Open AccessOn the structure of the singular set of solutions in one class of 3D time-optimal control problems
Author(s) -
А. А. Успенский,
П. Д. Лебедев
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210309
Subject(s) - singularity , mathematics , class (philosophy) , vertex (graph theory) , set (abstract data type) , optimal control , representation (politics) , extreme point , function (biology) , mathematical analysis , mathematical optimization , combinatorics , computer science , graph , artificial intelligence , evolutionary biology , politics , political science , law , biology , programming language
A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.