A1 Journal article (refereed)
Sub-Finsler Geodesics on the Cartan Group (2019)
Ardentov, A. A., Le Donne, E., & Sachkov, Y. L. (2019). Sub-Finsler Geodesics on the Cartan Group. Regular and Chaotic Dynamics, 24(1), 36-60. https://doi.org/10.1134/S1560354719010027
JYU authors or editors
Publication details
All authors or editors: Ardentov, Andrei A.; Le Donne, Enrico; Sachkov, Yuri L.
Journal or series: Regular and Chaotic Dynamics
ISSN: 1560-3547
eISSN: 1468-4845
Publication year: 2019
Volume: 24
Issue number: 1
Pages range: 36-60
Publisher: Pleiades Publishing
Publication country: Russian Federation
Publication language: English
DOI: https://doi.org/10.1134/S1560354719010027
Publication open access: Other way freely accessible online
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/63287
Web address where publication is available: https://arxiv.org/abs/1810.05431
Abstract
This paper is a continuation of the work by the same authors on the Cartan groupequipped with the sub-Finsler∞norm. We start by giving a detailed presentation of thestructure of bang-bang extremal trajectories. Then we prove upper bounds on the number ofswitchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang,or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove thatevery two points can be connected by a piecewise smooth minimizer, and we give a uniformbound on the number of such pieces.
Keywords: control theory; mathematical optimisation; differential equations
Free keywords: Sub-Finsler geometry; time-optimal control; geometric control; Cartan group
Contributing organizations
Related projects
- Geometry of subRiemannian groups: regularity of finite-perimeter sets, geodesics, spheres, and isometries with applications and generalizations to biLipschitz homogenous spaces
- Le Donne, Enrico
- Research Council of Finland
- GeoMeG Geometry of Metric groups
- Le Donne, Enrico
- European Commission
Ministry reporting: Yes
Reporting Year: 2019
JUFO rating: 1