP004-012] ; Natural Science Foundation of China under NSFC[61120106011]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000361073600020
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20772
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Kuize
作者单位	1.Harbin Engn Univ, Coll Automat, Harbin 150001, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Nanyang Technol Univ, Ctr E City, EXQUISITUS, Singapore 639798, Singapore 4.Northwestern Polytech Univ, Sch Marine Sci & Technol, Xian 710072, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Kuize,Zhang, Lijun,Xie, Lihua. Invertibility and nonsingularity of Boolean control networks[J]. AUTOMATICA,2015,60:155-164.
APA	Zhang, Kuize,Zhang, Lijun,&Xie, Lihua.(2015).Invertibility and nonsingularity of Boolean control networks.AUTOMATICA,60,155-164.
MLA	Zhang, Kuize,et al."Invertibility and nonsingularity of Boolean control networks".AUTOMATICA 60(2015):155-164.