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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 1, Pages 147–158
(Mi timm211)
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The Galilei group in an optimal control problem
I. V. Koz'min Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
In the paper, results of studying an optimal control problem for the motion of a material point under control
constraints are presented. The invariance of this problem with respect to the extended Galilei group is used.
From the viewpoint of calculations, the symmetry allows us to construct a family of solutions through an
extremal determined numerically. From the analytical viewpoint, the symmetry gives an opportunity to reduce
system's dimension and to investigate properties of extremals.
Keywords:
controlled mechanical systems, symmetries.
Received: 22.12.2008
Citation:
I. V. Koz'min, “The Galilei group in an optimal control problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 147–158; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S162–S173
Linking options:
https://www.mathnet.ru/eng/timm211 https://www.mathnet.ru/eng/timm/v15/i1/p147
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Abstract page: | 202 | Full-text PDF : | 82 | References: | 31 | First page: | 1 |
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