Minimum time function of a non-autonomous control system

被引：0
|
作者：
Pogodaev, Nikolay I. [1 ]
Voronov, Vsevolod A. [1 ]
机构：
[1] Russian Acad Sci, Siberian Branch, Matrosov Inst Syst Dynam & Control Theory, Irkutsk, 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：
Minimum time function; Non-autonomous system; Fast Marching Method; First order PDE; REGULARITY; BOUNDARY;
D O I：
10.1016/j.ifacol.2018.11.508
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
For a time-dependent control system we consider a "reversed" minimum time problem, which consists in finding the minimum time needed by the system, whose state is initially located in a given set, to reach a given point. We show that the minimum time function constructed in this way is a unique viscosity solution of a static first order PDE, provided that, at every point of the extended phase space, admissible velocities form a convex set containing zero in the interior. We also describe a version of the Fast Marching Method (FMM) that effectively solves this PDE. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
引用
收藏
页码：704 / 707
页数：4
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