Banach空间中无限维线性系统的能控性  

Controllability of Infinite Dimensional Linear Systems in Banach Spaces

作　　者：于欣[1] 刘康生[2] 陈彭年[3] 

机构地区：[1]浙江大学宁波理工学院信息与优化技术研究所,浙江宁波315100 [2]浙江大学数学系,杭州310027 [3]中国计量学院数学系,杭州310034

出　　处：《数学年刊（A辑）》2007年第5期589-600,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10501039和No.10571161);宁波博士(青年)基金(No.2005A610005);宁波理工学院院基金(No.1141157G501)资助的项目

摘　　要：研究在非自反状态空间和自反控制空间中无限维线性系统x(t)=Ax(t)+Bu(t)的精确能控性和精确零能控性.当A生成C-半群时,得到这个系统关于L^p([O,T],U),1<p≤∞精确能控和精确零能控的等价判据.当A生成C_o-半群时,也得到系统关于L ~p([O,T],U),1<p≤∞的精确零能控的充要条件.这些结论是对经典控制理论的有益发展和补充,还给出所得抽象结论的两个应用.In this paper, exact controllability and exact null controllability of infinite dimensional linear systems are considered in non-reflexive state space and reflexive control space. For the systems governed by C-semigroups, the criteria for exact controllability and exact null controllability via controls in L^P（[0, T], U）, 1 〈 p ≤∞ are obtained. For the systems governed by C0-semigroups, the authors also get a necessary and sufficient condition for exact null controllability via controls in LP（[0, T], U）, 1 〈 p ≤∞. Two applications are given to illustrate the abstract results.

关 键 词：精确能控性 精确零能控 自反空间 CO-半群 C-半群 

分 类 号：O177[理学—数学] O231[理学—基础数学]