Output feedback stabilization of stochastic nonlinear systems with unknown output function
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- 英文论文题名：Output feedback stabilization of stochastic nonlinear systems with unknown output function
- 论文作者：Meng-Meng Jiang ; Xue-Jun Xie
- 英文论文作者：Meng-Meng Jiang ; Xue-Jun Xie ; Institute of Automation ; Qufu Normal University
- 年：2017
- 作者机构：Institute of Automation,Qufu Normal University;
- 英文论文关键词：Stochastic nonlinear systems ; output feedback stabilization ; output function
- 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：5
- 文件大小：227k
- 原文格式：D
- 会议级别：全国
摘要
This paper studies the problem of output feedback stabilization for a class of stochastic nonlinear systems with the unknown output function. For stochastic nonlinear systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and C~2 Lyapunov function and using the homogeneous domination method, an output feedback controller is constructed to render the closed-loop system globally stable in probability and all states can be regulated to the origin almost surely.
This paper studies the problem of output feedback stabilization for a class of stochastic nonlinear systems with the unknown output function. For stochastic nonlinear systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and C~2 Lyapunov function and using the homogeneous domination method, an output feedback controller is constructed to render the closed-loop system globally stable in probability and all states can be regulated to the origin almost surely.
This paper studies the problem of output feedback stabilization for a class of stochastic nonlinear systems with the unknown output function. For stochastic nonlinear systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and C~2 Lyapunov function and using the homogeneous domination method, an output feedback controller is constructed to render the closed-loop system globally stable in probability and all states can be regulated to the origin almost surely.
引文
[1]R.Z.Hasminskii,Stochastic Stability of Differential Equations.Norwell:Kluwer Academic Publishers,1980.
[2]M.Krsti,and H.Deng,Stabilization of Nonlinear Unertain Systems.New York:Springer-Verlag,1998.
[3]X.R.Mao,Stochastic Differential Equations and Their Applications.Chichester:Horwood Publishing,2007.
[4]Z.G.Pan,and T.Basar,Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion,SIAM Journal on Control and Optimization,37(3):957-995,1999.
[5]H.Deng,M.Krsti,and R.J.Williams,Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,IEEE Trans.Automatic Control,46(8):1237-1253,2001.
[6]S.J.Liu,X.F.Zhang,and Z.P.Jiang,Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems,Automatica,43:238-251,2007.
[7]Z.J.Wu,X.J.Xie,and S.Y.Zhang,Adaptive backstepping controller design using stochastic small-gain theorem.Automatica,43:609-620,2007.
[8]S.J.Liu,X.F.Zhang,and Z.P.Jiang,Global output-feedback stabilization for a class of stochastic nonminimum-phase nonlinear systems,Automatica,44:1944-1957,2008.
[9]X.Yu,and X.J.Xie,Output feedback regulation of stochastic nonlinear systems with stochastic i ISS inverse dynamics,IEEE Trans.Automatic Control,55(2):304-320,2010.
[10]W.Q.Li,Y.W.Jing,and S.Y.Zhang,Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,Automatica,46:752-760,2010.
[11]X.J.Xie,and N.Duan,Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system,IEEE Trans.Automatic Control,55(5):1197-1202,2010.
[12]X.Yu,X.J.Xie,and N.Nuan,Small-gain control method for stochastic nonlinear systems with stochastic i ISS inverse dynamics,Automatica,46:1790-1798,2010.
[13]X.J.Xie,N.Duan,and C.R.Zhao,A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems,IEEE Trans.Automatic Control,59(5):1303-1309,2014.
[14]H.Ito,and Y.Nishimura,Stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates,Automatica,62:51-64,2015.
[15]H.Wang,and Q.X.Zhu,Finite-time stabilization of highorder stochastic nonlinear systems in strict-feedback form,Automatica,54:284-291,2015.
[16]H.Ito,and Y.Nishimura,An i ISS framework for stochastic robustness of interconnected nonlinear systems,IEEE Trans.Automatic Control,61(6):1508-1523,2016.
[17]S.S.Xiong,and Q.X.Zhu,Decentralized risk-sensitive design for large-scale stochastic interconnected systems with timevarying delays,Journal of the Franklin Institute,353(7):1527-1552,2016.
[18]H.Wang,and Q.X.Zhu,Global Stabilization of Stochastic Nonlinear Systems via C1and C∞Controllers,IEEE Trans.Automatic Control,published online:DOI:10.1109/TAC.2016.2644379.
[19]X.H.Yan,and Y.G.Liu,Global output-feedback asymptotic stabilization for a class of uncertain nonlinear systems with uncertain growth rate,in Proceedings of 30th Chinese Control Conference,2011:6556-6561.
[20]J.Y.Zhai,and C.J.Qian,Global control of nonlinear systems with uncertain output function using homogeneous domination approach,International Journal of Robust and Nonlinear Control,22(14):1543-1561,2012.
[21]J.Y.Zhai,W.Q.Ai,and S.M.Fei,Global output feedback stabilization for a class of uncertain nonlinear systems,IET Control Theory and Applications,7(2):305-313,2013.
