Stochastic stabilization of linear systems under delayed and noisy feedback control
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- 英文论文题名：Stochastic stabilization of linear systems under delayed and noisy feedback control
- 论文作者：ZONG Xiaofeng ; LI Tao ; ZHANG Ji-Feng
- 英文论文作者：ZONG Xiaofeng ; LI Tao ; ZHANG Ji-Feng ; School of Automation ; China University of Geosciences ; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems ; Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice ; Department of Mathematics ; East China Normal University ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences ; School of Mathematical Sciences ; University of Chinese Academy of Sciences
- 年：2017
- 作者机构：School of Automation,China University of Geosciences;Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems;Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,Department of Mathematics,East China Normal University;Academy of Mathematics and Systems Science,Chinese Academy of Sciences;School of Mathematical Sciences,University of Chinese Academy of Sciences;
- 英文论文关键词：Stabilization ; Feedback control ; Noise ; Delay
- 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：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：240k
- 原文格式：D
- 会议级别：全国
摘要
This paper is to study the stabilizability and stabilization issues of linear dynamical systems based on the delayed and noisy feedback control. For the general linear systems, the necessary conditions and sufficient conditions for mean square and almost sure stabilizability are deduced and the corresponding feedback controls are designed according to the generalized algebraic Riccati equation. It is revealed that the stabilizability is up to the system parameters(delays, noises, and unstable eigenvalues of the original system) and unstable systems can be stabilized in mean square if the feedback control is disturbed by noises with small intensities. It is showed that second-order integrator systems must be stabilizable for any given noise intensity and delay.
This paper is to study the stabilizability and stabilization issues of linear dynamical systems based on the delayed and noisy feedback control. For the general linear systems, the necessary conditions and sufficient conditions for mean square and almost sure stabilizability are deduced and the corresponding feedback controls are designed according to the generalized algebraic Riccati equation. It is revealed that the stabilizability is up to the system parameters(delays, noises, and unstable eigenvalues of the original system) and unstable systems can be stabilized in mean square if the feedback control is disturbed by noises with small intensities. It is showed that second-order integrator systems must be stabilizable for any given noise intensity and delay.
This paper is to study the stabilizability and stabilization issues of linear dynamical systems based on the delayed and noisy feedback control. For the general linear systems, the necessary conditions and sufficient conditions for mean square and almost sure stabilizability are deduced and the corresponding feedback controls are designed according to the generalized algebraic Riccati equation. It is revealed that the stabilizability is up to the system parameters(delays, noises, and unstable eigenvalues of the original system) and unstable systems can be stabilized in mean square if the feedback control is disturbed by noises with small intensities. It is showed that second-order integrator systems must be stabilizable for any given noise intensity and delay.
引文
[1]R.Khasminskii,Stochastic stability of differential equations.Springer,2011.
[2]X.Mao,Stochastic Differential Equations and their Applications,ser.Horwood Publishing Series in Mathematics&Applications.Chichester:Horwood Publishing Limited,1997.
[3]G.Yin and F.Xi,Stability of regime-switching jump diffusions,SIAM Journal on Control and Optimization,48(7):4525–4549,2010.
[4]X.Mao and C.Yuan,Stochastic differential equations with Markovian switching.World Scientific,2006.
[5]G.Yin and C.Zhu,Hybrid Switching Diffusions:Properties and Applications.Springer,New York,2010.
[6]L.Arnold,H.Crauel,and V.Wihstutz,Stabilization of linear systems by noise,SIAM Journal on Control and Optimization,21(3):451–461,1983.
[7]F.Deng,Q.Luo,X.Mao,and S.Pang,Noise suppresses or expresses exponential growth,Systems&Control Letters,57(3):262–270,2008.
[8]G.Hu,M.Liu,X.Mao,and M.Song,Noise expresses exponential growth under regime switching,Systems&Control Letters,58(9):691–699,2009.
[9]X.Mao,Stochastic stabilization and destabilization,Systems&Control Letters,23(4):279–290,1994.
[10]X.Mao,Stochastic self-stabilization,Stochastics:An International Journal of Probability and Stochastic Processes,57(1-2):57–70,1996.
[11]X.Mao,G.G.Yin,and C.Yuan,Stabilization and destabilization of hybrid systems of stochastic differential equations,Automatica,43(2):264–273,2007.
