Linear quadratic problem with unbounded control in Hilbert spaces

被引：3
|
作者：
Wu, HZ [1 ]
Li, XJ [1 ]
机构：
[1] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China
来源：
CHINESE SCIENCE BULLETIN | 1998年 / 43卷 / 20期
基金：
中国国家自然科学基金;
关键词：
LQ problem; unbounded control; two-point boundary value problem; Fredholm integral equation; Riccati integral equation;
D O I：
10.1007/BF02883971
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
A finite horizon linear quadratic optimal control problem in Hilbert space is considered, in which the controls are unbounded and the state weight operators are allowed to be indefinite and not necessarily smoothing. It is proved that any optimal control and optimal trajectory are continuous. The closed-loop synthesis for optimal control is given via the solution to Fredholm integral equation and also the solution to Riccati integral equation, which exists under some mild conditions.
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页码：1712 / 1717
页数：6
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