[22]W.Q.Ai,J.Y.Zhai,and S.M.Fei,Decentralized global output feedback stabilization for a class of uncertain nonlinear systems,Transactions of the Institute of Measurement and Control,35(6):777-787,2013.
[23]W.Q.Ai,J.Y.Zhai,and S.M.Fei,Universal adaptive regulation for a class of nonlinear systems with unknown time delays and output function via output feedback,International Journal of the Franklin Institute,350(10):3168-3187,2013.
[24]S.J.Liu,S.Z.Ge,and X.F.Zhang,Adaptive output-feedback control for a class of uncertain stochastic nonlinear systems with time delay,International Journal of Control,81(8):1210-1220,2008.
[25]H.K.Khalil,Nonlinear Systems.New Jersey:Prentice-Hall,2002.
[2]M.Krsti,and H.Deng,Stabilization of Nonlinear Unertain Systems.New York:Springer-Verlag,1998.
[3]X.R.Mao,Stochastic Differential Equations and Their Applications.Chichester:Horwood Publishing,2007.
[4]Z.G.Pan,and T.Basar,Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion,SIAM Journal on Control and Optimization,37(3):957-995,1999.
[5]H.Deng,M.Krsti,and R.J.Williams,Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,IEEE Trans.Automatic Control,46(8):1237-1253,2001.
[6]S.J.Liu,X.F.Zhang,and Z.P.Jiang,Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems,Automatica,43:238-251,2007.
[7]Z.J.Wu,X.J.Xie,and S.Y.Zhang,Adaptive backstepping controller design using stochastic small-gain theorem.Automatica,43:609-620,2007.
[8]S.J.Liu,X.F.Zhang,and Z.P.Jiang,Global output-feedback stabilization for a class of stochastic nonminimum-phase nonlinear systems,Automatica,44:1944-1957,2008.
[9]X.Yu,and X.J.Xie,Output feedback regulation of stochastic nonlinear systems with stochastic i ISS inverse dynamics,IEEE Trans.Automatic Control,55(2):304-320,2010.
[10]W.Q.Li,Y.W.Jing,and S.Y.Zhang,Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,Automatica,46:752-760,2010.
[11]X.J.Xie,and N.Duan,Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system,IEEE Trans.Automatic Control,55(5):1197-1202,2010.
[12]X.Yu,X.J.Xie,and N.Nuan,Small-gain control method for stochastic nonlinear systems with stochastic i ISS inverse dynamics,Automatica,46:1790-1798,2010.
[13]X.J.Xie,N.Duan,and C.R.Zhao,A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems,IEEE Trans.Automatic Control,59(5):1303-1309,2014.
[14]H.Ito,and Y.Nishimura,Stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates,Automatica,62:51-64,2015.
[15]H.Wang,and Q.X.Zhu,Finite-time stabilization of highorder stochastic nonlinear systems in strict-feedback form,Automatica,54:284-291,2015.
[16]H.Ito,and Y.Nishimura,An i ISS framework for stochastic robustness of interconnected nonlinear systems,IEEE Trans.Automatic Control,61(6):1508-1523,2016.
[17]S.S.Xiong,and Q.X.Zhu,Decentralized risk-sensitive design for large-scale stochastic interconnected systems with timevarying delays,Journal of the Franklin Institute,353(7):1527-1552,2016.
[18]H.Wang,and Q.X.Zhu,Global Stabilization of Stochastic Nonlinear Systems via C1and C∞Controllers,IEEE Trans.Automatic Control,published online:DOI:10.1109/TAC.2016.2644379.
[19]X.H.Yan,and Y.G.Liu,Global output-feedback asymptotic stabilization for a class of uncertain nonlinear systems with uncertain growth rate,in Proceedings of 30th Chinese Control Conference,2011:6556-6561.
[20]J.Y.Zhai,and C.J.Qian,Global control of nonlinear systems with uncertain output function using homogeneous domination approach,International Journal of Robust and Nonlinear Control,22(14):1543-1561,2012.
[21]J.Y.Zhai,W.Q.Ai,and S.M.Fei,Global output feedback stabilization for a class of uncertain nonlinear systems,IET Control Theory and Applications,7(2):305-313,2013.
[22]W.Q.Ai,J.Y.Zhai,and S.M.Fei,Decentralized global output feedback stabilization for a class of uncertain nonlinear systems,Transactions of the Institute of Measurement and Control,35(6):777-787,2013.
[23]W.Q.Ai,J.Y.Zhai,and S.M.Fei,Universal adaptive regulation for a class of nonlinear systems with unknown time delays and output function via output feedback,International Journal of the Franklin Institute,350(10):3168-3187,2013.
[24]S.J.Liu,S.Z.Ge,and X.F.Zhang,Adaptive output-feedback control for a class of uncertain stochastic nonlinear systems with time delay,International Journal of Control,81(8):1210-1220,2008.
[25]H.K.Khalil,Nonlinear Systems.New Jersey:Prentice-Hall,2002.