Email this article Sub-Finsler structures on the Engel group
- Authors: Ardentov A.A.1, Sachkov Y.L.1
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Affiliations:
- Ailamazyan Program Systems Institute of the Russian Academy of Sciences
- Issue: Vol 485, No 4 (2019)
- Pages: 395-398
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/13538
- DOI: https://doi.org/10.31857/S0869-56524854395-398
- ID: 13538
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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
A. A. Ardentov
Ailamazyan Program Systems Institute of the Russian Academy of Sciences
Author for correspondence.
Email: aaa@pereslavl.ru
Russian Federation, 4а, Petra Pervogo street, Veskovo, Pereslavskiy district, Yaroslavskaja region, 152020
Yu. L. Sachkov
Ailamazyan Program Systems Institute of the Russian Academy of Sciences
Email: yusachkov@gmail.com
Russian Federation, 4а, Petra Pervogo street, Veskovo, Pereslavskiy district, Yaroslavskaja region, 152020
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