Sub-Finsler structures on the Engel group | Zendy

A. A. Ardentov | Zendy; Yu. L. Sachkov | Zendy

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Sub-Finsler structures on the Engel group

Author(s) -

A. A. Ardentov,

Yu. L. Sachkov

Publication year - 2019

Publication title -

доклады академии наук

Language(s) - English

Resource type - Journals

ISSN - 0869-5652

DOI - 10.31857/s0869-56524854395-398

Subject(s) - mathematics , invariant (physics) , lie group , group (periodic table) , boundary (topology) , distribution (mathematics) , mathematical analysis , pure mathematics , nilpotent , flow (mathematics) , geometry , physics , mathematical physics , quantum mechanics

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.

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