Model Reduction for Switched Genetic Regulatory Networks with Time-Varying Delays
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- 英文论文题名：Model Reduction for Switched Genetic Regulatory Networks with Time-Varying Delays
- 论文作者：Mengqi Xue ; Yang Tang ; Ligang Wu ; Feng Qian
- 英文论文作者：Mengqi Xue ; Yang Tang ; Ligang Wu ; Feng Qian ; Key Laboratory of Advanced Control and Optimization for Chemical Processes ; East China University of Science and Technology ; Research Institute of Intelligent Control and Systems ; Harbin Institute of Technology
- 年：2017
- 作者机构：Key Laboratory of Advanced Control and Optimization for Chemical Processes,East China University of Science and Technology;Research Institute of Intelligent Control and Systems,Harbin Institute of Technology;
- 英文论文关键词：Switched System ; Genetic Regulatory Networks ; Model Reduction ; Time-Varying Delays
- 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：O175
- 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：365k
- 原文格式：D
- 会议级别：全国
摘要
The model reduction problem is studied in this work for the switched genetic regulatory networks(GRNs) with timevarying delays. The attention is focused on constructing a reduced-order model to approximate the considered high-order GRNs under that the switching signal is subject to some certain constraints, such that the error system between the original system and the reduced-order one is exponentially stable with a weighted H∞ performance. By utilizing the bounding technique as well as the dwell time method, the stability conditions and the weighted H_∞ performance are established for the error system. Then, the solvability conditions for the reduced-order models for the GRNs are also established by using the projection method. Finally,numerical simulation is presented to illustrate the effectiveness of the proposed method.
The model reduction problem is studied in this work for the switched genetic regulatory networks(GRNs) with timevarying delays. The attention is focused on constructing a reduced-order model to approximate the considered high-order GRNs under that the switching signal is subject to some certain constraints, such that the error system between the original system and the reduced-order one is exponentially stable with a weighted H_∞ performance. By utilizing the bounding technique as well as the dwell time method, the stability conditions and the weighted H_∞ performance are established for the error system. Then, the solvability conditions for the reduced-order models for the GRNs are also established by using the projection method. Finally,numerical simulation is presented to illustrate the effectiveness of the proposed method.
The model reduction problem is studied in this work for the switched genetic regulatory networks(GRNs) with timevarying delays. The attention is focused on constructing a reduced-order model to approximate the considered high-order GRNs under that the switching signal is subject to some certain constraints, such that the error system between the original system and the reduced-order one is exponentially stable with a weighted H_∞ performance. By utilizing the bounding technique as well as the dwell time method, the stability conditions and the weighted H_∞ performance are established for the error system. Then, the solvability conditions for the reduced-order models for the GRNs are also established by using the projection method. Finally,numerical simulation is presented to illustrate the effectiveness of the proposed method.
引文
[1]W.Zhang,J.-a.Fang,and W.Cui,“Exponential stability of switched genetic regulatory networks with both stable and unstable subsystems,”Journal of the Franklin InstituteEngineering and Applied Mathematics,vol.350,no.8,pp.2322–2333,2013.
[2]K.Ratnavelu,M.Kalpana,and P.Balasubramaniam,“Asymptotic stability of markovian switching genetic regulatory networks with leakage and mode-dependent time delays,”Journal of the Franklin Institute-Engineering and Applied Mathematics,vol.353,no.7,pp.1615–1638,2016.
[3]Y.Sun,G.Feng,and J.Cao,“Stochastic stability of markovian switching genetic regulatory networks,”Physics Letters A,vol.373,no.1819,pp.1646–1652,2009.
[4]T.Chen,H.L.He,G.M.Church et al.,“Modeling gene expression with differential equations.”in Pacific symposium on biocomputing,vol.4,no.29,1999,p.4.
[5]M.B.Elowitz and S.Leibler,“A synthetic oscillatory network of transcriptional regulators,”Nature,vol.403,no.6767,pp.335–338,2000.
[6]D.Zhang,L.Yu,Q.G.Wang,and C.J.Ong,“Estimator design for discrete-time switched neural networks with asynchronous switching and time-varying delay,”IEEE Transactions on Neural Networks and Learning Systems,vol.23,no.5,pp.827–834,2012.
[7]Z.Wang,H.Wu,J.Liang,J.Cao,and X.Liu,“On modeling and state estimation for genetic regulatory networks with polytopic uncertainties,”IEEE Transactions on Nano Bioscience,vol.12,no.1,pp.13–20,2013.
