Attractor and Stability of Delayed Boolean Networks with State Constraints
详细信息 查看官网全文
- 英文论文题名：Attractor and Stability of Delayed Boolean Networks with State Constraints
- 论文作者：ZHENG Yating ; LI Haitao ; XU Xiaojing
- 英文论文作者：ZHENG Yating ; LI Haitao ; XU Xiaojing ; School of Mathematics and Statistics ; Shandong Normal University
- 年：2017
- 作者机构：School of Mathematics and Statistics,Shandong Normal University;
- 英文论文关键词：Delayed Boolean Network ; Attractor ; Stability ; State Constraint ; Semi-Tensor Product of Matrices
- 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：O157.5
- 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：210k
- 原文格式：D
- 会议级别：全国
摘要
This paper investigates the attractor and stability of delayed Boolean networks(DBNs) with/without state constraints by using the semi-tensor product of matrices. Firstly, the dynamics of DBNs with/without state constraints is converted into an equivalent algebraic form via the semi-tensor product of matrices. Secondly, based on the algebraic form, a new formula is proposed for the calculation of number of attractors for DBNs with state constraints. Thirdly, a necessary and sufficient condition is presented for the stability of DBNs with state constraints. Finally, an example is worked out to show the application of the obtained new results.
This paper investigates the attractor and stability of delayed Boolean networks(DBNs) with/without state constraints by using the semi-tensor product of matrices. Firstly, the dynamics of DBNs with/without state constraints is converted into an equivalent algebraic form via the semi-tensor product of matrices. Secondly, based on the algebraic form, a new formula is proposed for the calculation of number of attractors for DBNs with state constraints. Thirdly, a necessary and sufficient condition is presented for the stability of DBNs with state constraints. Finally, an example is worked out to show the application of the obtained new results.
This paper investigates the attractor and stability of delayed Boolean networks(DBNs) with/without state constraints by using the semi-tensor product of matrices. Firstly, the dynamics of DBNs with/without state constraints is converted into an equivalent algebraic form via the semi-tensor product of matrices. Secondly, based on the algebraic form, a new formula is proposed for the calculation of number of attractors for DBNs with state constraints. Thirdly, a necessary and sufficient condition is presented for the stability of DBNs with state constraints. Finally, an example is worked out to show the application of the obtained new results.
引文
[1]F.Ay,F.Xu,and T.Kahveci,Scalable steady state analysis of Boolean biological regulatory networks,PLo S ONE,4(12):e7992,2009.
[2]D.Cheng,and H.Qi,Controllability and observability of Boolean control networks,Automatica,45(7):1659–1667,2009
[3]D.Cheng,H.Qi,and Z.Li,Analysis and Control of Boolean Networks:A Semi-tensor Product Approach,London:Springer,2011.
[4]D.Cheng,H.Qi,Z.Li,and J.B.Liu,Stability and stabilization of Boolean networks,Int.J.Robust Nonlinear Contr.,21(2):134–156,2011.
[5]D.Cheng,H.Qi,and Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications,Singapore:World Scientific,2012.
[6]D.Cheng,F.He,H.Qi,and T.Xu,Modeling,analysis and control of networked evolutionary games,IEEE Trans.Aut.Contr.,60(9):2402–2415,2015.
[7]T.H.Chueh,and H.Lu,Inference of biological pathway from gene expression profiles by time delay Boolean networks,Plos One,7(8):e42095,2012.
[8]E.Fornasini,and M.Valcher,On the periodic trajectories of Boolean control networks.Automatica,49(5):1506–1509,2013.
[9]E.Fornasini,and M.Valcher,Observability,reconstructibility and state observers of Boolean control networks,IEEE Trans.Aut.Contr.,58(6):1390–1401,2013.
[10]E.Fornasini,and M.Valcher,Optimal control of Boolean control networks,IEEE Trans.Aut.Contr.,59(5):1258–1270,2014.
[11]B.C.Goodwin,Temporal Organization in Cells:A Dynamic Theory of Cellular Control Processes,Academic Press,1963.
