Stabilization of a Class of Stochastic Feedforward Uncertain Systems via Time-Varying State Feedback
详细信息 查看官网全文
- 英文论文题名：Stabilization of a Class of Stochastic Feedforward Uncertain Systems via Time-Varying State Feedback
- 论文作者：Ticao Jiao ; Wei Xing Zheng
- 英文论文作者：Ticao Jiao ; Wei Xing Zheng ; College of Electrical and Electronic Engineering ; Shandong University of Technology ; School of Computing ; Engineering and Mathematics ; Western Sydney University
- 年：2017
- 作者机构：College of Electrical and Electronic Engineering,Shandong University of Technology;School of Computing,Engineering and Mathematics,Western Sydney University;
- 英文论文关键词：Stochastic feedforward nonlinear systems ; stabilization ; time-varying state feedback
- 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：248k
- 原文格式：D
- 会议级别：全国
摘要
This paper is devoted to the stabilization problem for a class of stochastic feedforward nonlinear systems with unknown growth rate by time-varying state feedback. As the first contribution, a general LaSalle-type theorem is established for stochastic time-varying systems with the aid of the generalized weakly positive definite function. Then a time-varying state feedback control scheme is established for a class of stochastic feedforward systems with uncertainties in the unknown growth rate. Via the established LaSalle-type theorem, it is shown that all signals of the resulting closed-loop system converge to zero almost surely. A numerical example is presented to demonstrate the validity of the theoretical results.
This paper is devoted to the stabilization problem for a class of stochastic feedforward nonlinear systems with unknown growth rate by time-varying state feedback. As the first contribution, a general LaSalle-type theorem is established for stochastic time-varying systems with the aid of the generalized weakly positive definite function. Then a time-varying state feedback control scheme is established for a class of stochastic feedforward systems with uncertainties in the unknown growth rate. Via the established LaSalle-type theorem, it is shown that all signals of the resulting closed-loop system converge to zero almost surely. A numerical example is presented to demonstrate the validity of the theoretical results.
This paper is devoted to the stabilization problem for a class of stochastic feedforward nonlinear systems with unknown growth rate by time-varying state feedback. As the first contribution, a general LaSalle-type theorem is established for stochastic time-varying systems with the aid of the generalized weakly positive definite function. Then a time-varying state feedback control scheme is established for a class of stochastic feedforward systems with uncertainties in the unknown growth rate. Via the established LaSalle-type theorem, it is shown that all signals of the resulting closed-loop system converge to zero almost surely. A numerical example is presented to demonstrate the validity of the theoretical results.
引文
[1]T.T.Soong,Random Differential Equations in Science and Engineering.New York:Academic Press,1973.
[2]R.Z.Khasminskii,Stochastic Stability of Differential Equations.Berlin:Springer Science and Business Media,2011.
[3]W.-H.Chen,W.X.Zheng,and Y.Shen,“Delay-dependent stochastic stability and H∞-control of uncertain neutral stochastic systems with time delay,”IEEE Transactions on Automatic Control,vol.54,no.7,pp.1660-1667,2009.
[4]L.Wu,W.X.Zheng,and H.Gao,“Dissipativity-based sliding mode control of switched stochastic systems,”IEEE Transactions on Automatic Control,vol.58,no.3,pp.785-791,2013.
[5]T.C.Jiao,W.X.Zheng,and S.Y.Xu,“On stability of a class of switched nonlinear systems subject to random disturbances,”IEEE Transactions on Circuits and Systems I:Regular Papers,vol.63,no.12,pp.2278-2289,2016.
[6]T.C.Jiao,W.X.Zheng,and S.Y.Xu,“Stability analysis for a class of random nonlinear impulsive systems,”International Journal of Robust and Nonlinear Control,vol.27,no.7,pp.1171-1193,2017.
[7]G.D.Zong,D.Yang,L.l.Hou,and Q.Wang,“Robust finitetime H∞control for Markovian jump systems with partially known transition probabilities,”Journal of the Franklin Institute,vol.350,no.6,pp.1562-1578,2013.
[8]Z.D.Ai and G.D.Zong,“Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems,”Applied Mathematics and Computation,vol.245,pp.462-473,2014.
[9]T.C.Jiao,S.Y.Xu,J.W.Lu,Y.L.Wei,and Y.Zou,“Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via La Salle-Yoshizawa-type theorem,”International Journal of Control,vol.89,no.1,pp.69-83,2016.
[10]Y.Chen and W.X.Zheng,“Stability analysis and control for switched stochastic delayed systems,”International Journal of Robust and Nonlinear Control,vol.26,no.2,pp.303-328,2016.
[11]X.Y.Zhao and F.Q.Deng,“A new type of stability theoremfor stochastic systems with application to stochastic stabilization,”IEEE Transactions on Automatic Control,vol.61,no.1,pp.240-245,2015.
[12]X.R.Mao,“La Salle-type theorems for stochastic differential delay equations,”Journal of Mathematical Analysis and Applications,vol.236,no.2,pp.350-369,1999.
[13]X.Yu and X.J.Xie,“Output feedback regulation of stochastic nonlinear systems with stochastic i ISS inverse dynamics,”IEEE Transactions on Automatic Control,vol.55,no.2,pp.304-320,2010.
[14]M.Frédéric and B.Samuel,“Tracking trajectories of the cartpendulum system,”Automatica,vol.39,no.4,pp.677-684,2003.
[15]H.W.Jo,H.L.Choi,and J.T.Lim,“Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain,”Systems and Control Letters,vol.71,pp.44-53,2014.
