Control systems on nilpotent Lie groups of dimension ≤ 4: Equivalence and classification

被引：4

作者：

Bartlett, Catherine E. ^{[1
]}

Biggs, Rory ^{[2
]}

Remsing, Claudiu C. ^{[1
]}

机构：

[1] Rhodes Univ, Dept Math, ZA-6140 Grahamstown, South Africa

[2] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2017年 / 54卷

基金：

新加坡国家研究基金会;

关键词：

Control system; Sub-Riemannian structure; Nilpotent Lie group; CARNOT-CARATHEODORY METRICS; SUB-RIEMANNIAN STRUCTURES; HOMOGENEOUS NILMANIFOLDS; ISOMETRIES; SPACES;

D O I：

10.1016/j.difgeo.2017.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Left-invariant control affine systems on simply connected nilpotent Lie groups of dimension <= 4 are considered. First, we classify these control systems under two natural equivalence relations. Second, the associated cost-extended systems (with invariant quadratic Lagrangian) are classified. The latter classification is reinterpreted in terms of invariant affine distributions equipped with quadratic cost; also, we obtain a classification of the invariant sub-Riemannian (and Riemannian) structures. A few remarks conclude the paper. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：282 / 297

页数：16

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