Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems
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...
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| Veröffentlicht in: | Regular & chaotic dynamics 2020, Vol.25 (1), p.33-39 |
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| container_title | Regular & chaotic dynamics |
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| creator | Sachkov, Yuri L. |
| description | 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. |
| doi_str_mv | 10.1134/S1560354720010050 |
| format | Article |
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Chaot. Dyn</stitle><date>2020</date><risdate>2020</risdate><volume>25</volume><issue>1</issue><spage>33</spage><epage>39</epage><pages>33-39</pages><issn>1560-3547</issn><eissn>1560-3547</eissn><eissn>1468-4845</eissn><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.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1560354720010050</doi><tpages>7</tpages></addata></record> |
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| subjects | Dynamical Systems and Ergodic Theory Lie groups Mathematics Mathematics and Statistics Time optimal control |
| title | Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems |
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