TY - JOUR
T1 - COMBINED ALGORITHMS FOR CONSTRUCTING A SOLUTION TO THE TIME–OPTIMAL PROBLEM IN THREE-DIMENSIONAL SPACE BASED ON THE SELECTION OF EXTREME POINTS OF THE SCATTERING SURFACE
AU - Lebedev, Pavel D.
AU - Uspenskii, Alexander A.
N1 - This research was supported by the Russian Science Foundation (grant no. 19-11-00105, https://rscf.ru/en/project/19-11-00105/).
PY - 2022
Y1 - 2022
N2 - A class of time-optimal control problems in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve Γ is chosen as the target set. We distinguish pseudo-vertices that are characteristic points on Γ and responsible for the appearance of a singularity in the function of the optimal result. We reveal analytical relationships between pseudo-vertices and extreme points of a singular set belonging to the family of bisectors. The found analytical representation for the extreme points of the bisector is taken as the basis for numerical algorithms for constructing a singular set. The effectiveness of the developed approach for solving non-smooth dynamic problems is illustrated by an example of numerical-analytical construction of resolving structures for the time-optimal control problem. © 2022, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
AB - A class of time-optimal control problems in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve Γ is chosen as the target set. We distinguish pseudo-vertices that are characteristic points on Γ and responsible for the appearance of a singularity in the function of the optimal result. We reveal analytical relationships between pseudo-vertices and extreme points of a singular set belonging to the family of bisectors. The found analytical representation for the extreme points of the bisector is taken as the basis for numerical algorithms for constructing a singular set. The effectiveness of the developed approach for solving non-smooth dynamic problems is illustrated by an example of numerical-analytical construction of resolving structures for the time-optimal control problem. © 2022, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85144943120
UR - https://elibrary.ru/item.asp?id=50043146
U2 - 10.15826/umj.2022.2.009
DO - 10.15826/umj.2022.2.009
M3 - Article
VL - 8
SP - 115
EP - 126
JO - Ural Mathematical Journal
JF - Ural Mathematical Journal
SN - 2414-3952
IS - 2 (15)
ER -