A Lower Closure Theorem for Abstract Control Problems with L(p)-Bounded Controls

被引：6

作者：

Berkovitz, L. D. ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1974年 / 14卷 / 05期

基金：

美国国家科学基金会;

关键词：

Lower closure theorems; generalized control theory; control theory; calculus of variations;

D O I：

10.1007/BF00932846

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

A lower closure theorem for an abstract control problem is proved. The functional is J(phi, u) = integral(G)f(0) (t, (M phi)(t), u(t)) dt and the state equations are N phi(t) = f(t, (M phi)(t), u(t)). It is shown that, if {(phi(k), u(k),)} is a sequence of admissible controls u(k) and corresponding trajectories phi(k) such that lim inf J(phi(k), u(k)) < + infinity and such that phi(k) -> phi weakly, M phi(k) -> M phi strongly, N phi(k) -> N phi weakly, and {u(k)} is bounded in some L(p) norm, then there is a control u such that (phi, u) is admissible and lim inf J(phi(k), u(k)) >= J(phi, u).

引用

页码：521 / 528

页数：8