Geodesic
On characteristic distibutions of left-invariant optimal-control systems
Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 70-81.

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We investigate abnormal extremals of left-invariant systems of optimal control on Lie groups. Examples of computations of the characteristic distribution for control problems on Lie groups with Lie algebras with the structure of free and pseudo-free products of depth 2 are analyzed. It is shown that the characteristic distribution can, in general, be multidimensional. 
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D. I. Pirshtuk. On characteristic distibutions of left-invariant optimal-control systems. Trudy Instituta matematiki, Tome 25 (2017) no. 2, pp. 70-81. http://geodesic.mathdoc.fr/item/TIMB_2017_25_2_a6/

[1] Agrachev A. A., Sachkov Yu. L., Geometricheskaya teoriya upravleniya, Fizmatlit, M., 2005

[2] Sachkov Yu. L., Sachkova E. F., “Vyrozhdennye anormalnye traektorii v subrimanovoi zadache s vektorom rosta”, Differents. uravneniya, 53:3 (2017), 362–374 | DOI | Zbl

[3] Sachkov Yu. L., “Eksponentsialnoe otobrazhenie v obobschennoi zadache Didony”, Matem. sb., 194:9 (2003), 63–90 | DOI | MR | Zbl

[4] Maikova O. E., “Mnogoobrazie osobykh ekstremalei v zadache upravleniya tyagachom s $n$ pritsepami”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2002, no. 3, 51–54 | MR

[5] Molodenkov A. V., Sapunkov Ya. G., “Osobye rezhimy upravleniya v zadache optimalnogo razvorota kosmicheskogo apparata i ikh prilozheniya”, Vestnik NNGU, 2011, no. 4–2, 237–238

[6] Montgomery R., “Abnormal Optimal Controls and Open Problems in Nonholonomic Steering”, IFAC Proceedings Volumes, 25:13 (1992), 121–126 | DOI

[7] Le Donne E., etc., “Extremals curves in nilpotent Lie groups”, Geometric and Functional Analysis, 23:4 (2009), 1371–1401 | DOI | MR

[8] Grayson M,, Grossman R., “Models for Free Nilponent Lie Algerbras”, J. Algebra, 35 (1988), 177–191 | MR

[9] Anzaldo-Meneses A., Monroy-Perez F., “Charges in magnetic fields and sub-Riemannian geodesics”, Contemporary Trends In Nonlinear Geometric Control Theory And Its Applications, 2002, 183–202 | DOI | MR | Zbl

[10] Doubrov B., Zelenko I., “On local geometry of non-holonomic rank 2 distributions”, Journal of the London Mathematical Society, 80:3 (2009), 545–566 | DOI | MR | Zbl

[11] Gauthier J.-P., Sachkov Yu.L., “On the free Carnot (2, 3, 5, 8) group”, Program systems: theory and applications, 6:2 (2015), 45–61 | DOI | MR

[12] Burbaki N., Algebra. Chast 1. Algebraicheskie struktury. Lineinaya i polilineinaya algebra, GIFML, M., 1962

[13] Khamfris Dzh., Vvedenie v teoriyu algebr Li i ikh predstavlenii, MTsNMO, M., 2003

[14] Dynkin E. B., “Struktura poluprostykh algebr Li”, UMN, 2:4 (1947), 59–127 | MR

[15] Tits J., “Sur les constantes de structure et le theoreme d'existence des algebres de Lie semi-simples”, Publications Mathematiques de l'IHES, 31 (1966), 21–58 | DOI | MR