Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions

DOI10.1070/RM10019zbMath1502.53045OpenAlexW4214924433WikidataQ115325608 ScholiaQ115325608MaRDI QIDQ5074410

Yuri L. Sachkov

Publication date: 9 May 2022

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm10019

zbMATH Keywords

optimal controlLie groupsgeodesicscut locussub-Riemannian geometrycut timeleft-invariant sub-Riemannian structurelength minimizing

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Nilpotent and solvable Lie groups (22E25) Optimality conditions for problems involving ordinary differential equations (49K15) Sub-Riemannian geometry (53C17)

Related Items (9)

Sub-Lorentzian distance and spheres on the Heisenberg group ⋮ The sub-Riemannian geometry of screw motions with constant pitch ⋮ Some controllable and uncontrollable degenerate four-level quantum systems ⋮ Abnormal trajectories in the sub-Riemannian \((2,3,5,8)\) problem ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(SU(2)\times{ \mathbb{R} }\) and \(SO(3)\times{ \mathbb{R} }\) with three-dimensional generating distributions ⋮ Almost multiplicity free subgroups of compact Lie groups and polynomial integrability of sub-Riemannian geodesic flows ⋮ The sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(\operatorname{SU}(1,1)\times \mathbb{R}\) and \(\operatorname{SO}_0(2,1)\times \mathbb{R}\) with three-dimensional generating distributions ⋮ On controllability of a highly degenerate four-level quantum system with a ``chained coupling Hamiltonian

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