Strong controllability of mix-valued logical control networks
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- 英文论文题名：Strong controllability of mix-valued logical control networks
- 论文作者：Qunxi Zhu ; Bingquan Chen ; Yang Liu ; Jianquan Lu
- 英文论文作者：Qunxi Zhu ; Bingquan Chen ; Yang Liu ; Jianquan Lu ; College of Mathematics ; Physics and Information Engineering ; Zhejiang Normal University ; College of Mathematical Sciences ; Fudan University ; School of Mathematics ; Southeast University
- 年：2017
- 作者机构：College of Mathematics,Physics and Information Engineering,Zhejiang Normal University;College of Mathematical Sciences,Fudan University;School of Mathematics,Southeast University;
- 英文论文关键词：Mix-valued logical control network ; semi-tensor product ; primitive matrices ; strong controllability
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TP13
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：215k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the strong controllability of mix-valued logical control networks are investigated. The definition of strong controllability is presented for mix-valued logical control networks. Necessary and sufficient conditions are obtained for the strong controllability of mix-valued logical control networks by the properties of primitive matrices. Numerical examples are given to demonstrate the effectiveness of the obtained main results.
In this paper, the strong controllability of mix-valued logical control networks are investigated. The definition of strong controllability is presented for mix-valued logical control networks. Necessary and sufficient conditions are obtained for the strong controllability of mix-valued logical control networks by the properties of primitive matrices. Numerical examples are given to demonstrate the effectiveness of the obtained main results.
In this paper, the strong controllability of mix-valued logical control networks are investigated. The definition of strong controllability is presented for mix-valued logical control networks. Necessary and sufficient conditions are obtained for the strong controllability of mix-valued logical control networks by the properties of primitive matrices. Numerical examples are given to demonstrate the effectiveness of the obtained main results.
引文
[1]A.Adamatzky.On dynamically non-trivial three-valued logics:oscillatory and bifurcatory species.Chaos Solitons&Fractals,18(5):917-936,2003.
[2]A.Berman and R.J.Plemmons.Nonnegative Matrices in Mathematical Sciences.Academic Press,1979.
[3]D.Z.Cheng.Semi-tensor product of matrices-Theory and Applications.2007.
[4]D.Z.Cheng,Z.Q.Li,and H.S.Qi.Realization of Boolean control networks.Automatica,46(1):62-69,2010.
[5]D.Z.Cheng,H.S.Qi,and Z.Q.Li.Analysis and Control of Boolean Networks:A Semi-tensor Product Approach.London,Springer,2011.
[6]D.Z.Cheng and Y.Zhao.Normal form of general logic mappings.in Proceedings of 30th Chinese Control Conference,1416(1):6368-6373,2011.
[7]D.Z.Cheng,Y.Zhao,and X.R.Xu.Mix-valued logic and its applications.Journal of Shandong University,46(10):32-44,2011.
[8]E.Kaplan,J.E.Marsden,and K.R.Sreenivasan.Perspectives and Problems in Nolinear Science.Springer New York,2003.
[9]S.A.Kauffman.Metabolic stability and epigenesis in randomly constructed genetic nets.Journal of Theoretical Biology,22(3):437-67,1969.
[10]D.Laschov and M.Margaliot.Controllability of Boolean control networks via Perron-Frobenius theory.Automatica,48(6):1218-1223,2012.
[11]F.F.Li.Pinning control design for the stabilization of Boolean networks.IEEE Transactions on Neural Networks&Learning Systems,27(7):1585-1590,2016.
[12]H.T.Li and Y.Z.Wang.Consistent stabilizability of switched Boolean networks.Neural Networks,46(46C):183-189,2013.
[13]H.T.Li and Y.Z.Wang.Controllability analysis and control design for switched Boolean networks with state and input constraints.SIAM Journal on Control&Optimization,53(5):2955-2979,2015.
[14]R.Li,M.Yang,and T.G.Chu.State feedback stabilization for probabilistic Boolean networks.Automatica,50(4):1272-1278,2014.
