二维Mindlin-Timoshenko板系统的稳定性与最优性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1465-1491.

二维Mindlin-Timoshenko板系统的稳定性与最优性

章春国*(),付煜之,刘宇标

^{杭州电子科技大学数学系杭州 310018}

收稿日期:2020-02-21 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 章春国 E-mail:cgzhang@hdu.edu.cn
基金资助:
国家自然科学基金(61374096)

Stability and Optimality of 2-D Mindlin-Timoshenko Plate System

Chunguo Zhang*(),Yuzhi Fu,Yubiao Liu

^{Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou 310018}

Received:2020-02-21 Online:2021-10-26 Published:2021-10-08
Contact: Chunguo Zhang E-mail:cgzhang@hdu.edu.cn
Supported by:
the NSFC(61374096)

摘要/Abstract

摘要：

该文研究的是具有局部边界控制的二维Mindlin-Timoshenko板系统，运用滚动时域法，将无限时域最优性问题转化为有限时域的最优性问题进行研究.借助乘子法技巧，首先对每一有限时域系统的解做先验估计，并得到能观性不等式，进而证明了系统能量是一致指数衰减的.进一步，借助对偶系统，应用变分原理和Bellman最优性原理，得到了无限时域系统的次优性条件，并证明了最优轨线也是指数衰减的.

关键词: Mindlin-Timoshenko板, 滚动时域法, 最优性, 指数衰减

Abstract:

In this paper, 2-D Mindlin Timoshenko plate system with local boundary control is studied. By using the receding horizon control method, the infinite time domain optimality problem is transformed into the finite time domain optimality problem. With the help of the multiplier technique, a priori estimation is made for any finite time domain system, and the observability inequality is obtained, which proves that the energy of the system is uniformly exponentially decay. Furthermore, with the aid of dual system, by means of the variational principle and Bellman optimality principle, the suboptimal conditions of the system in infinite time domain are obtained, and it is proved that the optimal trajectory is also exponential decay.

Key words: 2-D Mindlin Timoshenko plate, Receding horizon control method, Optimality, Exponential decay

中图分类号:

O231.4

章春国,付煜之,刘宇标. 二维Mindlin-Timoshenko板系统的稳定性与最优性[J]. 数学物理学报, 2021, 41(5): 1465-1491.

Chunguo Zhang,Yuzhi Fu,Yubiao Liu. Stability and Optimality of 2-D Mindlin-Timoshenko Plate System[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1465-1491.

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