基于Luenberger观测器的不确定系统鲁棒状态反馈设计

doi:10.16183/j.cnki.jsjtu.2022.328

上海交通大学学报 ›› 2024, Vol. 58 ›› Issue (4): 492-497.doi: 10.16183/j.cnki.jsjtu.2022.328

基于Luenberger观测器的不确定系统鲁棒状态反馈设计

赵东东, 闫磊, 周兴文, 耿宗盛, 阎石()

兰州大学信息科学与工程学院,兰州 730000

收稿日期:2022-08-26 修回日期:2022-09-14 接受日期:2022-09-19 出版日期:2024-04-28 发布日期:2024-04-30
通讯作者: 阎石,教授,博士生导师,电话(Tel.):093-18912778;E-mail:yanshi@lzu.edu.cn.
作者简介:赵东东(1989-),副教授,主要研究方向为不确定性动态系统、机器人、机器学习.
基金资助:
国家自然科学基金项目(U22B2040);国家自然科学基金项目(62233003);甘肃省自然科学基金项目(20JR10RA638);中央高校基本科研业务费(lzujbky-2021-67)

Robust State Feedback Design for Uncertain Systems Based on Luenberger Observer

ZHAO Dongdong, YAN Lei, ZHOU Xingwen, GENG Zongsheng, YAN Shi()

School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China

Received:2022-08-26 Revised:2022-09-14 Accepted:2022-09-19 Online:2024-04-28 Published:2024-04-30

摘要/Abstract

摘要：

针对不确定系统测量输出矩阵含有不确定参数的问题,提出一种基于新龙伯格(Luenberger)类型观测器的鲁棒状态反馈设计方法.首先,针对实践中状态变量难以测量的问题,通过观测状态的反馈来进行观测器设计,考虑不确定系统中测量输出矩阵含有不确定参数的情况,设计一种新龙伯格类型观测器;其次,在新龙伯格类型观测器基础上,结合多仿射表示和松弛变量框架,得到与李亚普诺夫函数相关的凸线性矩阵不等式(LMI)条件,进而对闭环系统进行基于线性矩阵不等式组的鲁棒稳定性分析;最后,通过实验检验上述条件的可行性,证明该方法的实用性和有效性.

关键词: 不确定系统, 龙伯格观测器, 多仿射表示, 鲁棒设计, 观测状态

Abstract:

This paper proposes a robust state feedback design method based on a new Luenberger observer for uncertain systems with measurement output matrices containing uncertain parameters. First, in view of the problem that it is challenging to measure state variables in practice, an observer is designed through the feedback of the observation state. Considering the situation that the measurement output matrix contains uncertain parameters in the uncertain system, a new Luenberger observer is designed. Then, based on the new Luenberger observer, and combined with the multi-affine representation and the slack variable framework, the convex linear matrix inequality condition related to the Lyapunov function is obtained, and the robust stability analysis based on linear matrix inequalities is conducted for the closed-loop system. Finally, the feasibility of the above condition is tested by an experiment to show the applicability and effectiveness of the proposed method.

Key words: uncertain systems, Luenberger observer, multi-affine representations, robust design, observed-state

中图分类号:

TP13

赵东东, 闫磊, 周兴文, 耿宗盛, 阎石. 基于Luenberger观测器的不确定系统鲁棒状态反馈设计[J]. 上海交通大学学报, 2024, 58(4): 492-497.

ZHAO Dongdong, YAN Lei, ZHOU Xingwen, GENG Zongsheng, YAN Shi. Robust State Feedback Design for Uncertain Systems Based on Luenberger Observer[J]. Journal of Shanghai Jiao Tong University, 2024, 58(4): 492-497.

图/表 2

参考文献 14

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差异(δ₁, δ₂)	加权因子 (β₂, β_p)	转移特性(γ₂, γ_p)	H_∞性能μ_c
(0, 0)	(1, 1)	(1.5×10^-4, 1.5×10^-4)	1.0561
(0.1, 0)	(1, 1)	(0.421 8, 0.397 0)	1.6531
(0, 0.1)	(1, 1)	(0.038 4, 0.038 4)	1.5573
(0.1, 0.1)	(1, 1)	(0.481 9, 0.428 9)	2.3533
(0.2, 0.2)	(10, 1)	(3.845 1, 3.703 4)	13.3457
(0.2, 0.2)	(1, 1)	(3.939 4, 3.515 5)	无可行解
(0.2, 0.2)	(1, 10)	(4.879 7, 3.137 5)	9.6805

基于Luenberger观测器的不确定系统鲁棒状态反馈设计

Robust State Feedback Design for Uncertain Systems Based on Luenberger Observer

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