Sub-Finsler Structures on the Engel Group
- Authors: Sachkov Y.L.1, Ardentov A.A.1
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Affiliations:
- Ailamazyan Program Systems Institute, Russian Academy of Sciences
- Issue: Vol 99, No 2 (2019)
- Pages: 171-174
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225651
- DOI: https://doi.org/10.1134/S1064562419020224
- ID: 225651
Cite item
Abstract
A one-parameter family of left-invariant sub-Finsler problems on a four-dimensional nilpotent Lie group of depth 3 with two generators is considered. The indicatrix of sub-Finsler structures is a square rotated by an arbitrary angle in the distribution. Methods of optimal control theory are applied. Abnormal and singular normal trajectories are described, and their optimality is proved. Singular trajectories arriving at the boundary of the reachable set in fixed time are characterized. A bang-bang phase flow is constructed, and estimates for the number of switchings on bang-bang trajectories are obtained. The structure of all normal extremals is described. Mixed trajectories are studied.
About the authors
Yu. L. Sachkov
Ailamazyan Program Systems Institute, Russian Academyof Sciences
Author for correspondence.
Email: yusachkov@gmail.com
Russian Federation, Pereslavl-Zalessky, Yaroslavl oblast, 152020
A. A. Ardentov
Ailamazyan Program Systems Institute, Russian Academyof Sciences
Author for correspondence.
Email: aaa@pereslavl.ru
Russian Federation, Pereslavl-Zalessky, Yaroslavl oblast, 152020