带有未知内部扰动的星形Euler-Bernoulli梁网络的指数跟踪控制

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 596-610.

带有未知内部扰动的星形Euler-Bernoulli梁网络的指数跟踪控制

张雅轩^1,*(),许跟起²,郭燕妮¹

¹ 中国民航大学理学院数学系天津 300300
² 天津大学数学学院天津 300350

收稿日期:2017-05-27 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 张雅轩 E-mail:bunnyxuan@tju.edu.cn
基金资助:
国家自然科学基金(61503385);国家自然科学基金(11705279);中央高校基本科研业务费(3122018L004);天津市教委科研计划项目(2018KJ253)

Exponential Tracking Control for a Star-Shaped Network of Euler-Bernoulli Beams with Unknown Internal Disturbance

Yaxuan Zhang^1,*(),Genqi Xu²,Yanni Guo¹

¹ Department of Mathematics, College of Science, Civil Aviation University of China, Tianjin 300300
² College of Mathematics, Tianjin University, Tianjin 300350

Received:2017-05-27 Online:2019-06-26 Published:2019-06-27
Contact: Yaxuan Zhang E-mail:bunnyxuan@tju.edu.cn
Supported by:
the NSFC(61503385);the NSFC(11705279);the Fundamental Research Funds for the Central Universities(3122018L004);the Scientific Research Project of Tianjin Municipal Education Commission(2018KJ253)

摘要/Abstract

摘要：

该文研究了带有未知内部扰动的星形Euler-Bernoulli梁网络的指数跟踪控制问题.首先将该问题等价转化为跟踪网络与被跟踪网络的误差网络的镇定问题.利用滑模控制思想，对误差网络设计了非线性反馈控制方案.通过对状态空间选取适当的范数，运用单调算子理论得到了误差网络的适定性.通过构造适当的Lyapunov函数，证明误差网络按任一收敛率指数稳定.这表明跟踪网络能够按任一给定速率以指数速度跟踪到目标网络.

关键词: 跟踪控制, 未知内部扰动, 星形Euler-Bernoulli梁网络, 滑模控制, 指数镇定

Abstract:

In this paper, the exponential tracking control for a star-shaped network of Eulerbernoulli beams with unknown internal disturbance is studied. The problem is transformed into the stabilization of the error system between the objective network and the active network. The idea of sliding-mode control is used to design a nonlinear feedback control law. The solvability of the error system is obtained via monotone operator theory under an appropriately chosen space norm. The error system is proved to be exponentially stabilized at any decay rate by a suitable Lyapunov functional. So the objective network can track the active network exponentially at any designated rate.

Key words: Tracking control, Unknown internal disturbance, Star-shaped network of Eulerbernoulli beams, Sliding-mode control, Exponential stabilization

中图分类号:

O231.9

张雅轩,许跟起,郭燕妮. 带有未知内部扰动的星形Euler-Bernoulli梁网络的指数跟踪控制[J]. 数学物理学报, 2019, 39(3): 596-610.

Yaxuan Zhang,Genqi Xu,Yanni Guo. Exponential Tracking Control for a Star-Shaped Network of Euler-Bernoulli Beams with Unknown Internal Disturbance[J]. Acta mathematica scientia,Series A, 2019, 39(3): 596-610.

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