半线性热系统的有限维非敏控制  

Finite dimensional non-sensitive control mehtod for the semilinear heat systems

作　　者：颜于清[1] 张素红[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310023

出　　处：《浙江工业大学学报》2010年第1期75-78,共4页Journal of Zhejiang University of Technology

基　　金：博士科研启动基金资助项目(109010629)

摘　　要：研究了有限区域上初始条件只是部分已知的半线性热系统,且其未知初值属于L2(Ω)上的有限维子空间.所谓有限维非敏控制问题,即找一控制函数,使得指定状态变量的泛函是非灵敏依赖于初始值扰动的.并证明了有限维非敏控制问题等价于相应耦合系统的有限维精确能控性问题.最后通过构造极小泛函的方法找到线性系统的非敏控制以及利用不动点方法证明了非线性项满足全局Lipshitz条件的半线性热系统是满足有限维非敏能控的.并且此结果对于初始值来说是全局的.The semilinear heat system with partially known initial conditions is studied in this paper. The unknown initial data belongs to a finite dimensional subspace of L^2 （Ω）. The finite dimensional insensitizing control problem is a kind of issue to find a control function, in which the functional of specified state variable is non-sensitive dependent on the initial value of disturbances. It is proved that finite-dimensional non-sensitive control problem is equivalent to finite-dimensional exact controllable problem in the corresponding coupled system. The non-sensitive control method in linear system is found through constructing minimum functional. Then it is proved by fixed point theorem that the semilinear heat system with nonlinear item satisfying global Lipshitz condition is finite-dimensional insensitizing controllable. This result is global for initial value.

关 键 词：有限维非敏控制 半线性热系统 不动点定理 

分 类 号：O231.2[理学—运筹学与控制论]