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 editorsArdentov, Andrei A.; Le Donne, Enrico; Sachkov, Yuri L.

Journal or seriesRegular and Chaotic Dynamics

ISSN1560-3547

eISSN1468-4845

Publication year2019

Volume24

Issue number1

Pages range36-60

PublisherPleiades Publishing

Publication countryRussian Federation

Publication languageEnglish

DOIhttps://doi.org/10.1134/S1560354719010027

Publication open accessOther 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 availablehttps://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.


Keywordscontrol theorymathematical optimisationdifferential equations

Free keywordsSub-Finsler geometry; time-optimal control; geometric control; Cartan group


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Ministry reportingYes

Reporting Year2019

JUFO rating1


Last updated on 2023-03-10 at 11:46