Stabilization for stochastic one-sided Lipschitz nonlinear differential inclusion system
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- 英文论文题名：Stabilization for stochastic one-sided Lipschitz nonlinear differential inclusion system
- 论文作者：Jun Huang ; Lei Yu
- 英文论文作者：Jun Huang ; Lei Yu ; School of Mechanical and Electrical Engineering ; Soochow University
- 年：2017
- 作者机构：School of Mechanical and Electrical Engineering,Soochow University;
- 英文论文关键词：Differential inclusion ; One-sided Lipschitz ; Stabilization
- 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：TP13
- 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：247k
- 原文格式：D
- 会议级别：全国
摘要
This paper considers the stabilization problem for one-sided Lipschitz nonlinear differential inclusion system with stochastic disturbance. Firstly, the stability theory of stochastic differential equation is extended to stochastic differential inclusion. Then, the feedback law is constructed to make the closed-loop system exponentially stable in mean square. Finally, two numerical examples are simulated to show the effectiveness of the proposed method.
This paper considers the stabilization problem for one-sided Lipschitz nonlinear differential inclusion system with stochastic disturbance. Firstly, the stability theory of stochastic differential equation is extended to stochastic differential inclusion. Then, the feedback law is constructed to make the closed-loop system exponentially stable in mean square. Finally, two numerical examples are simulated to show the effectiveness of the proposed method.
This paper considers the stabilization problem for one-sided Lipschitz nonlinear differential inclusion system with stochastic disturbance. Firstly, the stability theory of stochastic differential equation is extended to stochastic differential inclusion. Then, the feedback law is constructed to make the closed-loop system exponentially stable in mean square. Finally, two numerical examples are simulated to show the effectiveness of the proposed method.
引文
[1]J.Aubin,A.Cellina,Differential Inclusions:Set-valued Maps and Viability Theory,Springer Verlag,New York,1984.
[2]T.Hu,Z.Lin,Properties of the composite quadratic Lyapunov functions,IEEE Transactions on Automatic Control,49:1162-1167,2004.
[3]T.Hu,A.Teel,L.Zaccarian,Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions,IEEE Transactions on Automatic Control,51:1770-1786,2006.
[4]T.Hu,Nonlinear control design for linear differential inclusions via convex hull of quadratics,Automatica,43:685-692,2007.
[5]X.Cai,L.Liu,W.Zhang,Saturated control design for linear differential inclusions subject to disturbance,Nonlinear Dynamics,58:487-496,2009.
[6]L.Liu,Z.Han,X.Cai,J.Huang,Robust stabilization of linear differential inclusion system with time delay,Mathematics and Computers in Simulation,80:951-958,2010.
[7]J.Huang,Z.Han,X.Cai,L.Liu,Robust stabilization of linear differential inclusions with affine uncertainty,Circuits,Systems,and Signal Processing,30:1369-1382,2011.
[8]X.Cai,Robust stabilisation for nonlinear differential inclusion systems subject to disturbances,Acta Automatica Sinica,36:1327-1331,2010.
[9]E.Hairer,S.Norsett,G.Wanner,Solving ordinary differential equations II:stiff and DAE problems,Springer Verlag,Berlin,1993.
[10]M.Abbaszadeh,H.Marquez,Nonlinear observer design for one-sided Lipschitz systems,in Proceedings of the American Control Conference,Baltimore,USA,2010:5284-5289.
[11]W.Zhang,H.Su,F.Zhu,D.Yue,A Note on observers for discrete-time Lipschitz nonlinear systems,IEEE Transactions on Circuits&Systems II,59:123-127,2012.
[12]W.Zhang,H.Su,Y.Liang,Z.Han,Non-linear observer design for one-sided Lipschitz systems:an linear matrix inequality approach,IET Control Theory&Applications,6:1297-1303,2012.
[13]H.Beikzadeh,H.Marquez,Observer-based H∞control using the incremental gain for one-sided Lipschitz nonlinear systems,in Proceedings of the American Control Conference,Portland,USA,2014:4653-4658.
[14]J.Song,S.He,Finite-time H∞control for quasi-one-sided Lipschitz nonlinear systems,Neurocomputing,149:1433-1439,2015.
[15]X.Cai,Z.Wang,L.Liu,Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay,Neurocomputing,165:182-189,2015.
[16]Y.Dong,W.Liu,S.Liang,Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties,International Journal of Robust&Nonlinear Control,DOI:10.1002/rnc.3648,2016.
[17]W.Zhang,H.Su,F.Zhu,S.Bhattacharyya,Improved exponential observer design for one-sided Lipschitz nonlinear systems,International Journal of Robust&Nonlinear Control,26:3958-3973,2016.
