| 一类分布式分数阶反应扩散系统的边界反馈镇定 |
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| 引用本文： | 张晴,寇春海,蔡锐阳. 一类分布式分数阶反应扩散系统的边界反馈镇定[J]. 上海师范大学学报(自然科学版), 2020, 49(5): 487-504 |
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| 作者姓名： | 张晴 寇春海 蔡锐阳 |
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| 作者单位： | 东华大学理学院,上海201620;东华大学信息科学与技术学院,上海201620 |
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| 基金项目： | The Natural Science Foundation of Shanghai (19ZR1400500) |
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| 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。
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| 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 |
| 收稿时间： | 2020-07-27 |
Boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems |
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| ZHANG Qing,KOU Chunhai and CAI Ruiyang. Boundary feedback stabilization for a class of distributed-order fractional reaction diffusion systems[J]. Journal of Shanghai Normal University(Natural Sciences), 2020, 49(5): 487-504 |
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| Authors: | ZHANG Qing KOU Chunhai CAI Ruiyang |
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| Affiliation: | College of Science, Donghua University, Shanghai 201620, China,College of Science, Donghua University, Shanghai 201620, China and College of Information Science and Technology, Donghua University, Shanghai 201620, China |
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| 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. |
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| Keywords: | distributed-order fractional system reaction diffusion system backstepping transformation stability boundary control |
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