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2020影响因子

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## 留言板

 引用本文: 庄波, 崔宝同, 楼旭阳, 陈娟. 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. 自动化学报, 2022, 48(11): 2729−2743
Zhuang Bo, Cui Bao-Tong, Lou Xu-Yang, Chen Juan. Backstepping-based output feedback boundary control for coupled fractional reaction-diffusion systems. Acta Automatica Sinica, 2022, 48(11): 2729−2743 doi: 10.16383/j.aas.c190389
 Citation: Zhuang Bo, Cui Bao-Tong, Lou Xu-Yang, Chen Juan. Backstepping-based output feedback boundary control for coupled fractional reaction-diffusion systems. Acta Automatica Sinica, 2022, 48(11): 2729−2743

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

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)
###### 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: 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.
• 图  1  耦合系统的边界输出反馈控制

Fig.  1  Output feedback boundary control for coupled systems

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

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

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

图  5  存在测量噪声的情况

Fig.  5  The case with measurement noise

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

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

图  8  闭环系统的各状态分量

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

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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##### 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

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