Exact Controllability of Probabilistic Boolean Control Networks
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- 英文论文题名：Exact Controllability of Probabilistic Boolean Control Networks
- 论文作者：Zhiqiang Li ; Gaihong Feng ; Jinjin Liu ; Ning Li
- 英文论文作者：Zhiqiang Li ; Gaihong Feng ; Jinjin Liu ; Ning Li ; School of Mathematics and Information Science ; Henan University of Economics and Law ; Zhengzhou Shengda University of Economics ; Business and Management
- 年：2017
- 作者机构：School of Mathematics and Information Science,Henan University of Economics and Law;Zhengzhou Shengda University of Economics,Business and Management;
- 英文论文关键词：probabilistic Boolean control network ; exact controllability ; exact reachability ; reachability matrix
- 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（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 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：6
- 文件大小：208k
- 原文格式：D
- 会议级别：全国
摘要
This paper deals with the exact reachability and controllability of probabilistic Boolean control networks(PBCNs).Exact controllability of PBCNs is the generalization of controllability of Boolean control networks(BCNs). Firstly, the maximum probability transfer matrix for PBCNs is constructed, and elements of the matrix denote the maximum probability with which one state transfer to another one. Secondly, sufficient conditions for exact controllability of PBCNs are given. Moreover, an algorithm is obtained to construct the control sequence, which force the initial state to the ideal state. Finally, a numerical example is presented to show the efficiency of the approach.
This paper deals with the exact reachability and controllability of probabilistic Boolean control networks(PBCNs).Exact controllability of PBCNs is the generalization of controllability of Boolean control networks(BCNs). Firstly, the maximum probability transfer matrix for PBCNs is constructed, and elements of the matrix denote the maximum probability with which one state transfer to another one. Secondly, sufficient conditions for exact controllability of PBCNs are given. Moreover, an algorithm is obtained to construct the control sequence, which force the initial state to the ideal state. Finally, a numerical example is presented to show the efficiency of the approach.
This paper deals with the exact reachability and controllability of probabilistic Boolean control networks(PBCNs).Exact controllability of PBCNs is the generalization of controllability of Boolean control networks(BCNs). Firstly, the maximum probability transfer matrix for PBCNs is constructed, and elements of the matrix denote the maximum probability with which one state transfer to another one. Secondly, sufficient conditions for exact controllability of PBCNs are given. Moreover, an algorithm is obtained to construct the control sequence, which force the initial state to the ideal state. Finally, a numerical example is presented to show the efficiency of the approach.
引文
[1]Kauffman S A.Metabolic stability and epigenesis in randomly constructed genetic nets.Journal of Theoretical Biology,Vol.22:437–467,1969.
[2]Kauffman S A.The Origins of Order:Self-organization and Selection in Evolution.New York:Oxford University Press,1993.
[3]Heidel J,Maloney J,Farrow J,Rogers J.Finding cycles in synchronous Boolean networks with applications to biochemical systems,Int.J.Bifurcat.Chaos,Vol.13(3):535–552,2003.
[4]Cheng D Z,Qi H S,Zhao Y.An Introduction to Semi-Tensor Product of Matrices and Its Applications[M],World Scientific Publishing,2012.
[5]Cheng D Z,Qi H S,Li Z Q.Analysis and Control of Boolean Networks?A Semi-tensor Product Approach.London:Springer,2011.
[6]Cheng D Z,Qi H S.A linear representation of dynamics of Boolean networks[J].IEEE Trans.Auto.Contr.,55(10):2251–2258,2010.
[7]Cheng D Z,Qi H S.Algebraic state space approach to logical dynamic systems and its applications,Control theory and Applications,Vol.31(12):1632–1639,2015.(In Chinese)
[8]Zhong J,Lu J,Liu Y,Cao J,Synchronization in an array of output-coupled Boolean networks with time delay,IEEE Transactions on Neural Networks and Learning Systems,2014,25(12):2288-2294
[9]Akutsu T,Hayashida M,Ching W K,Ng M K.Control of Boolean networks:Hardness results and algorithms for tree structured networks,J.Theoretical Biology,Vol.244,670–679,2007.
[10]Cheng D Z,Qi H S.Controllability and observability of Boolean control networks,Automatica,45(7):1659–1667,2009.
[11]Zhao Y,Cheng D Z,and Qi H S.Input-state incidence matrix of Boolean control networks and its applications.Syst.Contr.Letters,59(12):767–774,2010.
