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一类分布式分数阶反应扩散系统的边界反馈镇定
张晴1, 寇春海1, 蔡锐阳2
1.东华大学 理学院, 上海 201620;2.东华大学 信息科学与技术学院, 上海 201620
摘要:
研究了一类分布式分数阶反应扩散系统的边界反馈镇定问题。首先分析了目标系统的稳定性,并运用backstepping方法得到了系统的状态反馈控制器和具体的核矩阵函数表达式,使所研究的系统镇定。在此基础上,考虑了异位和同位两类输出测量,并分别设计出相应的观测器和输出反馈控制器,最终实现闭环系统的渐近稳定。
关键词:  分布式分数阶系统  反应扩散系统  backstepping变换  稳定性  边界控制
DOI:10.3969/J.ISSN.1000-5137.2020.05.001
分类号:O231.1
基金项目:The Natural Science Foundation of Shanghai (19ZR1400500)
Boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems
ZHANG Qing1, KOU Chunhai1, CAI Ruiyang2
1.College of Science, Donghua University, Shanghai 201620, China;2.College of Information Science and Technology, Donghua University, Shanghai 201620, China
Abstract:
In this paper, the problem of boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems is studied. Firstly, the stability of the target system is analyzed. By using the backstepping method, the explicit kernel matrix function is obtained, and a new state feedback controller is designed to stabilize the original system. Then we consider two kinds of output measurements, that is, the non-collocated output and the collocated output. In the two cases, the corresponding observers and output feedback controllers are designed, respectively, to achieve the asymptotical stability of the studied system.
Key words:  distributed-order fractional system  reaction diffusion system  backstepping transformation  stability  boundary control