[15]Z.Q.Li,H.M.Xiao,and J.L.Song.Reachability and controllability of mix-valued control networks.In International Conference on Advanced Mechatronic Systems,pages 329-334,2012.
[16]Y.Liu,H.W.Chen,J.Q.Lu,and B.Wu.Controllability of probabilistic Boolean control networks based on transition probability matrices.Automatica,52(C):340-345,2015.
[17]Y.Liu,J.Q.Lu,and B.Wu.Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks.ESAIM Control Optimisation&Calculus of Variations,20(1):158-173,2014.
[18]Y.Liu,L.J.Sun,J.Q.Lu,and J.L.Liang.Feedback controller design for the synchronization of Boolean control networks.IEEE Transactions on Neural Networks&Learning Systems,27(9):1991-1996,2016.
[19]Z.B.Liu and Y.Z.Wang.Disturbance decoupling of mixvalued logical networks via the semi-tensor product method.Automatica,48(8):1839-1844,2012.
[20]J.Q.Lu,J.Zhong,D.W.C.Ho,Y.Tang,and J.D.Cao.On controllability of delayed Boolean control networks.SIAMJournal on Control&Optimization,54(2):475-494,2016.
[21]J.Q.Lu,J.Zhong,C.Huang,and J.D.Cao.On pinning controllability of Boolean control networks.IEEE Transactions on Automatic Control,61(6):1658-1663,2016.
[22]B.P.Molinari.A strong controllability and observability in linear multivariable control.IEEE Transactions on Automatic Control,21(5):761-764,1976.
[23]M.Nagasaki,A.Saito,A.Doi,H.Matsuno,and S.Miyano.Foundations of systems biology.MIT Press.
[24]P.Rocha and E.Zerz.Strong controllability and extendibility of discrete multidimensional behaviors.Systems&Control Letters,54(4):375-380,2005.
[25]B.Shyla and G.Nagendrappa.Bi-decomposition of function sets in multiple-valued logic for circuit design and data mining.Artificial Intelligence Review,20(3):233-267,2003.
[26]A.R.Sourour.On strong controllability of infinitedimensional linear systems.Journal of Mathematical Analysis&Applications,87(2):460-462,1982.
[27]S.M.Swei,T.Iwasaki,and M.Corless.Quadratic controllability,strong controllability,and a related output feedback property.SIAM Journal on Control&Optimization,39(5):1373-1390,2000.
[28]L.G.Volkert and M.Conrad.The role of weak interactions in biological systems:the dual dynamics model.Journal of Theoretical Biology,193(2):287-306,1998.
[29]J.Zhong,J.Q.Lu,Y.Liu,and J.D.Cao.Synchronization in an array of output-coupled Boolean networks with time delay.IEEE Transactions on Neural Networks&Learning Systems,25(12):2288-2294,2014.
[30]Q.X.Zhu,Y.Liu,J.Q.Lu,and J.D.Cao.Strong controllability and minimum pinning control of boolean control networks via stp of matrices.Preprint.
[2]A.Berman and R.J.Plemmons.Nonnegative Matrices in Mathematical Sciences.Academic Press,1979.
[3]D.Z.Cheng.Semi-tensor product of matrices-Theory and Applications.2007.
[4]D.Z.Cheng,Z.Q.Li,and H.S.Qi.Realization of Boolean control networks.Automatica,46(1):62-69,2010.
[5]D.Z.Cheng,H.S.Qi,and Z.Q.Li.Analysis and Control of Boolean Networks:A Semi-tensor Product Approach.London,Springer,2011.
[6]D.Z.Cheng and Y.Zhao.Normal form of general logic mappings.in Proceedings of 30th Chinese Control Conference,1416(1):6368-6373,2011.
[7]D.Z.Cheng,Y.Zhao,and X.R.Xu.Mix-valued logic and its applications.Journal of Shandong University,46(10):32-44,2011.
[8]E.Kaplan,J.E.Marsden,and K.R.Sreenivasan.Perspectives and Problems in Nolinear Science.Springer New York,2003.
