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.

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参考文献 14

[1]	金鹏, 马倩, 周国鹏. 负荷扰动互联电力系统模糊自适应输出跟踪与干扰抗御[J]. 控制理论与应用, 2021, 38(5): 571-577.
	JIN Peng, MA Qian, ZHOU Guopeng. Fuzzy adaptive output tracking and disturbance rejection for interconnected power systems with load disturbance[J]. Control Theory & Applications, 2021, 38(5): 571-577.
[2]	陈龙胜, 王琦, 何国毅. 非仿射纯反馈非线性切换系统自适应控制[J]. 上海交通大学学报, 2020, 54(9): 981-986. doi: 10.16183/j.cnki.jsjtu.2020.137
	CHEN Longsheng, WANG Qi, HE Guoyi. Adaptive control of non-affine pure feedback nonlinear switching systems[J]. Journal of Shanghai Jiao Tong University, 2020, 54(9): 981-986.
[3]	陈刚, 李志勇. 集合约束下多智能体系统分布式固定时间优化控制[J]. 自动化学报, 2022, 48(9): 2254-2264.
	CHEN Gang, LI Zhiyong. Distributed fixed-time optimal control of multi-agent system with set constraints[J]. Acta Automatica Sinica, 2022, 48(9): 2254-2264.
[4]	LI Z J, XIA Y Q, WANG D H, et al. Neural network-based control of networked trilateral teleoperation with geometrically unknown constraints[J]. IEEE Transactions on Cybernetics, 2016, 46(5): 1051-1064. doi: 10.1109/TCYB.2015.2422785 pmid: 25956001
[5]	SHANG W W, XIE F, ZHANG B, et al. Adaptive cross-coupled control of cable-driven parallel robots with model uncertainties[J]. IEEE Robotics and Automation Letters, 2020, 5(3): 4110-4117. doi: 10.1109/LSP.2016. URL
[6]	GEROMEL J C, KOROGUI R H, BERNUSSOU J. H₂ and H_∞ robust output feedback control for continuous time polytopic systems[J]. IET Control Theory Applications, 2007, 1(5): 1541-1549. doi: 10.1049/iet-cta:20060460 URL
[7]	GE S S, LI Z J. Robust adaptive control for a class of MIMO nonlinear systems by state and output feedback[J]. IEEE Transactions on Automatic Control, 2014, 59(6): 1624-1629. doi: 10.1109/TAC.9 URL
[8]	CHESI G. H₂ and H_∞ robust output feedback control for continuous time polytopic systems[J]. IEEE Transactions on Automatic Control, 2014, 59(6): 1618-1623. doi: 10.1109/TAC.2013.2293453 URL
[9]	LIEN C H, YU K W. LMI optimization approach on robustness and H_∞ control analysis for observer-based control of uncertain systems[J]. Chaos, Solitons & Fractals, 2008, 36(3): 617-627. doi: 10.1016/j.chaos.2006.06.076 URL
[10]	PEAUCELLE D, EBIHARA Y, HOSOE Y. Robust observed-state feedback design for discrete-time systems rational in the uncertainties[J]. Automatica, 2017, 76: 96-102. doi: 10.1016/j.automatica.2016.10.003 URL
[11]	PEREIRA R L, DE OLIVEIRA M S. On robust stabilization of discrete-time LPV/LFR systems[J]. IEEE Transactions on Automatic Control, 2023, 68(1): 448-453. doi: 10.1109/TAC.2022.3140255 URL
[12]	LUENBERGER D. An introduction to observers[J]. IEEE Transactions on Automatic Control, 1971, 16(6): 596-602. doi: 10.1109/TAC.1971.1099826 URL
[13]	LOFBERG J. YALMIP: A toolbox for modeling and optimization in MATLAB[C]// 2004 IEEE International Conference on Robotics and Automation. Taipei, China: IEEE, 2004: 284-289.
[14]	TOH K C, TODD M J, TÜTÜNCÜ R H. On the Implementation and usage of SDPT3-A Matlab software package for semidefinite-quadratic-linear programming, version 4.0[M]//Handbook on semidefinite, conic and polynomial optimization. Boston, MA: Springer, 2012: 715-754.

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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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