Strong and Weak Convexity in Nonlinear Differential Games

被引：10

作者：

Ivanov, Grigorii E. ^{[1
]}

Golubev, Maxim O. ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Dept Higher Math, 9 Inst Skiy Per, Dolgoprudnyi 141700, Moscow Region, Russia

来源：

IFAC PAPERSONLINE | 2018年 / 51卷 / 32期

基金：

俄罗斯基础研究基金会;

关键词：

Weak convexity; Minkowski operator; signed distance function; multivalued mapping; SETS;

D O I：

10.1016/j.ifacol.2018.11.345

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We obtain sufficient conditions for the values of the Minkowski operators to be weakly convex and smooth. These operators play the same role in nonlinear differential games as the Minkowski sum and the Minkowski difference do in linear differential games: they are basic operators in algorithms of computing reachable sets and optimal strategies. We also prove that the signed distance to convex sets is a Lipschitz continuous function of the set with respect to the Hausdorff distance. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

引用

页码：13 / 18

页数：6

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