一类扩散波方程的PDP反馈控制和稳定性分析

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1088-1096.

一类扩散波方程的PDP反馈控制和稳定性分析

范东霞(),赵东霞*(),史娜(),王婷婷()

^{中北大学理学院数学学科部太原 030051}

收稿日期:2020-09-24 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 赵东霞 E-mail:119256724@qq.com;zhaodongxia6@sina.com;1835446397@qq.com;807790440@qq.com
作者简介:范东霞, E-mail: 119256724@qq.com|史娜, E-mail: 1835446397@qq.com|王婷婷, E-mail: 807790440@qq.com
基金资助:
国家自然科学基金青年基金(61603351);山西省自然科学基金面上项目(201801D121027);国家自然科学基金青年基金(201701-D221121);中北大学第十七届研究生科技立项(20201747)

The PDP Feedback Control and Stability Analysis of a Diffusive Wave Equation

Dongxia Fan(),Dongxia Zhao*(),Na Shi(),Tingting Wang()

^{School of Science, North University of China, Taiyuan 030051}

Received:2020-09-24 Online:2021-08-26 Published:2021-08-09
Contact: Dongxia Zhao E-mail:119256724@qq.com;zhaodongxia6@sina.com;1835446397@qq.com;807790440@qq.com
Supported by:
the NSFC(61603351);the NSF of Shanxi Province(201801D121027);the NSF of Shanxi Province(201701-D221121);the 17th Postgraduate Science and Technology Project of The North University of China(20201747)

摘要/Abstract

摘要：

该文从简化的Hayami扩散波方程模型出发，建立了具有瞬时位置和时滞位置线性组合（PDP）的反馈控制模型，讨论了闭环系统解的适定性，然后利用能量范数构造Lyapunov函数，建立了闭环系统的指数稳定性.最后，将控制参数的取值范围与已有文献结果进行对比，得出了该文参数条件更为宽泛的结论，体现了PDP反馈控制器的优越性.

关键词: 扩散波方程, PDP反馈, Lyapunov函数, 指数稳定性

Abstract:

In this paper, a position and delayed position (PDP) feedback controller is established for the Hayami diffusive wave equation. The well-posedness of the closed system is studied firstly, and then, by the method of Lyapunov function, the exponential stability is obtained. Finally, compared with the previous results, the range of the control parameters is expanded in this paper, which shows the efficiency and feasibility of PDP feedback.

Key words: Diffusive wave equation, PDP feedback, Lyapunov function, Exponential stability

中图分类号:

O231.4

范东霞,赵东霞,史娜,王婷婷. 一类扩散波方程的PDP反馈控制和稳定性分析[J]. 数学物理学报, 2021, 41(4): 1088-1096.

Dongxia Fan,Dongxia Zhao,Na Shi,Tingting Wang. The PDP Feedback Control and Stability Analysis of a Diffusive Wave Equation[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1088-1096.

参考文献 12

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