Variance-Constrained Control for Uncertain Stochastic Systems via Disturbance Observers
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- 英文论文题名：Variance-Constrained Control for Uncertain Stochastic Systems via Disturbance Observers
- 论文作者：Yunlong Liu ; Ping Zhou ; Mingzhi Liu
- 英文论文作者：Yunlong Liu ; Ping Zhou ; Mingzhi Liu ; Key Laboratory of Integrated Automation for Process Industry ; Ministry of Education ; Northeastern University ; Tianjin Airlines Company Limited
- 年：2017
- 作者机构：Key Laboratory of Integrated Automation for Process Industry,Ministry of Education,Northeastern University;Tianjin Airlines Company Limited;
- 英文论文关键词：Stochastic System ; Variance Constraint ; Disturbance Observer ; Composite Control
- 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：187k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the robust variance-constrained composite control problem is investigated for linear uncertain discretetime stochastic systems. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The purpose of this problem is to design a disturbance observer to estimate the disturbance generated by an exogenous system, then construct the control strategy by integrating the output of the disturbance observer with state-feedback control law, such that, for all admissible parameter uncertainties, the system state of the closed-loop system is mean square bounded, and the steady state variance of each state is not more than the individual prescribed upper bound. And a LMI method is developed to deal with the control problem, which is related to a linear matrix inequality. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed design approach.
In this paper, the robust variance-constrained composite control problem is investigated for linear uncertain discretetime stochastic systems. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The purpose of this problem is to design a disturbance observer to estimate the disturbance generated by an exogenous system, then construct the control strategy by integrating the output of the disturbance observer with state-feedback control law, such that, for all admissible parameter uncertainties, the system state of the closed-loop system is mean square bounded, and the steady state variance of each state is not more than the individual prescribed upper bound. And a LMI method is developed to deal with the control problem, which is related to a linear matrix inequality. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed design approach.
In this paper, the robust variance-constrained composite control problem is investigated for linear uncertain discretetime stochastic systems. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The purpose of this problem is to design a disturbance observer to estimate the disturbance generated by an exogenous system, then construct the control strategy by integrating the output of the disturbance observer with state-feedback control law, such that, for all admissible parameter uncertainties, the system state of the closed-loop system is mean square bounded, and the steady state variance of each state is not more than the individual prescribed upper bound. And a LMI method is developed to deal with the control problem, which is related to a linear matrix inequality. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed design approach.
引文
[1]R.E.Skelton,T.Iwasaki,and K.M.Grigoriadis,A Unified Algebraic Approach to Linear Control Design.New York:Taylor-Francis,1997.
[2]E.G.Jr.Collins and R.E.Skelton,A theory of state covariance assignment for discrete systems,IEEE Trans.on Automatic Control,32(1):35-41,1987.
[3]A.F.Hotz and R.E.Skelton,A covariance control theory,Int.J.Control,46(1):13-32,1987.
[4]Y.S.Hung and F.Yang,Robust H∞filtering with error variance constraints for uncertain discrete time-varying systems with uncertainty,Automatica,39(7):1185-1194,2003.
[5]G.Zhu,K.Grigoriadis,and R.E.Skelton,Covariance control design for the HST,AIAA J.,18(2):230-236,1995.
[6]Z.Wang,W.C.Ho.Daniel,and X.Liu,Variance-constrained control for uncertain stochastic systems with missing measurements,IEEE Trans.on Systems,Man,and Cybernetics,35(5):746-753,2005.
[7]Z.Wang,F.Yang,W.C.Ho.Daniel,and X.Liu,Robust variance-constrained H∞control for stochastic systems with multiplicative noises,Jounrnal of Mathematical Analysis and Applications,328(1):487-502,2007.
[8]Z.Wang,J.Zhu,and H.Unbehauen,Robust filter design with timevarying parameter uncertainty and error variance constraints,Int.J.Control 72(1):30-38,1999.
[9]Z.Wang and B.Huang,Robust H2/H∞filtering for linear systems with error variance constraints,IEEE Trans.Signal Process,48(8):2463-2467,2000.
[10]Z.Wang,W.C.Ho.Daniel,and X.Liu,Variance-contrained filtering for uncertain stochastic systems with missing measurements,IEEE Trans.on Automatic Control,48(7):1254-1258,2003
[11]X.Wei,L.Guo,Composite disturbance-observer-based control and H∞control for complex continuous models,Int.J.Robust Nonlinear Control,20:106-118,2010.
