摘要
该文研究Timoshenko梁的边界最优控制问题.首先运用线性算子半群理论得到了系统的适定性;进而针对目标涵数,借助伴随系统得到系统的最优性(最大值)原理和相应的最优控制;最后通过齐次系统特征函数渐近展开,给出最优控制与最优轨线详尽的计算步骤.
This paper studies the boundary optimal control problem governed by a Timoshenko beam equation. Firstly, the well posedness of the system is token by using the theory of the linear operator semigroup. Based on the objective function, the optimality principle（the maximum principle） and the corresponding optimal control are obtained by using the adjoint system.Finally, by the eigenfunction asymptotic expansion of the homogeneous system, the exhaustive calculation steps of optimal control and optimal trajectory are given.
作者
章春国
刘宇标
刘维维
Zhang Chunguo;Eiu Yubiao;Liu Weiwei(Department of Mathematics,Hangzhou Dianzi University,Hangzhou 310018)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2018年第3期454-466,共13页
Acta Mathematica Scientia
基金
国家自然科学基金(61374096)~~
