基于反步法的耦合分数阶反应扩散系统边界输出反馈控制

庄波; 崔宝同; 楼旭阳; 陈娟

doi:10.16383/j.aas.c190389

基于反步法的耦合分数阶反应扩散系统边界输出反馈控制

doi: 10.16383/j.aas.c190389

庄波^{1, 2,},
崔宝同^{1, 2,},
楼旭阳^{1, 2,},
陈娟^3,

1.
江南大学轻工过程先进控制教育部重点实验室无锡 214122 中国
2.
江南大学物联网工程学院无锡214122 中国
3.
塔林理工大学计算机系统系塔林 19086 爱沙尼亚

基金项目: 国家自然科学基金(61807016), 中国博士后科学基金(2018M642160), 高等学校学科创新引智计划(B12018), 江西省青年自然科学基金(20161BAB212032), 江西省教育厅科学技术基金(GJJ181068)资助

详细信息

作者简介:
庄波：江南大学物联网工程学院博士研究生. 2008年获得山东师范大学信息科学与工程学院硕士学位. 主要研究方向为分布参数系统控制. 本文通信作者.E-mail: bozhuang@jiangnan.edu.cn

崔宝同：江南大学物联网工程学院教授. 2003年获得华南理工大学自动化科学与工程学院博士学位. 主要研究方向为复杂系统控制理论与应用.E-mail: btcui@jiangnan.edu.cn

楼旭阳：江南大学物联网工程学院教授. 2009年获得江南大学控制理论与控制工程专业工学博士学位. 主要研究方向为网络化机电系统的优化与控制, 混杂系统的分析与控制.E-mail: louxy@jiangnan.edu.cn

陈娟：爱沙尼亚塔林理工大学博士后研究员. 2018年获得江南大学物联网工程学院工学博士学位. 主要研究方向为分数阶分布参数系统的边界控制和边界观测器设计.E-mail: karenchenjuan.student@sina.com

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出版历程
- 收稿日期: 2019-05-20
- 录用日期: 2019-10-01
- 网络出版日期: 2022-08-08
- 刊出日期: 2022-11-22

Backstepping-based Output Feedback Boundary Control for Coupled Fractional Reaction-diffusion Systems

ZHUANG Bo^{1, 2
,},
CUI Bao-Tong^{1, 2
,},
LOU Xu-Yang^{1, 2
,},
CHEN Juan^3
,

1.
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China
2.
School of IoT Engineering, Jiangnan University, Wuxi 214122, China
3.
Department of Computer Systems, Tallinn University of Technology, Tallinn 19086, Estonia

Funds: Supported by National Natural Science Foundation of China (61807016), China Postdoctoral Science Foundation (2018M642160), the 111 Project (B12018), Jiangxi Natural Science Foundation Youth Project (20161BAB212032), and Technology Project of Jiangxi Provincial Education Department (GJJ181068)

More Information

Author Bio:
ZHUANG Bo　Ph.D. candidate at the School of IoT Engineering, Jiangnan University. He received his master degree from Shandong Normal University in 2008. His research interest covers control of distributed parameter systems. Corresponding author of this paper

CUI Bao-Tong　Professor at the School of IoT Engineering, Jiangnan University. He received his Ph.D. degree from the College of Automation Science and Engineering, South China University of Technology in 2003. His research interest covers control theory of complex systems and its applications

LOU Xu-Yang　Professor at the School of IoT Engineering, Jiangnan University. He received his Ph.D. degree in control theory and control engineering from Jiangnan University in 2009. His research interest covers optimization and control of networked electromechanical systems, analysis and control of hybrid systems

CHEN Juan　Post-doctoral fellow at Tallinn University of Technology, Estonia. She received her Ph.D. degree from the School of IoT Engineering, Jiangnan University in 2018. Her research interest covers boundary control and boundary observer design of fractional distributed parameter systems

摘要

摘要: 针对具有空间依赖耦合系数的分数阶反应扩散系统, 利用反步法设计了基于观测器的边界输出反馈控制器, 证明了观测增益和控制增益核函数矩阵方程的适定性. 针对误差系统和输出反馈的闭环系统, 利用分数阶Lyapunov方法分析了系统的Mittag-Leffler稳定性, 且利用Wirtinger不等式改进了耦合系统稳定的条件. 当系统具有空间依赖的耦合系数时, 难以求得控制增益和观测增益核函数的解析解, 为此, 给出了核函数偏微分方程的数值解方法. 数值仿真验证了理论结果.
- 分数阶偏微分方程 /
- 反应扩散系统 /
- 反步法 /
- 边界控制 /
- 输出反馈
Abstract: An observer-based boundary output feedback controller is designed by backstepping method for fractional reaction-diffusion systems with space-dependent coupling coefficients. The well-posednesses are proved for the kernel function matrix equations of the observer gains and control gains. For the error system and close-loop system of output feedback, the Mittag-Leffler stabilities of the systems are analyzed by the fractional Lyapunov method, and the stability conditions of the coupled systems are improved by using the Wirtinger＇s inequality. For the system with spatially-varying coupling coefficients, it is difficult to obtain analytical solutions of the kernel functions for the controller and the observer. Therefore, numerical methods of partial differential equations of the kernel functions are given. Numerical simulations verify the theoretical results.
- Fractional partial equations /
- reaction-diffusion systems /
- backstepping /
- boundary control /
- output feedback

HTML全文

图 1 耦合系统的边界输出反馈控制

Fig. 1 Output feedback boundary control for coupled systems

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图 2 开环和闭环系统的状态$ L^2 $范数

Fig. 2 The state $ L^2 $ norm of open-loop and close-loop systems

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图 3 观测增益, 控制增益核函数和控制输入

Fig. 3 The observer gain and control gain kernel functions, and control input

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图 4 闭环系统状态各状态分量的演变

Fig. 4 Evolution of state compoments of the close-loop system

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图 5 存在测量噪声的情况

Fig. 5 The case with measurement noise

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图 6 开环和闭环系统的状态$ L^2 $范数

Fig. 6 The state $ L^2 $ norm of open-loop and close-loop systems

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图 7 观测增益, 控制增益核函数和控制输入

Fig. 7 The observer gain and control gain kernel functions, and control input

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图 8 闭环系统的各状态分量

Fig. 8 Evolution of state compoments of the close-loop system

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图 9 不同控制参数下闭环系统的状态$ L^2 $范数

Fig. 9 State $ \tilde{c} $-norm of close-loop systems under different control parameters

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