Geodesic
Symmetries in left-invariant optimal control problems
Sbornik. Mathematics, Tome 211 (2020) no. 2, pp. 275-290 Cet article a éte moissonné depuis la source Math-Net.Ru

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Left-invariant optimal control problems on Lie groups are considered. When studying the optimality of extreme trajectories, the crucial role is played by symmetries of the exponential map that are induced by symmetries of the conjugate subsystem of the Hamiltonian system of the Pontryagin maximum principle. A general construction is obtained for these symmetries of the exponential map for connected Lie groups with generic coadjoint orbits of codimension not exceeding one and with a connected stabilizer. Bibliography: 32 titles.
Keywords: symmetry, geometric control theory, Riemannian geometry, sub-Riemannian geometry. 
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A. V. Podobryaev. Symmetries in left-invariant optimal control problems. Sbornik. Mathematics, Tome 211 (2020) no. 2, pp. 275-290. http://geodesic.mathdoc.fr/item/SM_2020_211_2_a4/

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