Geodesic
The Galilei group in an optimal control problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 147-158

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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. 
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     author = {I. V. Koz'min},
     title = {The {Galilei} group in an optimal control problem},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {147--158},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a11/}
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I. V. Koz'min. The Galilei group in an optimal control problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 147-158. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a11/