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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 291, Pages 276–291
DOI: https://doi.org/10.1134/S0371968515040214 (Mi tm3681) 		 
This article is cited in 17 scientific papers (total in 17 papers)

On solving approach problems for control systems

V. N. Ushakovab, V. I. Ukhobotovc, A. V. Ushakova, G. V. Parshikova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg, Russia
c Chelyabinsk State University, Chelyabinsk, Russia
Full-text PDF (984 kB) Citations (17)
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DOI: https://doi.org/10.1134/S0371968515040214
Abstract: We study the problem of making a control system in a finite-dimensional Euclidean space approach a compact set at a fixed instant of time. The technique presented in the paper for solving the approach problem is based on constructions involving solvability sets. To construct approximately the solvability set, we apply a backward (in time) procedure that involves storing controls selected during the construction of this set. We also give examples of simulation of approach problems for mechanical systems.
Funding agency Grant number
Russian Science Foundation 15-11-10018
Ministry of Education and Science of the Russian Federation 02.А03.21.0006
The research presented in Sections 1 and 2 was supported by the Russian Science Foundation under grant 15-11-10018. The research presented in Section 3 was supported by the Ministry of Education and Science of the Russian Federation within the Program for State Support of Leading Universities (contract 02.A03.21.0006 of August 27, 2013).
Received: August 15, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 291, Pages 263–278
DOI: https://doi.org/10.1134/S0081543815080210
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. N. Ushakov, V. I. Ukhobotov, A. V. Ushakov, G. V. Parshikov, “On solving approach problems for control systems”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 276–291; Proc. Steklov Inst. Math., 291 (2015), 263–278
Citation in format AMSBIB
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\paper On solving approach problems for control systems
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 276--291
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 17 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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