[8]L.Wu,D.W.C.Ho,and J.Lam,“H-infinity model reduction for continuous-time switched stochastic hybrid systems,”International Journal of Systems Science,vol.40,no.12,pp.1241–1251,2009.
[9]L.Wu and W.X.Zheng,“Weighted h(infinity)model reduction for linear switched systems with time-varying delay,”Automatica,vol.45,no.1,pp.186–193,2009.
[10]H.J.Gao,J.Lam,C.H.Wang,and S.Y.Xu,“H-infinity model reduction for discrete time-delay systems:delayindependent and dependent approaches,”International Journal of Control,vol.77,no.4,pp.321–335,2004.
[11]M.Bastug,M.Petreczky,R.Wisniewski,and J.Leth,“Model reduction by moment matching for linear switched systems,”in American Control Conference,ser.Proceedings of the American Control Conference,2014,Conference Proceedings,pp.3942–3947.
[12]M.Bastug,M.Petreczky,R.Wisniewski,and J.Leth,“Model reduction by nice selections for linear switched systems,”IEEE Transactions on Automatic Control,vol.PP,no.99,pp.1–1,2016.
[13]J.P.Hespanha,“Uniform stability of switched linear systems:Extensions of lasalle’s invariance principle,”IEEE Transactions on Automatic Control,vol.49,no.4,pp.470–482,2004.
[14]S.Xu and J.Lam,“A survey of linear matrix inequality techniques in stability analysis of delay systems,”International Journal of Systems Science,vol.39,no.12,pp.1095–1113,2008.
[2]K.Ratnavelu,M.Kalpana,and P.Balasubramaniam,“Asymptotic stability of markovian switching genetic regulatory networks with leakage and mode-dependent time delays,”Journal of the Franklin Institute-Engineering and Applied Mathematics,vol.353,no.7,pp.1615–1638,2016.
[3]Y.Sun,G.Feng,and J.Cao,“Stochastic stability of markovian switching genetic regulatory networks,”Physics Letters A,vol.373,no.1819,pp.1646–1652,2009.
[4]T.Chen,H.L.He,G.M.Church et al.,“Modeling gene expression with differential equations.”in Pacific symposium on biocomputing,vol.4,no.29,1999,p.4.
[5]M.B.Elowitz and S.Leibler,“A synthetic oscillatory network of transcriptional regulators,”Nature,vol.403,no.6767,pp.335–338,2000.
[6]D.Zhang,L.Yu,Q.G.Wang,and C.J.Ong,“Estimator design for discrete-time switched neural networks with asynchronous switching and time-varying delay,”IEEE Transactions on Neural Networks and Learning Systems,vol.23,no.5,pp.827–834,2012.
[7]Z.Wang,H.Wu,J.Liang,J.Cao,and X.Liu,“On modeling and state estimation for genetic regulatory networks with polytopic uncertainties,”IEEE Transactions on Nano Bioscience,vol.12,no.1,pp.13–20,2013.
[8]L.Wu,D.W.C.Ho,and J.Lam,“H-infinity model reduction for continuous-time switched stochastic hybrid systems,”International Journal of Systems Science,vol.40,no.12,pp.1241–1251,2009.
[9]L.Wu and W.X.Zheng,“Weighted h(infinity)model reduction for linear switched systems with time-varying delay,”Automatica,vol.45,no.1,pp.186–193,2009.
[10]H.J.Gao,J.Lam,C.H.Wang,and S.Y.Xu,“H-infinity model reduction for discrete time-delay systems:delayindependent and dependent approaches,”International Journal of Control,vol.77,no.4,pp.321–335,2004.
[11]M.Bastug,M.Petreczky,R.Wisniewski,and J.Leth,“Model reduction by moment matching for linear switched systems,”in American Control Conference,ser.Proceedings of the American Control Conference,2014,Conference Proceedings,pp.3942–3947.
[12]M.Bastug,M.Petreczky,R.Wisniewski,and J.Leth,“Model reduction by nice selections for linear switched systems,”IEEE Transactions on Automatic Control,vol.PP,no.99,pp.1–1,2016.
[13]J.P.Hespanha,“Uniform stability of switched linear systems:Extensions of lasalle’s invariance principle,”IEEE Transactions on Automatic Control,vol.49,no.4,pp.470–482,2004.
[14]S.Xu and J.Lam,“A survey of linear matrix inequality techniques in stability analysis of delay systems,”International Journal of Systems Science,vol.39,no.12,pp.1095–1113,2008.