[18]A.Friedman,Stochastic Differential Equations and Applications,Academic Press,New York,1976.
[19]L.Wu,W.Zheng,H.Gao,Dissipativity-based sliding mode control of switched stochastic systems,IEEE Transactions on Automatic Control,58:785-791,2013.
[20]F.Li,L.Wu,P.Shi,C.Lim,State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties,Automatica,51:385-393,2015.
[21]H.Li,P.Shi,D.Yao,L.Wu,Observer-based adaptive sliding mode control for nonlinear Markovian jump systems,Automatica,64:133-142,2016.
[22]K.Guesmi,N.Essounbouli,A.Hamzaoui,J.Zaytoon,N.Manamanni,Shifting nonlinear phenomena in a DC-DC converter using a fuzzy logic controller,Mathematics and Computers in Simulation,76:398-409,2008.
[2]T.Hu,Z.Lin,Properties of the composite quadratic Lyapunov functions,IEEE Transactions on Automatic Control,49:1162-1167,2004.
[3]T.Hu,A.Teel,L.Zaccarian,Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions,IEEE Transactions on Automatic Control,51:1770-1786,2006.
[4]T.Hu,Nonlinear control design for linear differential inclusions via convex hull of quadratics,Automatica,43:685-692,2007.
[5]X.Cai,L.Liu,W.Zhang,Saturated control design for linear differential inclusions subject to disturbance,Nonlinear Dynamics,58:487-496,2009.
[6]L.Liu,Z.Han,X.Cai,J.Huang,Robust stabilization of linear differential inclusion system with time delay,Mathematics and Computers in Simulation,80:951-958,2010.
[7]J.Huang,Z.Han,X.Cai,L.Liu,Robust stabilization of linear differential inclusions with affine uncertainty,Circuits,Systems,and Signal Processing,30:1369-1382,2011.
[8]X.Cai,Robust stabilisation for nonlinear differential inclusion systems subject to disturbances,Acta Automatica Sinica,36:1327-1331,2010.
[9]E.Hairer,S.Norsett,G.Wanner,Solving ordinary differential equations II:stiff and DAE problems,Springer Verlag,Berlin,1993.
[10]M.Abbaszadeh,H.Marquez,Nonlinear observer design for one-sided Lipschitz systems,in Proceedings of the American Control Conference,Baltimore,USA,2010:5284-5289.
[11]W.Zhang,H.Su,F.Zhu,D.Yue,A Note on observers for discrete-time Lipschitz nonlinear systems,IEEE Transactions on Circuits&Systems II,59:123-127,2012.
[12]W.Zhang,H.Su,Y.Liang,Z.Han,Non-linear observer design for one-sided Lipschitz systems:an linear matrix inequality approach,IET Control Theory&Applications,6:1297-1303,2012.
[13]H.Beikzadeh,H.Marquez,Observer-based H∞control using the incremental gain for one-sided Lipschitz nonlinear systems,in Proceedings of the American Control Conference,Portland,USA,2014:4653-4658.
[14]J.Song,S.He,Finite-time H∞control for quasi-one-sided Lipschitz nonlinear systems,Neurocomputing,149:1433-1439,2015.
[15]X.Cai,Z.Wang,L.Liu,Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay,Neurocomputing,165:182-189,2015.
[16]Y.Dong,W.Liu,S.Liang,Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties,International Journal of Robust&Nonlinear Control,DOI:10.1002/rnc.3648,2016.
[17]W.Zhang,H.Su,F.Zhu,S.Bhattacharyya,Improved exponential observer design for one-sided Lipschitz nonlinear systems,International Journal of Robust&Nonlinear Control,26:3958-3973,2016.
[18]A.Friedman,Stochastic Differential Equations and Applications,Academic Press,New York,1976.
[19]L.Wu,W.Zheng,H.Gao,Dissipativity-based sliding mode control of switched stochastic systems,IEEE Transactions on Automatic Control,58:785-791,2013.
[20]F.Li,L.Wu,P.Shi,C.Lim,State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties,Automatica,51:385-393,2015.
[21]H.Li,P.Shi,D.Yao,L.Wu,Observer-based adaptive sliding mode control for nonlinear Markovian jump systems,Automatica,64:133-142,2016.
[22]K.Guesmi,N.Essounbouli,A.Hamzaoui,J.Zaytoon,N.Manamanni,Shifting nonlinear phenomena in a DC-DC converter using a fuzzy logic controller,Mathematics and Computers in Simulation,76:398-409,2008.