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Mat. Zametki, 2019, Volume 105, Issue 1, Pages 42–64 (Mi mz11888)  

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

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
Russian Foundation for Basic Research 17-01-00805
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.

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DOI: https://doi.org/10.4213/mzm11888

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English version:
Mathematical Notes, 2019, 105:1, 36–55

Bibliographic databases:

UDC: 517.977
Received: 12.12.2017

Citation: 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
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\paper Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set
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\vol 105
\issue 1
\pages 42--64
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