[16]F.Mazenc and M.Malisoff,“Asymptotic stabilization for feedforward systems with delayed feedbacks,”Automatica,vol.49,no.3,pp.780-787,2013.
[17]W.T.Zha,J.Y.Zhai,and S.M.Fei,“Global output feedback control for a class of high-order feedforward nonlinear systems with input delay,”ISA Transactions,vol.52,no.4,pp.494-500,2013.
[18]X.L.Jia,S.Y.Xu,T.C.Jiao,Y.M.Chu,and Y.Zou,“Global state regulation by output feedback for feedforward systems with input and output dependent incremental rate,”Journal of the Franklin Institute,vol.352,no.6,pp.2526-2538,2015.
[19]T.C.Jiao,G.Z.Cui,J.W.Lu,and Q.Ma,“State feedback control for a class of stochastic high-order feedforward nonlinear systems with time-varying delays:A homogeneous domination approach,”Transactions of the Institute of Measurement and Control,vol.36,no.8,pp.1041-1050,2014.
[20]T.C.Jiao,S.Y.Xu,Y.L.Wei,Y.M.Chu,and Y.Zou,“Decentralized global stabilization for stochastic high-order feedforward nonlinear systems with time-varying delays,”Journal of the Franklin Institute,vol.351,no.10,pp.4872-4891,2014.
[2]R.Z.Khasminskii,Stochastic Stability of Differential Equations.Berlin:Springer Science and Business Media,2011.
[3]W.-H.Chen,W.X.Zheng,and Y.Shen,“Delay-dependent stochastic stability and H∞-control of uncertain neutral stochastic systems with time delay,”IEEE Transactions on Automatic Control,vol.54,no.7,pp.1660-1667,2009.
[4]L.Wu,W.X.Zheng,and H.Gao,“Dissipativity-based sliding mode control of switched stochastic systems,”IEEE Transactions on Automatic Control,vol.58,no.3,pp.785-791,2013.
[5]T.C.Jiao,W.X.Zheng,and S.Y.Xu,“On stability of a class of switched nonlinear systems subject to random disturbances,”IEEE Transactions on Circuits and Systems I:Regular Papers,vol.63,no.12,pp.2278-2289,2016.
[6]T.C.Jiao,W.X.Zheng,and S.Y.Xu,“Stability analysis for a class of random nonlinear impulsive systems,”International Journal of Robust and Nonlinear Control,vol.27,no.7,pp.1171-1193,2017.
[7]G.D.Zong,D.Yang,L.l.Hou,and Q.Wang,“Robust finitetime H∞control for Markovian jump systems with partially known transition probabilities,”Journal of the Franklin Institute,vol.350,no.6,pp.1562-1578,2013.
[8]Z.D.Ai and G.D.Zong,“Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems,”Applied Mathematics and Computation,vol.245,pp.462-473,2014.
[9]T.C.Jiao,S.Y.Xu,J.W.Lu,Y.L.Wei,and Y.Zou,“Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via La Salle-Yoshizawa-type theorem,”International Journal of Control,vol.89,no.1,pp.69-83,2016.
[10]Y.Chen and W.X.Zheng,“Stability analysis and control for switched stochastic delayed systems,”International Journal of Robust and Nonlinear Control,vol.26,no.2,pp.303-328,2016.
[11]X.Y.Zhao and F.Q.Deng,“A new type of stability theoremfor stochastic systems with application to stochastic stabilization,”IEEE Transactions on Automatic Control,vol.61,no.1,pp.240-245,2015.
[12]X.R.Mao,“La Salle-type theorems for stochastic differential delay equations,”Journal of Mathematical Analysis and Applications,vol.236,no.2,pp.350-369,1999.
[13]X.Yu and X.J.Xie,“Output feedback regulation of stochastic nonlinear systems with stochastic i ISS inverse dynamics,”IEEE Transactions on Automatic Control,vol.55,no.2,pp.304-320,2010.
[14]M.Frédéric and B.Samuel,“Tracking trajectories of the cartpendulum system,”Automatica,vol.39,no.4,pp.677-684,2003.
[15]H.W.Jo,H.L.Choi,and J.T.Lim,“Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain,”Systems and Control Letters,vol.71,pp.44-53,2014.
[16]F.Mazenc and M.Malisoff,“Asymptotic stabilization for feedforward systems with delayed feedbacks,”Automatica,vol.49,no.3,pp.780-787,2013.
[17]W.T.Zha,J.Y.Zhai,and S.M.Fei,“Global output feedback control for a class of high-order feedforward nonlinear systems with input delay,”ISA Transactions,vol.52,no.4,pp.494-500,2013.
[18]X.L.Jia,S.Y.Xu,T.C.Jiao,Y.M.Chu,and Y.Zou,“Global state regulation by output feedback for feedforward systems with input and output dependent incremental rate,”Journal of the Franklin Institute,vol.352,no.6,pp.2526-2538,2015.
[19]T.C.Jiao,G.Z.Cui,J.W.Lu,and Q.Ma,“State feedback control for a class of stochastic high-order feedforward nonlinear systems with time-varying delays:A homogeneous domination approach,”Transactions of the Institute of Measurement and Control,vol.36,no.8,pp.1041-1050,2014.
[20]T.C.Jiao,S.Y.Xu,Y.L.Wei,Y.M.Chu,and Y.Zou,“Decentralized global stabilization for stochastic high-order feedforward nonlinear systems with time-varying delays,”Journal of the Franklin Institute,vol.351,no.10,pp.4872-4891,2014.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |