非线性系统观测器的设计:LMI方法

杨洪金, 井元伟, 肇和平

杨洪金, 井元伟, 肇和平. 非线性系统观测器的设计:LMI方法[J]. 信息与控制, 2011, 40(4): 433-437.
引用本文: 杨洪金, 井元伟, 肇和平. 非线性系统观测器的设计:LMI方法[J]. 信息与控制, 2011, 40(4): 433-437.
YANG Hongjin, JING Yuanwei, ZHAO Heping. Observer Design for Nonlinear Systems:An LMI Approach[J]. INFORMATION AND CONTROL, 2011, 40(4): 433-437.
Citation: YANG Hongjin, JING Yuanwei, ZHAO Heping. Observer Design for Nonlinear Systems:An LMI Approach[J]. INFORMATION AND CONTROL, 2011, 40(4): 433-437.

非线性系统观测器的设计:LMI方法

详细信息
    作者简介:

    杨洪金(1977- ),男,硕士生.研究领域为非线性系统观测器设计等.
    井元伟(1956- ),男,教授,博士生导师.研究领域为非线性系统控制,网络控制等.
    肇和平(1954- ),男,高级工程师.研究领域为数控机床及机器人应用.

    通讯作者:

    杨洪金, yanghj521@126.com

  • 中图分类号: TP273

Observer Design for Nonlinear Systems:An LMI Approach

  • 摘要: 对满足Lipschitz条件的非线性系统给出了全维、降维观测器存在的充分条件并分别进行了证明,重点设计了新形式的降维状态观测器,观测器增益矩阵的获得完全取决于线性矩阵不等式(LMI)的解的情况,应用线性矩阵不等式工具箱使得设计更加方便,消除了增益矩阵选取的盲目性.通过对实际模型的仿真分析可知,两种观测器的状态估计误差均能渐近收敛到零,表明了该方法的有效性.
    Abstract: The sufficient conditions for the existence of the full-order and the reduced-order observers about Lipschitz nonlinear systems are given and proved.At the same time,a new form of reduced-order state observer is designed.Based on the solving of linear matrix inequality(LMI),the gain matrix of observer can be obtained completely and be easily designed by LMI tool box.The approach avoids the blindness in selecting the gain matrix.The simulation result of a practical model shows that the two kinds of state estimation errors asymptotically converge to zero.It indicates that the approach is efficient.
  • [1] Kalman R E.On a new approach to filtering and prediction problems[J].Transactions of the ASME-Journal of Basic Engineering,1960,82(Series D):35-45.
    [2] Luenberger D G.An introduction to observers[J].IEEE Transactions on Automatic Control,1971,16(6):596-602.  
    [3] Rajamani R.Observers for Lipschitz nonlinear systems[J].IEEE Transactions on Automatic Control,1998,43(3):397-401.  
    [4] Pagilla P R,Zhu Y L.Controller and observer design for Lipschitz nonlinear systems[C]//American Control Conference.Piscataway,NJ,USA:IEEE,2004:2379-2384.
    [5] Pertew A M,Marquez H J,Zhao Q.Design of unknown input observers for Lipschitz nonlinear systems[C]//American Control Conference.Piscataway,NJ,USA:IEEE,2006:4198-4203.
    [6] Chen W T,Mehrdad S.Unknown input observer design for a class of nonlinear systems:An LMI approach[C]//American Control Conference.Piscataway,N J,USA:IEEE,2006:834-838.
    [7] Zemouche A,Boutayeb M.Observer design for Lipschitz nonlinear systems:The discrete-time case[J].IEEE Transactions on Circuits and Systems,2006,53(8):777-781.  
    [8] Abbaszadeh M,Marquez H J.A robust observer design method for continuous-time Lipschitz nonlinear systems[C]//45th IEEE Conference on Decision and Control.Piscataway,NJ,USA:IEEE,2006:3795-3799.
    [9] Liu J,Lu J B,Dou X H,et al.State observer design and application for Lipschitz nonlinear systems[C]//IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Appli-cation.Piscataway,NJ,USA:IEEE,2008:213-217.
    [10] Carnevale D,Karagiannis D,Astolfi A.Reduced-order observer design for systems with non-monotonic nonlinearities[C]//45th IEEE Conference on Decision and Control.Piscataway,NJ,USA:IEEE,2006:5269-5274.
    [11] Zhu Y L,Pagilla P R.Adaptive controller and observer design for a class of nonlinear systems[C]//42nd IEEE Conference on Decision and Control.Piscataway,NJ,USA:IEEE,2003:1687-1692.
    [12] Kalsi K,Lian J M,Hui S,et al.Sliding-mode observers for uncertain systems[C]//American Control Conference.Piscataway,NJ,USA:IEEE,2009:1189-1194.
    [13] Sadaka H,Shafai B,Sipahi R.Robust PI observer design for linear time-delay systems[C]//IEEE Control Applications and Intelligent Control.Piscataway,NJ,USA:IEEE,2009:1209-1213.
    [14] 朱芳来.类Lyapunov非线性系统降维观测器设计[J].控制理论与应用,2004,21(4):607-610.Zhu F L.Design of reduced-order observers for nonlinear systems via Lyapunov-like method[J].Control Theory & Applications,2004,21(4):607-610.
    [15] Zhu F L,Han Z Z.A note on observers for Lipschitz nonlinear systems[J].IEEE Transactions on Automatic Control,2002,47(10):1751-1754.  
计量
  • 文章访问数:  3105
  • HTML全文浏览量:  26
  • PDF下载量:  272
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-04-01
  • 发布日期:  2011-08-19

目录

    /

    返回文章
    返回
    x