二维Mindlin-Timoshenko板系统的稳定性与最优性  

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

作　　者：章春国[1] 付煜之 刘宇标 Zhang Chunguo;Fu Yuzhi;Liu Yubiao(Department of Mathematics,College of Science,Hangzhou Dianzi University,Hangzhou 310018)

机构地区：[1]杭州电子科技大学数学系,杭州310018

出　　处：《数学物理学报（A辑）》2021年第5期1465-1491,共27页Acta Mathematica Scientia

基　　金：国家自然科学基金(61374096)。

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.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.

关 键 词：Mindlin-Timoshenko板 滚动时域法 最优性 指数衰减 

分 类 号：O231.4[理学—运筹学与控制论]