Geodesic
Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set
Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 42-64.

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We consider a model nilpotent convex problem with two-dimensional control from an arbitrary convex set $\Omega$. For the case in which $\Omega$ is a polygon, the problem is solved explicitly. For the case of an arbitrary set $\Omega$, we completely describe the asymptotics of optimal trajectories and the geometric properties of the optimal synthesis.
Keywords: optimal synthesis, two-dimensional control, nilpotent convex problem. 
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     author = {L. V. Lokoutsievskiy and V. A. Mirikova},
     title = {Optimal {Synthesis} in a {Model} {Problem} with {Two-Dimensional} {Control} {Lying} in an {Arbitrary} {Convex} {Set}},
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L. V. Lokoutsievskiy; V. A. Mirikova. Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set. Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 42-64. http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a4/

[1] L. V. Lokutsievskii, “Osobye rezhimy v upravlyaemykh sistemakh s mnogomernym upravleniem iz mnogogrannika”, Izv. RAN. Ser. matem., 78:5 (2014), 167–190 | DOI | MR | Zbl

[2] L. V. Lokutsievskii, “Ob optimalnom potoke v odnom klasse nilpotentno-vypuklykh zadach”, Optimalnoe upravlenie, Tr. MIAN, 291, MAIK «Nauka/Interperiodika», M., 2015, 157–181 | DOI