[12]M.Han,Y.Liu,and Y.Tu,Controllability of Boolean control networks with time delays both in states and inputs,Neurocomputing,129:467–475,2014.
[13]S.Kauffman,Metabolic stability and epigenesis in randomly constructed genetic nets,J.Theoretical Biology,22(3):437,1969.
[14]D.Laschov,and M.Margaliot,A maximum principle for single-input Boolean control networks,IEEE Trans.Aut.Contr.,56(4):913–917,2011.
[15]D.Laschov,and M.Margaliot,Controllability of Boolean control networks via the Perron-Frobenius theory,Automatica,48:1218–1223,2012.
[16]D.Laschov,and M.Margaliot,Minimum-time control of Boolean networks,SIAM J.Contr.Optim,51(4):2869–2892,2013.
[17]F.Li,and J.Sun,Controllability of Boolean control networks with time delays in states,Automatica,47(3):603–607,2011.
[18]F.Li,J.Sun,and Q.Wu,Observability of Boolean control networks with state time delays,IEEE Trans.Neural Networks,22(6):948–954,2011.
[19]F.Li,and X.Lu,Complete synchronization of temporal Boolean networks,Neural Networks,44:72–77,2013.
[20]H.Li,and Y.Wang,On reachability and controllability of switched Boolean control networks,Automatica,48(11):2917–2922,2012.
[21]H.Li,and Y.Wang,Output feedback stabilization control design for Boolean control networks,Automatica,49(12):3641–3645,2013.
[22]H.Li,Y.Wang,and Z.Liu,Stability analysis for switched Boolean networks under arbitrary switching signals,IEEE Trans.Aut.Contr.,59(7):1978–1982,2014.
[23]H.Li,Y.Wang,and L.Xie,Output tracking control of Boolean control networks via state feedback:constant reference signal case,Automatica,59:54–59,2015.
[24]H.Li,L.Xie,and Y.Wang,On robust control invariance of Boolean control networks,Automatica,68:392–396,2016.
[25]R.Li,M.Yang,and T.Chu,Synchronization of Boolean networks with time delays,Applied Mathematics and Computation,219(3):917–927,2012.
[26]Y.Liu,H.Chen,J.Lu,and B.Wu,Controllability of probabilistic Boolean control networks based on transition probability matrices,Automatica,52:340–345,2015.
[27]J.Lu,J.Zhong,D.W.C.Ho,Y.Tang,and J.Cao,On controllability of delayed Boolean control networks,SIAM J.Contr.Optim.,54(2):475–494,2016.
[28]M.Meng,J.Lam,J.Feng,and X.Li,l1-gain analysis and model reduction problem for Boolean control networks,Information Sciences,348:68–83,2016.
[29]R.R.Riveraduron,E.Camposcanton,I.Camposcanton,and D.J.Gauthier,Forced synchronization of autonomous dynamical Boolean networks,Chaos,25(8):912–918,2015.
[30]T.Tian,K.Burrage,P.M.Burrage,and M.Carletti,Stochastic delay differential equations for genetic regulatory networks,Journal of Computational and Applied Mathematics,205(2):696–707,2007.
[31]Y.Wang,Z.Wang,and J.Liang,On robust stability of stochastic genetic regulatory networks with time delays:a delay fractioning approach,IEEE Trans.Systems,Man,and Cybernetics,Part B(Cybernetics),40(3):729–740,2010.
[32]Y.Wang,A.Yu,and X.Zhang,Robust stability of stochastic genetic regulatory networks with time-varying delays:a delay fractioning approach,Neural Computing and Applications,23(5):1217–1227,2013.
[33]F.Wu,Delay-independent stability of genetic regulatory networks,IEEE Trans.Neur.Netw.,22(11):1685–1693,2011.
[34]Y.Wu,and T.Shen,An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems,Syst.Contr.Lett.,82:108–114,2015.
