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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 315, Pages 202–210
DOI: https://doi.org/10.4213/tm4223
(Mi tm4223)
 

Construction of Maxwell Points in Left-Invariant Optimal Control Problems

A. V. Podobryaev

Ailamazyan Program Systems Institute of Russian Academy of Sciences
References:
Abstract: We consider left-invariant optimal control problems on connected Lie groups. The Pontryagin maximum principle gives necessary optimality conditions. Namely, the extremal trajectories are the projections of trajectories of the corresponding Hamiltonian system on the cotangent bundle of the Lie group. The Maxwell points (i.e., the points where two different extremal trajectories meet each other) play a key role in the study of optimality of extremal trajectories. The reason is that an extremal trajectory cannot be optimal after a Maxwell point. We introduce a general construction for Maxwell points depending on the algebraic structure of the Lie group.
Keywords: Symmetry, Maxwell points, cut locus, geometric control theory, Riemannian geometry, sub-Riemannian geometry.
Funding agency Grant number
Russian Science Foundation 17-11-01387-П
This work is supported by the Russian Science Foundation under grant 17-11-01387-P.
Received: December 2, 2020
Revised: March 26, 2021
Accepted: June 29, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 315, Pages 190–197
DOI: https://doi.org/10.1134/S008154382105014X
Bibliographic databases:
Document Type: Article
UDC: 517.977+514.765
Language: Russian
Citation: A. V. Podobryaev, “Construction of Maxwell Points in Left-Invariant Optimal Control Problems”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 202–210; Proc. Steklov Inst. Math., 315 (2021), 190–197
Citation in format AMSBIB
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\by A.~V.~Podobryaev
\paper Construction of Maxwell Points in Left-Invariant Optimal Control Problems
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 202--210
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4223}
\crossref{https://doi.org/10.4213/tm4223}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 190--197
\crossref{https://doi.org/10.1134/S008154382105014X}
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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