Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems

2019, Vol. 15, no. 4, pp. 569-575

Author(s): Podobryaev A.

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.

Keywords: symmetry, geometric control theory, Riemannian geometry, sub-Riemannian geometry

Citation: Podobryaev A., Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp. 569-575

DOI:10.20537/nd190416

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Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems

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