[12]X.Yao,L.Guo,Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer,Automatica,49:2538-2545,2013.
[13]Y.Liu,Y.Zhang,and X.Yao,Composite antidisturbance control for a class of nonlinear stochastic systems via disturbance observer,Mathematical Problems in Engineering,2013(3):1-7,2013.
[14]S.Boyd,L.E.Ghaoui,E.Feron,and V.Balakrishnan,Linear Matrix Inequalities in System and Control Theory.Philadelphia,PA:SIAM Stud.Appl.Math.,1994.
[15]D.W.C.Ho and G.Lu,Robust stabilization for a class of discrete-time non-linear systems via output feedback:The unified LMI approach,Int.J.Control,76(2):105-115,2003.
[16]Z.Wang,F.Yang,W.C.Ho.Daniel,and X.Liu,Robust H∞control for networked systems with random packet losses,IEEE Trans.on Systems,Man,and Cybernetics,37(4):916-924,2007.
[17]R.G.Agniel and E.I.Jury,Almost sure boundedness of randomly sampled systems,SIAM J.Control Optim.,9:372-384,1971.
[18]W.L.De Koning,Optimal estimation of linear discrete time systems with stochastic parameters,Automatica,20:113-115,1984.
[2]E.G.Jr.Collins and R.E.Skelton,A theory of state covariance assignment for discrete systems,IEEE Trans.on Automatic Control,32(1):35-41,1987.
[3]A.F.Hotz and R.E.Skelton,A covariance control theory,Int.J.Control,46(1):13-32,1987.
[4]Y.S.Hung and F.Yang,Robust H∞filtering with error variance constraints for uncertain discrete time-varying systems with uncertainty,Automatica,39(7):1185-1194,2003.
[5]G.Zhu,K.Grigoriadis,and R.E.Skelton,Covariance control design for the HST,AIAA J.,18(2):230-236,1995.
[6]Z.Wang,W.C.Ho.Daniel,and X.Liu,Variance-constrained control for uncertain stochastic systems with missing measurements,IEEE Trans.on Systems,Man,and Cybernetics,35(5):746-753,2005.
[7]Z.Wang,F.Yang,W.C.Ho.Daniel,and X.Liu,Robust variance-constrained H∞control for stochastic systems with multiplicative noises,Jounrnal of Mathematical Analysis and Applications,328(1):487-502,2007.
[8]Z.Wang,J.Zhu,and H.Unbehauen,Robust filter design with timevarying parameter uncertainty and error variance constraints,Int.J.Control 72(1):30-38,1999.
[9]Z.Wang and B.Huang,Robust H2/H∞filtering for linear systems with error variance constraints,IEEE Trans.Signal Process,48(8):2463-2467,2000.
[10]Z.Wang,W.C.Ho.Daniel,and X.Liu,Variance-contrained filtering for uncertain stochastic systems with missing measurements,IEEE Trans.on Automatic Control,48(7):1254-1258,2003
[11]X.Wei,L.Guo,Composite disturbance-observer-based control and H∞control for complex continuous models,Int.J.Robust Nonlinear Control,20:106-118,2010.
[12]X.Yao,L.Guo,Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer,Automatica,49:2538-2545,2013.
[13]Y.Liu,Y.Zhang,and X.Yao,Composite antidisturbance control for a class of nonlinear stochastic systems via disturbance observer,Mathematical Problems in Engineering,2013(3):1-7,2013.
[14]S.Boyd,L.E.Ghaoui,E.Feron,and V.Balakrishnan,Linear Matrix Inequalities in System and Control Theory.Philadelphia,PA:SIAM Stud.Appl.Math.,1994.
[15]D.W.C.Ho and G.Lu,Robust stabilization for a class of discrete-time non-linear systems via output feedback:The unified LMI approach,Int.J.Control,76(2):105-115,2003.
[16]Z.Wang,F.Yang,W.C.Ho.Daniel,and X.Liu,Robust H∞control for networked systems with random packet losses,IEEE Trans.on Systems,Man,and Cybernetics,37(4):916-924,2007.
[17]R.G.Agniel and E.I.Jury,Almost sure boundedness of randomly sampled systems,SIAM J.Control Optim.,9:372-384,1971.
[18]W.L.De Koning,Optimal estimation of linear discrete time systems with stochastic parameters,Automatica,20:113-115,1984.