Invertibility and nonsingularity of Boolean control networks
Zhang, Kuize1,2; Zhang, Lijun1,4; Xie, Lihua3
Source PublicationAUTOMATICA
AbstractInvertibility 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.
KeywordBoolean control network Invertibility Nonsingularity Symbolic dynamics Weighted pair graph Semi-tensor product of matrices Control of the mammalian cell cycle
Funding ProjectFundamental 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 Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000361073600020
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Document Type期刊论文
Corresponding AuthorZhang, Kuize
Affiliation1.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
Recommended Citation
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.
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