Banach空间中无限维线性系统的能控性

Controllability of Infinite Dimensional Linear Systems in Banach Spaces

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.