常微分方程-薛定谔方程耦合系统的输出反馈镇定

doi:10.12341/jssmsE20096

系统科学与数学 ›› 2021, Vol. 41 ›› Issue (4): 887-897.DOI: 10.12341/jssmsE20096

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常微分方程-薛定谔方程耦合系统的输出反馈镇定

张小英¹，王平²，冯红银萍³

1. 山西农业大学基础部,太谷 030801; 2. 山西财经大学资源环境学院, 太原 030006; 3. 山西大学数学科学学院,太原 030006

出版日期:2018-04-25 发布日期:2021-06-25

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张小英, 王平, 冯红银萍. 常微分方程-薛定谔方程耦合系统的输出反馈镇定[J]. 系统科学与数学, 2021, 41(4): 887-897.

ZHANG Xiaoying, WANG Ping, FENG Hongyinping. Output Feedback Stabilization of a Coupled ODE-Schr\"{o}dinger Equation System[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 887-897.

Output Feedback Stabilization of a Coupled ODE-Schr\"{o}dinger Equation System

ZHANG Xiaoying¹ ,WANG Ping² ,FENG Hongyinping³

1. Department of Basic Courses, Shanxi Agricultural University, Taigu 030801; 2. College of Resources and Environment, Shanxi University of Finance and Economics, Taiyuan 030006; 3. School of Mathematical Sciences, Shanxi University, Taiyuan 030006

Online:2018-04-25 Published:2021-06-25

考虑带有薛定谔方程执行动态的常微分方程的镇定问题. 通过在常微分方程系统上应用Backstepping方法设计出状态反馈和基于观测器的输出反馈. 与偏微分方程Backstepping方法不同, 常微分方程Backstepping方法的核函数更加简单. 文章证明了闭环系统的适定性和指数稳定性,并且给出了数值模拟来验证理论结果.

关键词： 反推法, 耦合系统, , 指数稳定.

In this paper, we consider the stabilization of an ODE system through an actuator dynamics dominated by one dimensional Schr\"{o}dinger equation. By applying the backstepping transformation to the ODE system, both the full state feedback and the observer based output feedback are designed. Different from the PDE backstepping method, the kernel of the ODE backstepping is much simpler. The well-posedness and the exponential stability of the closed-loop system are proved. Some numerical simulations are given to validate the theoretical results.

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