[12]J.A.D.Appleby,X.Mao,and A.Rodkina,Stabilization and destabilization of nonlinear differential equations by noise,Automatic Control,IEEE Transactions on,53(3):683–691,2008.
[13]F.Deng,Q.Luo,and X.Mao,Stochastic stabilization of hybrid differential equations,Automatica,48(9):2321–2328,2012.
[14]F.Wu and S.Hu,Suppression and stabilisation of noise,International Journal of Control,82(11):2150–2157,2009.
[15]J.A.D.Appleby and X.Mao,Stochastic stabilisation of functional differential equations,Systems&Control Letters,54(11):1069–1081,2005.
[16]F.Wu,X.Mao,and S.Hu,Stochastic suppression and stabilization of functional differential equations,Systems&Control Letters,59(12):745–753,2010.
[17]X.Zong,F.Wu,G.Yin,Stochastic regularization and stabilization of hybrid functional differential equations,2015 IEEE54th Annual Conference on Decision and Control(CDC),1211-1216,2015.
[18]G.Yin,G.Zhao,and F.Wu,Regularization and stabilization of randomly switching dynamic systems,SIAM Journal on Applied Mathematics,72(5):1361–1382,2012.
[19]X.Zong,F.Wu,and T.Tianhai,Stability and stochastic stabilization of numerical solutions of regime-switching jump diffusion systems,Journal of Difference Equations and Applications,19(11):1733–1757,2013.
[20]Q.Guo,X.Mao,AND R.Yue,Almost Sure Exponential Stability of Stochastic Differential Delay Equations,SIAM Journal on Control and Optimization,54(4):1919-1933,2016.
[21]X.Zong,F.Wu,G.Yin,and Z.Jin,Almost sure and pthmoment stability and stabilization of regime-switching jump diffusion systems,SIAM Journal on Control and Optimization,52(4):2595–2622,2014.
[22]W.Zhang,H.Zhang,and B.S.Chen,Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion,IEEE Transactions on Automatic Control,53(7):1630-1642,2008.
[23]L.Hu,and X.Mao,Almost sure exponential stabilisation of stochastic systems by state-feedback control,Automatica,44(2):465-471,2008.
[24]Y.Zhang,R.Li,D.Li,Y.Hu,and X.Huo,Stabilization of the stochastic jump diffusion systems by state-feedback control,Journal of the Franklin Institute,351(3):1596-1614,2014.
[25]B.Song,J.H.Park,Z.Wu,and X.Li,New results on delay-dependent stability analysis and stabilization for stochastic time-delay systems,International Journal of Robust&Nonlinear Control,24(16):2546-2559,2014.
[26]H.Zhang and J.Xu,Control for It o?stochastic systems with input delay,IEEE Transactions on Automatic Control,62(1),350-365,2017.
[27]X.Mao,J.Lam,and L.Huang,Stabilisation of hybrid stochastic differential equations by delay feedback control,Systems&Control Letters,57(11):927–935,2008.
[28]L.Huang,and X.Mao,Robust delayed-state-feedback stabilization of uncertain stochastic systems,Automatica,45(5):1332–1339,2009.
[29]M.A.Rami,and X.Y.Zhou,Linear matrix inequalities,Riccati equations,and indefinite stochastic linear quadratic controls,IEEE Transactions on Automatic Control,45(6):1131-1143,2000.
[30]J.L.Willems and J.C.Willems,Feedback stabilizability for stochastic systems with state and control dependent noise,Automatica,12:277–283,1976.
[2]X.Mao,Stochastic Differential Equations and their Applications,ser.Horwood Publishing Series in Mathematics&Applications.Chichester:Horwood Publishing Limited,1997.
[3]G.Yin and F.Xi,Stability of regime-switching jump diffusions,SIAM Journal on Control and Optimization,48(7):4525–4549,2010.
[4]X.Mao and C.Yuan,Stochastic differential equations with Markovian switching.World Scientific,2006.
[5]G.Yin and C.Zhu,Hybrid Switching Diffusions:Properties and Applications.Springer,New York,2010.
[6]L.Arnold,H.Crauel,and V.Wihstutz,Stabilization of linear systems by noise,SIAM Journal on Control and Optimization,21(3):451–461,1983.
