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  

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

作　　者：庄波 崔宝同 楼旭阳[1,2] 陈娟 ZHUANG Bo;CUI Bao-Tong;LOU Xu-Yang;CHEN Juan(Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),Jiangnan University,Wuxi 214122,China;School of IoT Engineering,Jiangnan University,Wuxi 214122,China;Department of Computer Systems,Tallinn University of Technology,Tallinn 19086,Estonia)

机构地区：[1]江南大学轻工过程先进控制教育部重点实验室,中国无锡214122 [2]江南大学物联网工程学院,中国无锡214122 [3]塔林理工大学计算机系统系,爱沙尼亚塔林19086

出　　处：《自动化学报》2022年第11期2729-2743,共15页Acta Automatica Sinica

基　　金：国家自然科学基金(61807016);中国博士后科学基金(2018M 642160);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。

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.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.

关 键 词：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 

分 类 号：O231[理学—运筹学与控制论]