论文标题
最小时间和签名最小时间函数的凸分析
Convex Analysis of Minimal Time and Signed Minimal Time Functions
论文作者
论文摘要
在本文中，我们首先考虑在局部凸拓扑矢量（LCTV）空间的一般环境中的最小时间函数类别。在此框架中获得的结果基于目标集相对于恒定动力学的新型封闭性概念。然后，我们介绍并研究了一类新的签名最小时间函数，这是签名距离函数的概括。在给定数据的凸度假设下，获得了签名最小时间和距离函数的细分公式。
In this paper we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of closedness of target sets with respect to constant dynamics. Then we introduce and investigate a new class of signed minimal time functions, which are generalizations of the signed distance functions. Subdifferential formulas for the signed minimal time and distance functions are obtained under the convexity assumptions on the given data.
