Global control for a class of uncertain upper-triangular nonlinear systems with uncontrollable linearization
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- 英文论文题名：Global control for a class of uncertain upper-triangular nonlinear systems with uncontrollable linearization
- 论文作者：Zha Wenting ; Qian Chunjiang ; Zhai Junyong ; Fei Shumin
- 英文论文作者：Zha Wenting ; Qian Chunjiang ; Zhai Junyong ; Fei Shumin ; School of Mechanical Electronic & Information Engineering ; China University of Mining & Technology (Beijing) ; Key Laboratory of Measurement and Control of CSE ; Ministry of Education ; School of Automation ; Southeast University ; Department of Electrical and Computer Engineering ; The University of Texas at San Antonio
- 年：2017
- 作者机构：School of Mechanical Electronic & Information Engineering,China University of Mining & Technology (Beijing);Key Laboratory of Measurement and Control of CSE,Ministry of Education,School of Automation,Southeast University;Department of Electrical and Computer Engineering,The University of Texas at San Antonio;
- 英文论文关键词：upper-triangular nonlinear systems ; input dependent growth rate ; adding a power integrator ; homogeneous domination approach
- 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（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 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：251k
- 原文格式：D
- 会议级别：全国
摘要
This paper fucuses on the global control problem for a class of upper-triangular nonlinear systems whose linearization around the origin is not guaranteed to be controllable. Assuming that the nonlinearities satisfy the homogeneous growth conditions, a nonsmooth state-feedback controller is elaborately constructed based on the adding a power integrator technique and the homogeneous domination approach. By introducing the dynamic gain to deal with the input dependent growth rate, it can be proved that all the signals of the closed-loop system are bounded and the system states converge to the origin asymptotically.
This paper fucuses on the global control problem for a class of upper-triangular nonlinear systems whose linearization around the origin is not guaranteed to be controllable. Assuming that the nonlinearities satisfy the homogeneous growth conditions, a nonsmooth state-feedback controller is elaborately constructed based on the adding a power integrator technique and the homogeneous domination approach. By introducing the dynamic gain to deal with the input dependent growth rate, it can be proved that all the signals of the closed-loop system are bounded and the system states converge to the origin asymptotically.
This paper fucuses on the global control problem for a class of upper-triangular nonlinear systems whose linearization around the origin is not guaranteed to be controllable. Assuming that the nonlinearities satisfy the homogeneous growth conditions, a nonsmooth state-feedback controller is elaborately constructed based on the adding a power integrator technique and the homogeneous domination approach. By introducing the dynamic gain to deal with the input dependent growth rate, it can be proved that all the signals of the closed-loop system are bounded and the system states converge to the origin asymptotically.
引文
[1]A.R.Teel,Global stabilization and restricted tracking for multiple integrators with bounded controls,Systems&Control Letters,18(3):165–171,1992.
[2]A.R.Teel,A nonlinear small gain theorem for the analysis of control systems with saturation,IEEE Transactions on Automatic Control,41(9):1256–1270,1996.
[3]F.Mazenc and L.Praly,Adding integrations,saturated controls,and stabilization for feedforward systems,IEEE Transactions on Automatic Control,41(11):1559–1578,1996.
[4]R.Sepulchre,M.Jankovic and P.V.Kokotovic,Integrator forwarding:a new recursive nonlinear robust design,Automatica,33(5):979–984,1997.
[5]J.Tsinias,M.P.Tzamtzi,An explicit formula of bounded feedback stabilizers for feedforward systems,Systems&Control Letters,43(4):247–261,2001.
[6]S.Ding,C.Qian,S.Li and Q.Li,Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations,International Journal of Robust and Nonlinear Control,21(3):271–294,2011.
[7]W.Lin,C.Qian,Adding one power integrator:a tool for global stabilization of high-order lower-triangular systems,Systems&Control Letters,39(5):339–351,2000.
[8]M.T.Frye,R.Trevino and C.Qian,Output feedback stabilization of nonlinear feedforward systems using low gain homogeneous domination,Proceedings of 2007 IEEE Conference on Control and Automation,2007:422–427.
[9]W.Zha,J.Zhai and S.Fei,Global output feedback control for a class of high-order feedforward nonlinear systems with input delay,ISA Transactions,52(4):494–500,2013.
[10]X.Jia,S.Xu,G.Cui,B.Zhang and Q.Ma,Global adaptive regulation of feedforward nonlinear time-delay systems by output feedback,International Journal of Robust and Nonlinear Control,DOI:10.1002/rnc.3691,2016.
[11]W.Tian,C.Qian and H.Du,A generalised homogeneous solution for global stabilisation of a class of non-smooth uppertriangular systems,International Journal of Control,87(5):951–963,2014.
[12]X.Zhang,Q.Liu,L.Baron and E.K.Boukas,Feedback stabilization for high order feedforward nonlinear time-delay systems,Automatica,47(5):962–967,2011.
[2]A.R.Teel,A nonlinear small gain theorem for the analysis of control systems with saturation,IEEE Transactions on Automatic Control,41(9):1256–1270,1996.
[3]F.Mazenc and L.Praly,Adding integrations,saturated controls,and stabilization for feedforward systems,IEEE Transactions on Automatic Control,41(11):1559–1578,1996.
[4]R.Sepulchre,M.Jankovic and P.V.Kokotovic,Integrator forwarding:a new recursive nonlinear robust design,Automatica,33(5):979–984,1997.
[5]J.Tsinias,M.P.Tzamtzi,An explicit formula of bounded feedback stabilizers for feedforward systems,Systems&Control Letters,43(4):247–261,2001.
[6]S.Ding,C.Qian,S.Li and Q.Li,Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations,International Journal of Robust and Nonlinear Control,21(3):271–294,2011.
[7]W.Lin,C.Qian,Adding one power integrator:a tool for global stabilization of high-order lower-triangular systems,Systems&Control Letters,39(5):339–351,2000.
[8]M.T.Frye,R.Trevino and C.Qian,Output feedback stabilization of nonlinear feedforward systems using low gain homogeneous domination,Proceedings of 2007 IEEE Conference on Control and Automation,2007:422–427.
[9]W.Zha,J.Zhai and S.Fei,Global output feedback control for a class of high-order feedforward nonlinear systems with input delay,ISA Transactions,52(4):494–500,2013.
[10]X.Jia,S.Xu,G.Cui,B.Zhang and Q.Ma,Global adaptive regulation of feedforward nonlinear time-delay systems by output feedback,International Journal of Robust and Nonlinear Control,DOI:10.1002/rnc.3691,2016.
[11]W.Tian,C.Qian and H.Du,A generalised homogeneous solution for global stabilisation of a class of non-smooth uppertriangular systems,International Journal of Control,87(5):951–963,2014.
[12]X.Zhang,Q.Liu,L.Baron and E.K.Boukas,Feedback stabilization for high order feedforward nonlinear time-delay systems,Automatica,47(5):962–967,2011.