Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems
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
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Regular and Chaotic DynamicsDate
2020Copyright
© Pleiades Publishing, Ltd., 2020.
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.
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Sections 1–3 of this work were supported by the Academy of Finland (grant 277923) and by the European Research Council (ERC Starting Grant 713998 GeoMeG). Sections 4–6 of this work were supported by the Russian Science Foundation under grant 17-11-01387 and performed at the Ailamazyan Program Systems Institute of Russian Academy of Sciences.License
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