Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set
L. V. Lokoutsievskiya, V. A. Mirikovab
a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b OOO ``Execution RDC,'' Moscow, 129164 Russia
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.
optimal synthesis, two-dimensional control, nilpotent convex problem.
|Russian Science Foundation
|Russian Foundation for Basic Research
|The work of the first author was supported
by the Russian Science Foundation
under grant 14-50-00005.
It was carried out at Steklov Mathematical Institute of Russian Academy of Sciences.
This author wrote Secs. 1, 2, 3.1, and 5.1.
The work of the second author was supported
by the Russian Foundation for Basic Research
under grant 17-01-00805.
It was carried out at the Department of Mechanics and Mathematics
of Lomonosov Moscow State University.
That author wrote Secs. 3.2, 4.1, 4.2, and 5.2.
Author to whom correspondence should be addressed
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Mathematical Notes, 2019, 105:1, 36–55
L. V. Lokoutsievskiy, V. A. Mirikova, “Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set”, Mat. Zametki, 105:1 (2019), 42–64; Math. Notes, 105:1 (2019), 36–55
Citation in format AMSBIB
\by L.~V.~Lokoutsievskiy, V.~A.~Mirikova
\paper Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set
\jour Mat. Zametki
\jour Math. Notes
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