A1 Journal article (refereed)
Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems (2020)

Sachkov, Y. L. (2020). Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems. Regular and Chaotic Dynamics, 25(1), 33-39. https://doi.org/10.1134/S1560354720010050

JYU authors or editors

Publication details

All authors or editors: Sachkov, Yuri L.

Journal or series: Regular and Chaotic Dynamics

ISSN: 1560-3547

eISSN: 1468-4845

Publication year: 2020

Volume: 25

Issue number: 1

Pages range: 33-39

Publisher: Pleiades Publishing

Publication country: Russian Federation

Publication language: English

DOI: https://doi.org/10.1134/S1560354720010050

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67952

Publication is parallel published: https://arxiv.org/abs/1910.04740

Abstract

We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with a strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all Casimirs linear in momenta on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation on the dual of the Lie algebra. On this basis we show that extremal controls are either constant or periodic. Some related results for other Carnot groups are presented.

Keywords: calculus of variations; control theory; mathematical optimisation; differential geometry

Free keywords: optimal control; sub-Finsler geometry; Lie groups; Pontryagin maximum principle

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Related projects

Ministry reporting: Yes

VIRTA submission year: 2020

JUFO rating: 1