[35]X.Xu,and Y.Hong,Matrix approach to model matching of asynchronous sequential machines,IEEE Trans.Aut.Contr.,58(11):2974–2979,2013.
[36]M.Yang,R.Li,and T.Chu,Controller design for disturbance decoupling of Boolean control networks,Automatica,49(1):273–277,2013.
[37]L.Zhang,and K.Zhang,Controllability and observability of Boolean control networks with time-variant delays in states,IEEE Trans.Neur.Netw.Learn.Syst.,24:1478–1484,2013.
[38]L.Zhang,and K.Zhang,Controllability of time-variant Boolean control networks and its application to Boolean control networks with finite memories,Science China Information Sciences,56(10):1–12,2013.
[39]Y.Zhao,D.Cheng,and H.Qi,Input-state incidence matrix of Boolean control networks and its applications,Syst.Contr.Letters,59(12):767–774,2010.
[40]J.Zhong,J.Lu,Y.Liu,and J.Cao,Synchronization in an array of output-coupled Boolean networks with time delay,IEEE Trans.Neur.Netw.Learn.Syst.,25(12):2288–2294,2014.
[41]Y.Zou,and J.Zhu,System decomposition with respect to inputs for Boolean control networks,Automatica,50(4):1304–1309,2014.
[2]D.Cheng,and H.Qi,Controllability and observability of Boolean control networks,Automatica,45(7):1659–1667,2009
[3]D.Cheng,H.Qi,and Z.Li,Analysis and Control of Boolean Networks:A Semi-tensor Product Approach,London:Springer,2011.
[4]D.Cheng,H.Qi,Z.Li,and J.B.Liu,Stability and stabilization of Boolean networks,Int.J.Robust Nonlinear Contr.,21(2):134–156,2011.
[5]D.Cheng,H.Qi,and Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications,Singapore:World Scientific,2012.
[6]D.Cheng,F.He,H.Qi,and T.Xu,Modeling,analysis and control of networked evolutionary games,IEEE Trans.Aut.Contr.,60(9):2402–2415,2015.
[7]T.H.Chueh,and H.Lu,Inference of biological pathway from gene expression profiles by time delay Boolean networks,Plos One,7(8):e42095,2012.
[8]E.Fornasini,and M.Valcher,On the periodic trajectories of Boolean control networks.Automatica,49(5):1506–1509,2013.
[9]E.Fornasini,and M.Valcher,Observability,reconstructibility and state observers of Boolean control networks,IEEE Trans.Aut.Contr.,58(6):1390–1401,2013.
[10]E.Fornasini,and M.Valcher,Optimal control of Boolean control networks,IEEE Trans.Aut.Contr.,59(5):1258–1270,2014.
[11]B.C.Goodwin,Temporal Organization in Cells:A Dynamic Theory of Cellular Control Processes,Academic Press,1963.
[12]M.Han,Y.Liu,and Y.Tu,Controllability of Boolean control networks with time delays both in states and inputs,Neurocomputing,129:467–475,2014.
[13]S.Kauffman,Metabolic stability and epigenesis in randomly constructed genetic nets,J.Theoretical Biology,22(3):437,1969.
[14]D.Laschov,and M.Margaliot,A maximum principle for single-input Boolean control networks,IEEE Trans.Aut.Contr.,56(4):913–917,2011.
[15]D.Laschov,and M.Margaliot,Controllability of Boolean control networks via the Perron-Frobenius theory,Automatica,48:1218–1223,2012.
[16]D.Laschov,and M.Margaliot,Minimum-time control of Boolean networks,SIAM J.Contr.Optim,51(4):2869–2892,2013.
[17]F.Li,and J.Sun,Controllability of Boolean control networks with time delays in states,Automatica,47(3):603–607,2011.
[18]F.Li,J.Sun,and Q.Wu,Observability of Boolean control networks with state time delays,IEEE Trans.Neural Networks,22(6):948–954,2011.
[19]F.Li,and X.Lu,Complete synchronization of temporal Boolean networks,Neural Networks,44:72–77,2013.