[12]Dmitriy L,Michael M.Controllability of Boolean Control Networks via Perron-Frobenius Theory,Automatica,Vol.48(6):1218–1223,2012.
[13]Li F F,Sun J T.Controllability and optimal control of a temporal Boolean network,Neural Networks,34(10):10–17,2012.
[14]Li F F,Sun J T.Controllability of higher order Boolean control networks,Applied Mathematics and Computation,219(1),158–169,2012.
[15]Li H T,Wang Y Z.Output feedback stabilization control design for Boolean control networks.Automatica,49(12):3641–3645,2013.
[16]Li H T,Wang Y Z,Liu Z B.A semi-tensor product approach to pseudo-Boolean functions with application to Boolean control networks.Asian J of Control,16(4):1073–1081,2014.
[17]Li H T,Wang Y Z,Liu Z B.Observability of free Boolean networks by means of the semi-tensor product method.Journal of Systems Science and Complexity.Journal of Systems Science and Complexity,27(4):666–678,2014.
[18]Li H T.Global Stability and Controllability of Switched Boolean Networks.In:Proceeding of the 31st Chinese Control Conference(CCC),Hefei,July 2012,82–88.
[19]Yang Liu,Hongwei Chen and Bo Wu,Controllability of Boolean control networks with impulsive effects and forbidden states,Mathematical Methods in the Applied Sciences,Vol.37(1):1–9,2014.
[20]Li Z Q,Song J L.Controllability of Boolean control networks avoiding states set,Science China Information Sciences,2014,57(3):032205(13),doi:10.1007/s11432-013-4839-0.
[21]Yang,Q.,Li,H.,Liu,Y.Pinning control design for feedback stabilization of constrained Boolean control networks,Adv Differ Equ,2016:182.doi:10.1186/s13662-016-0909-0
[22]Min Meng,Jun-e Feng and Zhongsheng Hou,Synchronization of Interconnected Multi-valued Logical Networks,Asian Journal of Control,Vol.16(6):1659–1669,2014.
[23]Liu Z B,Wang Y Z,Li H T.Controllability of contextsensitive probabilistic mix-valued logical control networks with constraints.Asian Journal of Control,17(1):246–254,2015.
[24]Li F F,Sun J T.Controllability of Probabilistic Boolean Control Networks,Automatica,Vol.47(12):2765–2771,2011.
[25]Li F F,Sun J T.Stability and Stabilization Issue of Probabilistic Boolean Network.In:Proceeding of the 30th Chinese Control Conference(CCC),Yantai,2011,6380–6385
[26]Zhao Y,Cheng D Z.On controllability and stabilizablity of probabilistic Boolean control networks,Science China Information Sciences,2014,57(1):012202(14),doi:10.1007/s11432-013-4851-4.
[27]Yang Liu,Hongwei Chen,Jianquan Lu,Bo Wu,Controllability of probabilistic Boolean control networks based on transition probability matrices,Automatica,2015,Vol.52(2):340-345
[28]Lions J.L.Exact controllability,stabilization and perturbations for distributed parameter systems,SIAM Rev.Vol.30:1–68,1988.
[29]Rabah R,Karrakchou J.Exact controllability and complete stabilizability for linear systems in Hilbert spaces,Appl.Math.Lett.Vol.10(1):35–40,1997.
[30]Zeng Y,Xie Z S,Guo F M.On exact controllability and complete stabilizability for linear systems,Applied Mathematics Letters,Vol.26(7):766–768,2013.
[31]Peng S,Backward Stochastic Differential Equation and Exact Controllability of Stochastic Control Systems,Progress in Natural Science,Vol.4(3):274–284,1994.
[2]Kauffman S A.The Origins of Order:Self-organization and Selection in Evolution.New York:Oxford University Press,1993.
[3]Heidel J,Maloney J,Farrow J,Rogers J.Finding cycles in synchronous Boolean networks with applications to biochemical systems,Int.J.Bifurcat.Chaos,Vol.13(3):535–552,2003.
[4]Cheng D Z,Qi H S,Zhao Y.An Introduction to Semi-Tensor Product of Matrices and Its Applications[M],World Scientific Publishing,2012.
[5]Cheng D Z,Qi H S,Li Z Q.Analysis and Control of Boolean Networks?A Semi-tensor Product Approach.London:Springer,2011.
[6]Cheng D Z,Qi H S.A linear representation of dynamics of Boolean networks[J].IEEE Trans.Auto.Contr.,55(10):2251–2258,2010.
