This article is cited in 5 papers

Special issue: In honor of Valery Kozlov for his 70th birthday

Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems

Yuri L. Sachkov<sup>ab

a</sup> Department of Mathematics and Statistics, P.O. Box 35, FI-40014, University of Jyväskylä, Finland
^b Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia

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: optimal control, sub-Finsler geometry, Lie groups, Pontryagin maximum principle.

MSC: 49J15, 53C17

Received: 29.11.2019
Accepted: 11.12.2019

Language: English

DOI: 10.1134/S1560354720010050

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