[9]S.A.Kauffman.Metabolic stability and epigenesis in randomly constructed genetic nets.Journal of Theoretical Biology,22(3):437-67,1969.
[10]D.Laschov and M.Margaliot.Controllability of Boolean control networks via Perron-Frobenius theory.Automatica,48(6):1218-1223,2012.
[11]F.F.Li.Pinning control design for the stabilization of Boolean networks.IEEE Transactions on Neural Networks&Learning Systems,27(7):1585-1590,2016.
[12]H.T.Li and Y.Z.Wang.Consistent stabilizability of switched Boolean networks.Neural Networks,46(46C):183-189,2013.
[13]H.T.Li and Y.Z.Wang.Controllability analysis and control design for switched Boolean networks with state and input constraints.SIAM Journal on Control&Optimization,53(5):2955-2979,2015.
[14]R.Li,M.Yang,and T.G.Chu.State feedback stabilization for probabilistic Boolean networks.Automatica,50(4):1272-1278,2014.
[15]Z.Q.Li,H.M.Xiao,and J.L.Song.Reachability and controllability of mix-valued control networks.In International Conference on Advanced Mechatronic Systems,pages 329-334,2012.
[16]Y.Liu,H.W.Chen,J.Q.Lu,and B.Wu.Controllability of probabilistic Boolean control networks based on transition probability matrices.Automatica,52(C):340-345,2015.
[17]Y.Liu,J.Q.Lu,and B.Wu.Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks.ESAIM Control Optimisation&Calculus of Variations,20(1):158-173,2014.
[18]Y.Liu,L.J.Sun,J.Q.Lu,and J.L.Liang.Feedback controller design for the synchronization of Boolean control networks.IEEE Transactions on Neural Networks&Learning Systems,27(9):1991-1996,2016.
[19]Z.B.Liu and Y.Z.Wang.Disturbance decoupling of mixvalued logical networks via the semi-tensor product method.Automatica,48(8):1839-1844,2012.
[20]J.Q.Lu,J.Zhong,D.W.C.Ho,Y.Tang,and J.D.Cao.On controllability of delayed Boolean control networks.SIAMJournal on Control&Optimization,54(2):475-494,2016.
[21]J.Q.Lu,J.Zhong,C.Huang,and J.D.Cao.On pinning controllability of Boolean control networks.IEEE Transactions on Automatic Control,61(6):1658-1663,2016.
[22]B.P.Molinari.A strong controllability and observability in linear multivariable control.IEEE Transactions on Automatic Control,21(5):761-764,1976.
[23]M.Nagasaki,A.Saito,A.Doi,H.Matsuno,and S.Miyano.Foundations of systems biology.MIT Press.
[24]P.Rocha and E.Zerz.Strong controllability and extendibility of discrete multidimensional behaviors.Systems&Control Letters,54(4):375-380,2005.
[25]B.Shyla and G.Nagendrappa.Bi-decomposition of function sets in multiple-valued logic for circuit design and data mining.Artificial Intelligence Review,20(3):233-267,2003.
[26]A.R.Sourour.On strong controllability of infinitedimensional linear systems.Journal of Mathematical Analysis&Applications,87(2):460-462,1982.
[27]S.M.Swei,T.Iwasaki,and M.Corless.Quadratic controllability,strong controllability,and a related output feedback property.SIAM Journal on Control&Optimization,39(5):1373-1390,2000.
[28]L.G.Volkert and M.Conrad.The role of weak interactions in biological systems:the dual dynamics model.Journal of Theoretical Biology,193(2):287-306,1998.
[29]J.Zhong,J.Q.Lu,Y.Liu,and J.D.Cao.Synchronization in an array of output-coupled Boolean networks with time delay.IEEE Transactions on Neural Networks&Learning Systems,25(12):2288-2294,2014.
[30]Q.X.Zhu,Y.Liu,J.Q.Lu,and J.D.Cao.Strong controllability and minimum pinning control of boolean control networks via stp of matrices.Preprint.
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