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
Citation:
Sachkov Y. L., Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems, Regular and Chaotic Dynamics,
2020, Volume 25, Number 1,
pp. 33-39