ABNORMAL EXTREMALS OF LEFT-INVARIANT SUB-FINSLER QUASIMETRICS ON FOUR-DIMENSIONAL LIE GROUPS WITH THREE-DIMENSIONAL GENERATING DISTRIBUTIONS

被引：4

作者：

Berestovskii, V. N. ^{[1
]}

Zubareva, I. A. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2022年 / 63卷 / 04期

关键词：

extremal; left-invariant sub-Finsler quasimetric; Lie algebra; optimal control; polar; Pontryagin maximum principle; (strictly) abnormal extremal; time-optimal control problem; CURVATURES;

D O I：

10.1134/S0037446622040036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find the three-dimensional subspaces of four-dimensional Lie algebras which generate the algebras, as well as abnormal extremals on the connected Lie groups determined by these algebras and endowed with the left-invariant sub-Finsler quasimetrics defined by seminorms on the subspaces. Using the structure constants of Lie algebras and dual seminorms, we establish a criterion for the strict abnormality of the extremals.

引用

页码：620 / 636

页数：17

共 14 条

[1] Sub-Riemannian structures on 3D lie groups
Agrachev, A.
Barilari, D.
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2012, 18 (01) : 21 - 44
[2] Agrachev AA., 2004, CONTROL THEORY GEOME, DOI [10.1007/978-3-662-06404-7, DOI 10.1007/978-3-662-06404-7]
[3] ABNORMAL EXTREMALS OF LEFT-INVARIANT SUB-FINSLER QUASIMETRICS ON FOUR-DIMENSIONAL LIE GROUPS
Berestovskii, V. N.
Zubareva, I. A.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2021, 62 (03) : 383 - 399
[4] Curvatures of homogeneous sub-Riemannian manifolds
Berestovskii V.N.
[J]. European Journal of Mathematics, 2017, 3 (4) : 788 - 807
[5] [Берестовский Валерий Николаевич Berestovskii Valerii Nikolaevich], 2020, [Чебышевский сборник, Chebyshevskii sbornik], V21, P43
[6] BERESTOVSKII VN, 1988, SIBERIAN MATH J+, V29, P887
[7] Berestovskii VN., 1989, SOVIET MATH DOKL, V38, P60
[8] Biggs R, 2016, J LIE THEORY, V26, P1001
[9] Liu W., 1995, MEM AM MATH SOC, V564
[10] CURVATURES OF LEFT INVARIANT METRICS ON LIE GROUPS
MILNOR, J
[J]. ADVANCES IN MATHEMATICS, 1976, 21 (03) : 293 - 329

← 1 2 →