[7]Cheng D Z,Qi H S.Algebraic state space approach to logical dynamic systems and its applications,Control theory and Applications,Vol.31(12):1632–1639,2015.(In Chinese)
[8]Zhong J,Lu J,Liu Y,Cao J,Synchronization in an array of output-coupled Boolean networks with time delay,IEEE Transactions on Neural Networks and Learning Systems,2014,25(12):2288-2294
[9]Akutsu T,Hayashida M,Ching W K,Ng M K.Control of Boolean networks:Hardness results and algorithms for tree structured networks,J.Theoretical Biology,Vol.244,670–679,2007.
[10]Cheng D Z,Qi H S.Controllability and observability of Boolean control networks,Automatica,45(7):1659–1667,2009.
[11]Zhao Y,Cheng D Z,and Qi H S.Input-state incidence matrix of Boolean control networks and its applications.Syst.Contr.Letters,59(12):767–774,2010.
[12]Dmitriy L,Michael M.Controllability of Boolean Control Networks via Perron-Frobenius Theory,Automatica,Vol.48(6):1218–1223,2012.
[13]Li F F,Sun J T.Controllability and optimal control of a temporal Boolean network,Neural Networks,34(10):10–17,2012.
[14]Li F F,Sun J T.Controllability of higher order Boolean control networks,Applied Mathematics and Computation,219(1),158–169,2012.
[15]Li H T,Wang Y Z.Output feedback stabilization control design for Boolean control networks.Automatica,49(12):3641–3645,2013.
[16]Li H T,Wang Y Z,Liu Z B.A semi-tensor product approach to pseudo-Boolean functions with application to Boolean control networks.Asian J of Control,16(4):1073–1081,2014.
[17]Li H T,Wang Y Z,Liu Z B.Observability of free Boolean networks by means of the semi-tensor product method.Journal of Systems Science and Complexity.Journal of Systems Science and Complexity,27(4):666–678,2014.
[18]Li H T.Global Stability and Controllability of Switched Boolean Networks.In:Proceeding of the 31st Chinese Control Conference(CCC),Hefei,July 2012,82–88.
[19]Yang Liu,Hongwei Chen and Bo Wu,Controllability of Boolean control networks with impulsive effects and forbidden states,Mathematical Methods in the Applied Sciences,Vol.37(1):1–9,2014.
[20]Li Z Q,Song J L.Controllability of Boolean control networks avoiding states set,Science China Information Sciences,2014,57(3):032205(13),doi:10.1007/s11432-013-4839-0.
[21]Yang,Q.,Li,H.,Liu,Y.Pinning control design for feedback stabilization of constrained Boolean control networks,Adv Differ Equ,2016:182.doi:10.1186/s13662-016-0909-0
[22]Min Meng,Jun-e Feng and Zhongsheng Hou,Synchronization of Interconnected Multi-valued Logical Networks,Asian Journal of Control,Vol.16(6):1659–1669,2014.
[23]Liu Z B,Wang Y Z,Li H T.Controllability of contextsensitive probabilistic mix-valued logical control networks with constraints.Asian Journal of Control,17(1):246–254,2015.
[24]Li F F,Sun J T.Controllability of Probabilistic Boolean Control Networks,Automatica,Vol.47(12):2765–2771,2011.
[25]Li F F,Sun J T.Stability and Stabilization Issue of Probabilistic Boolean Network.In:Proceeding of the 30th Chinese Control Conference(CCC),Yantai,2011,6380–6385
[26]Zhao Y,Cheng D Z.On controllability and stabilizablity of probabilistic Boolean control networks,Science China Information Sciences,2014,57(1):012202(14),doi:10.1007/s11432-013-4851-4.
[27]Yang Liu,Hongwei Chen,Jianquan Lu,Bo Wu,Controllability of probabilistic Boolean control networks based on transition probability matrices,Automatica,2015,Vol.52(2):340-345
[28]Lions J.L.Exact controllability,stabilization and perturbations for distributed parameter systems,SIAM Rev.Vol.30:1–68,1988.
[29]Rabah R,Karrakchou J.Exact controllability and complete stabilizability for linear systems in Hilbert spaces,Appl.Math.Lett.Vol.10(1):35–40,1997.
[30]Zeng Y,Xie Z S,Guo F M.On exact controllability and complete stabilizability for linear systems,Applied Mathematics Letters,Vol.26(7):766–768,2013.
[31]Peng S,Backward Stochastic Differential Equation and Exact Controllability of Stochastic Control Systems,Progress in Natural Science,Vol.4(3):274–284,1994.
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