Closure, Lower Closure, and Semicontinuity Theorems in Optimal Control
作者
Lamberto Cesari
出处
期刊:SIAM journal on control [Society for Industrial and Applied Mathematics] 日期:1971-05-01卷期号:9 (2): 287-315被引量:35
标识
DOI:10.1137/0309022
摘要
First we discuss in detail the concept of lower closure for Lagrange problems, and we extend in various ways previous closure and lower closure theorems. In particular, we show that the present lower closure theorems and related concepts are extensions to Lagrange problems of optimal control of well-known semicontinuity theorems for free problems of the calculus of variations and the related concept of seminormality. Finally, we prove by a new approach that the convexity condition usually requested in lower closure theorems is, in a suitable sense, both a necessary and sufficient condition for lower closure.