Название: Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems
Авторы: A. V. Podobryaev
Журнал: Russian Journal of Nonlinear Dynamics
Год: 2019
Номер: 4
Том: 15
Страницы: 569–575
Образец цитирования:
A. V. Podobryaev, “Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems”, Russian Journal of Nonlinear Dynamics, 15:4 (2019), 569–575
Аннотация:
We consider left-invariant optimal control problems on connected Lie groups. We describe the symmetries of the exponential map that are induced by the symmetries of the vertical part of the Hamiltonian system of the Pontryagin maximum principle. These symmetries play a key role in investigation of optimality of extremal trajectories. For connected Lie groups such that the generic coadjoint orbit has codimension not more than 1 and a connected stabilizer we introduce a general construction for such symmetries of the exponential map.