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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 569–575 (Mi nd684)  

Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems

A. V. Podobryaev

Ailamazyan Program Systems Institute of RAS, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia

Abstract: 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

Funding Agency Grant Number
Russian Science Foundation 17-11-01387
This work was supported by the Russian Science Foundation under grant 17-11-01387 and performed at the A.K.Ailamazyan Program Systems Institute of the Russian Academy of Sciences.


DOI: https://doi.org/10.20537/nd190416

Full text: PDF file (257 kB)
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MSC: 49J15, 53C17
Received: 28.05.2019
Accepted:09.09.2019

Citation: A. V. Podobryaev, “Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems”, Nelin. Dinam., 15:4 (2019), 569–575

Citation in format AMSBIB
\Bibitem{Pod19}
\by A. V. Podobryaev
\paper Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 569--575
\mathnet{http://mi.mathnet.ru/nd684}
\crossref{https://doi.org/10.20537/nd190416}


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