An Infinite Horizon Linear Quadratic Problem with Unbounded Controls in Hilbert Space

作     者：Han Zhong WU Xun Jing LI Department of Mathematics,Fudan University,Shanghai 200433,P.R.China E-mail:hzwu@*** xjli@*** 

作者机构：Department of Mathematics Fudan University Shanghai 200433 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2001年第17卷第3期

页      面：527-540页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work is partially supported by the National Key Project of China the National Nature Science Foundation of China No.19901030 NSF of the Chinese State Education Ministry and Lab.of Math.for Nonlinear Sciences at Fudan University 

主　　题：Infinite horizon LQ problem Unbounded control Two-point boundary value problem Algebraic Riccati equation Frequency characteristic 

摘      要：An infinite horizon linear quadratic optimal control problem for analytic semigroup with unbounded control in Hilbert space is *** state weight operator is allowed to be inddefinite while the control weight operator is *** the exponential stabilization condition,it is proved that any optimal control and its optimal trajectory are *** positive real lemma as a necessary and sufficient condition for the unique solvability of this problem is *** closed-loop synthesis of optimal control is given via the solution to the algebraic Riccati equation.