[20]H.Li,and Y.Wang,On reachability and controllability of switched Boolean control networks,Automatica,48(11):2917–2922,2012.
[21]H.Li,and Y.Wang,Output feedback stabilization control design for Boolean control networks,Automatica,49(12):3641–3645,2013.
[22]H.Li,Y.Wang,and Z.Liu,Stability analysis for switched Boolean networks under arbitrary switching signals,IEEE Trans.Aut.Contr.,59(7):1978–1982,2014.
[23]H.Li,Y.Wang,and L.Xie,Output tracking control of Boolean control networks via state feedback:constant reference signal case,Automatica,59:54–59,2015.
[24]H.Li,L.Xie,and Y.Wang,On robust control invariance of Boolean control networks,Automatica,68:392–396,2016.
[25]R.Li,M.Yang,and T.Chu,Synchronization of Boolean networks with time delays,Applied Mathematics and Computation,219(3):917–927,2012.
[26]Y.Liu,H.Chen,J.Lu,and B.Wu,Controllability of probabilistic Boolean control networks based on transition probability matrices,Automatica,52:340–345,2015.
[27]J.Lu,J.Zhong,D.W.C.Ho,Y.Tang,and J.Cao,On controllability of delayed Boolean control networks,SIAM J.Contr.Optim.,54(2):475–494,2016.
[28]M.Meng,J.Lam,J.Feng,and X.Li,l1-gain analysis and model reduction problem for Boolean control networks,Information Sciences,348:68–83,2016.
[29]R.R.Riveraduron,E.Camposcanton,I.Camposcanton,and D.J.Gauthier,Forced synchronization of autonomous dynamical Boolean networks,Chaos,25(8):912–918,2015.
[30]T.Tian,K.Burrage,P.M.Burrage,and M.Carletti,Stochastic delay differential equations for genetic regulatory networks,Journal of Computational and Applied Mathematics,205(2):696–707,2007.
[31]Y.Wang,Z.Wang,and J.Liang,On robust stability of stochastic genetic regulatory networks with time delays:a delay fractioning approach,IEEE Trans.Systems,Man,and Cybernetics,Part B(Cybernetics),40(3):729–740,2010.
[32]Y.Wang,A.Yu,and X.Zhang,Robust stability of stochastic genetic regulatory networks with time-varying delays:a delay fractioning approach,Neural Computing and Applications,23(5):1217–1227,2013.
[33]F.Wu,Delay-independent stability of genetic regulatory networks,IEEE Trans.Neur.Netw.,22(11):1685–1693,2011.
[34]Y.Wu,and T.Shen,An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems,Syst.Contr.Lett.,82:108–114,2015.
[35]X.Xu,and Y.Hong,Matrix approach to model matching of asynchronous sequential machines,IEEE Trans.Aut.Contr.,58(11):2974–2979,2013.
[36]M.Yang,R.Li,and T.Chu,Controller design for disturbance decoupling of Boolean control networks,Automatica,49(1):273–277,2013.
[37]L.Zhang,and K.Zhang,Controllability and observability of Boolean control networks with time-variant delays in states,IEEE Trans.Neur.Netw.Learn.Syst.,24:1478–1484,2013.
[38]L.Zhang,and K.Zhang,Controllability of time-variant Boolean control networks and its application to Boolean control networks with finite memories,Science China Information Sciences,56(10):1–12,2013.
[39]Y.Zhao,D.Cheng,and H.Qi,Input-state incidence matrix of Boolean control networks and its applications,Syst.Contr.Letters,59(12):767–774,2010.
[40]J.Zhong,J.Lu,Y.Liu,and J.Cao,Synchronization in an array of output-coupled Boolean networks with time delay,IEEE Trans.Neur.Netw.Learn.Syst.,25(12):2288–2294,2014.
[41]Y.Zou,and J.Zhu,System decomposition with respect to inputs for Boolean control networks,Automatica,50(4):1304–1309,2014.