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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Special issue: In honor of Valery Kozlov for his 70th birthday
Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems
Yuri L. Sachkovab a 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
Аннотация:
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.
Ключевые слова:
optimal control, sub-Finsler geometry, Lie groups, Pontryagin maximum principle.
Поступила в редакцию: 29.11.2019 Принята в печать: 11.12.2019
Образец цитирования:
Yuri L. Sachkov, “Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems”, Regul. Chaotic Dyn., 25:1 (2020), 33–39
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1048 https://www.mathnet.ru/rus/rcd/v25/i1/p33
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Страница аннотации: | 186 | Список литературы: | 46 |
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