[1]李益国,沈炯,吕震中.不确定离散系统最优保性能控制的改进[J].东南大学学报(自然科学版),2002,32(3):424-426.[doi:10.3969/j.issn.1001-0505.2002.03.025]
 Li Yiguo,Shen Jiong,Lü Zhenzhong.Extension of optimal guaranteed cost control for uncertain discrete-time linear systems[J].Journal of Southeast University (Natural Science Edition),2002,32(3):424-426.[doi:10.3969/j.issn.1001-0505.2002.03.025]
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不确定离散系统最优保性能控制的改进()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
32
期数:
2002年第3期
页码:
424-426
栏目:
自动化
出版日期:
2002-05-20

文章信息/Info

Title:
Extension of optimal guaranteed cost control for uncertain discrete-time linear systems
作者:
李益国 沈炯 吕震中
东南大学动力工程系,南京 210096
Author(s):
Li Yiguo Shen Jiong Lü Zhenzhong
Department of Power Engineering, Southeast University, Nanjing 210096, China
关键词:
保性能控制 线性矩阵不等式 不确定性
Keywords:
guaranteed cost control linear matrix inequalities uncertainties
分类号:
TP13
DOI:
10.3969/j.issn.1001-0505.2002.03.025
摘要:
针对一类具有范数有界时变参数不确定性的离散时间线性系统,通过分析保性能控制与其闭环性能指标之间的关系,指出性能指标中的加权矩阵只需要半正定,而不要求必须正定; 并给出了在加权矩阵为半正定的情况下,利用线性矩阵不等式(LMI)实现保性能控制的方法; 最后通过一个例子说明了本文所提方法的有效性.该方法大大增加了保性能控制中权值选取的灵活性,使输出跟踪等问题都可以方便地通过适当变形转化为该问题的形式来求解,扩大了其应用范围.
Abstract:
For a class of discrete-time linear systems with norm-bounded time-varying parameter uncertainty, the relation between guaranteed cost control and its cost index is analyzed. It is found that the weighting matrices in the cost index can set to be semi-positive rather than positive. So it presents a new method to realize guaranteed cost control by linear matrix inequalities when the weighting matrices are semi-positive. Finally, an example is given to illustrate the validity of the method proposed. This method enhances the flexibility in selecting weighting matrices greatly and extends the scope applied. The problems such as output tracking problem can be solved through some transformation.

参考文献/References:

[1] 俞立.不确定离散系统的最优保性能控制[J].控制理论与应用,1999,16(5):639-642.
  Yu Li.Optimal guaranteed cost control for uncertain discrete-time linear systems[J].Control Theory and Applications,1999,16(5):639-642.(in Chinese)
[2] Yu Li.Guaranteed cost control of uncertain linear discrete-time systems[A].In:Proc of American Control Conference[C].Albuquerque,New Mexico,1997.3181-3184.
[3] Reza S O.Guaranteed cost control of uncertain systems with a time-multiplied quadratic cost function:an approach based on linear matrix inequalities[J].Automatica,1998,34(4):651-654.
[4] Ptersen I R,Mcfarlane D C.Optimal guaranteed cost control and filtering for uncertain linear systems[J].IEEE Trans on Automatic Control, 1994,39(9):1971-1977.
[5] Pascal Gahinet,Arkadii Nemirovskii,Alan J Laub,et al.The LMI control toolbox[A].In:Proc of the 33rd Conference on Decision and Control[C].Lake Buena Vista,1994.2038-2041.

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备注/Memo

备注/Memo:
基金项目: 教育部高等学校骨干教师计划、江苏省“333人才工程”计划和江苏省青年科技基金资助项目(BQ2000002).
作者简介: 李益国(1973—),男,博士生; 沈炯(联系人),男,博士,教授,博士生导师,Shenj@seu.edu.cn.
更新日期/Last Update: 2002-05-20