Minimum time function of a non-autonomous control system

作     者：Pogodaev, Nikolay I. Voronov, Vsevolod A. 

作者机构：Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences Irkutsk Russia 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2018年第51卷第32期

页      面：704-707页

核心收录：

主　　题：Control systems Phase space methods Set theory Fast marching methods First order Minimum time Minimum time problems Non autonomous system Nonautonomous Time dependent Viscosity solutions 

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. © 2018