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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 215–222
DOI: https://doi.org/10.4213/tm4341 (Mi tm4341) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Extremal Trajectories in a Time-Optimal Problem on the Group of Motions of a Plane with Admissible Control in a Circular Sector

Alexey P. Mashtakov, Yuri L. Sachkov

Ailamazyan Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, 152021 Russia
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DOI: https://doi.org/10.4213/tm4341
Abstract: We consider a time-optimal problem for a car model that can move forward on a plane and turn with a given minimum turning radius. Trajectories of this system are applicable in image processing for the detection of salient lines. We prove the controllability and existence of optimal trajectories. Applying the necessary optimality condition given by the Pontryagin maximum principle, we derive a Hamiltonian system for the extremals. We provide qualitative analysis of the Hamiltonian system and obtain explicit expressions for the extremal controls and trajectories.
Keywords: geometric control, model of a car, extremal trajectories, Pontryagin maximum principle, group of motions of a plane.
Funding agency Grant number
Russian Science Foundation 22-21-00877
The work of the first author (Sections 1, 4, 5) was supported by the Russian Science Foundation under grant no. 22-21-00877, https://rscf.ru/en/project/22-21-00877/.
Received: March 6, 2023
Revised: April 12, 2023
Accepted: April 19, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 200–207
DOI: https://doi.org/10.1134/S0081543823020141
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: Alexey P. Mashtakov, Yuri L. Sachkov, “Extremal Trajectories in a Time-Optimal Problem on the Group of Motions of a Plane with Admissible Control in a Circular Sector”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 215–222; Proc. Steklov Inst. Math., 321 (2023), 200–207
Citation in format AMSBIB
\Bibitem{MasSac23}
\by Alexey~P.~Mashtakov, Yuri~L.~Sachkov
\paper Extremal Trajectories in a Time-Optimal Problem on the Group of Motions of a Plane with Admissible Control in a Circular Sector
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 215--222
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4341}
\crossref{https://doi.org/10.4213/tm4341}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 200--207
\crossref{https://doi.org/10.1134/S0081543823020141}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85171189785}
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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