[7]F.Deng,Q.Luo,X.Mao,and S.Pang,Noise suppresses or expresses exponential growth,Systems&Control Letters,57(3):262–270,2008.
[8]G.Hu,M.Liu,X.Mao,and M.Song,Noise expresses exponential growth under regime switching,Systems&Control Letters,58(9):691–699,2009.
[9]X.Mao,Stochastic stabilization and destabilization,Systems&Control Letters,23(4):279–290,1994.
[10]X.Mao,Stochastic self-stabilization,Stochastics:An International Journal of Probability and Stochastic Processes,57(1-2):57–70,1996.
[11]X.Mao,G.G.Yin,and C.Yuan,Stabilization and destabilization of hybrid systems of stochastic differential equations,Automatica,43(2):264–273,2007.
[12]J.A.D.Appleby,X.Mao,and A.Rodkina,Stabilization and destabilization of nonlinear differential equations by noise,Automatic Control,IEEE Transactions on,53(3):683–691,2008.
[13]F.Deng,Q.Luo,and X.Mao,Stochastic stabilization of hybrid differential equations,Automatica,48(9):2321–2328,2012.
[14]F.Wu and S.Hu,Suppression and stabilisation of noise,International Journal of Control,82(11):2150–2157,2009.
[15]J.A.D.Appleby and X.Mao,Stochastic stabilisation of functional differential equations,Systems&Control Letters,54(11):1069–1081,2005.
[16]F.Wu,X.Mao,and S.Hu,Stochastic suppression and stabilization of functional differential equations,Systems&Control Letters,59(12):745–753,2010.
[17]X.Zong,F.Wu,G.Yin,Stochastic regularization and stabilization of hybrid functional differential equations,2015 IEEE54th Annual Conference on Decision and Control(CDC),1211-1216,2015.
[18]G.Yin,G.Zhao,and F.Wu,Regularization and stabilization of randomly switching dynamic systems,SIAM Journal on Applied Mathematics,72(5):1361–1382,2012.
[19]X.Zong,F.Wu,and T.Tianhai,Stability and stochastic stabilization of numerical solutions of regime-switching jump diffusion systems,Journal of Difference Equations and Applications,19(11):1733–1757,2013.
[20]Q.Guo,X.Mao,AND R.Yue,Almost Sure Exponential Stability of Stochastic Differential Delay Equations,SIAM Journal on Control and Optimization,54(4):1919-1933,2016.
[21]X.Zong,F.Wu,G.Yin,and Z.Jin,Almost sure and pthmoment stability and stabilization of regime-switching jump diffusion systems,SIAM Journal on Control and Optimization,52(4):2595–2622,2014.
[22]W.Zhang,H.Zhang,and B.S.Chen,Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion,IEEE Transactions on Automatic Control,53(7):1630-1642,2008.
[23]L.Hu,and X.Mao,Almost sure exponential stabilisation of stochastic systems by state-feedback control,Automatica,44(2):465-471,2008.
[24]Y.Zhang,R.Li,D.Li,Y.Hu,and X.Huo,Stabilization of the stochastic jump diffusion systems by state-feedback control,Journal of the Franklin Institute,351(3):1596-1614,2014.
[25]B.Song,J.H.Park,Z.Wu,and X.Li,New results on delay-dependent stability analysis and stabilization for stochastic time-delay systems,International Journal of Robust&Nonlinear Control,24(16):2546-2559,2014.
[26]H.Zhang and J.Xu,Control for It o?stochastic systems with input delay,IEEE Transactions on Automatic Control,62(1),350-365,2017.
[27]X.Mao,J.Lam,and L.Huang,Stabilisation of hybrid stochastic differential equations by delay feedback control,Systems&Control Letters,57(11):927–935,2008.
[28]L.Huang,and X.Mao,Robust delayed-state-feedback stabilization of uncertain stochastic systems,Automatica,45(5):1332–1339,2009.
[29]M.A.Rami,and X.Y.Zhou,Linear matrix inequalities,Riccati equations,and indefinite stochastic linear quadratic controls,IEEE Transactions on Automatic Control,45(6):1131-1143,2000.
[30]J.L.Willems and J.C.Willems,Feedback stabilizability for stochastic systems with state and control dependent noise,Automatica,12:277–283,1976.