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Эта публикация цитируется в 11 научных статьях (всего в 11 статьях)
Sub-Finsler Geodesics on the Cartan Group
Andrei A. Ardentova, Enrico Le Donneb, Yuri L. Sachkova a Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
b Department of Mathematics and Statistics, P.O. Box 35, FI-40014, University of Jyväskylä, Finland
Аннотация:
This paper is a continuation of the work by the same authors on the
Cartan group equipped with the sub-Finsler $\ell_\infty$ norm.
We start by giving a detailed presentation of the structure of bang-bang extremal trajectories.
Then we prove upper bounds on the number of switchings 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 that every two points can be connected by a piecewise smooth
minimizer, and we give a uniform bound on the number of such pieces.
Ключевые слова:
Sub-Finsler geometry, time-optimal control, geometric control, Cartan group.
Поступила в редакцию: 24.09.2018 Принята в печать: 16.10.2018
Образец цитирования:
Andrei A. Ardentov, Enrico Le Donne, Yuri L. Sachkov, “Sub-Finsler Geodesics on the Cartan Group”, Regul. Chaotic Dyn., 24:1 (2019), 36–60
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd388 https://www.mathnet.ru/rus/rcd/v24/i1/p36
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