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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2020, Volume 23, Number 4, Pages 365–380
DOI: https://doi.org/10.15372/SJNM20200402 (Mi sjvm754) 		 
Construction of reachable sets of controlled systems with second order of accuracy with respect to time step

A. A. Ershovab

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 Russia
b El’tsin Ural Federal University, Yekaterinburg, Russia
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DOI: https://doi.org/10.15372/SJNM20200402
Abstract: The paper investigates the pixel method for constructing reachable sets of a dynamic controlled system. Sufficient conditions for a control system have been obtained under which the explicit second order Runge–Kutta method (a modified Euler method) provides the second order of accuracy with respect to a time step in constructing reachable sets, even if discontinuous functions are in the class of admissible controls.
Key words: modified Euler method, second-order Runge–Kutta method, control system, reachable set, switching of control.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Russian Foundation for Basic Research 18-01-00221_à
This work was supported by RFBR (project no. 18-01-00221) and by RF Ministry of Education and Science (Government Decree no. 211, contract no. 02.A03.21.0006).
Received: 15.09.2018
Revised: 17.06.2019
Accepted: 16.07.2020
English version:
Numerical Analysis and Applications, 2020, Volume 13, Issue 4, Pages 306–320
DOI: https://doi.org/10.1134/S1995423920040023
Bibliographic databases:
Document Type: Article
UDC: 517.977.58
Language: Russian
Citation: A. A. Ershov, “Construction of reachable sets of controlled systems with second order of accuracy with respect to time step”, Sib. Zh. Vychisl. Mat., 23:4 (2020), 365–380; Num. Anal. Appl., 13:4 (2020), 306–320
Citation in format AMSBIB
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\paper Construction of reachable sets of controlled systems with second order of
accuracy with respect to time step
\jour Sib. Zh. Vychisl. Mat.
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\vol 23
\issue 4
\pages 365--380
\mathnet{http://mi.mathnet.ru/sjvm754}
\crossref{https://doi.org/10.15372/SJNM20200402}
\transl
\jour Num. Anal. Appl.
\yr 2020
\vol 13
\issue 4
\pages 306--320
\crossref{https://doi.org/10.1134/S1995423920040023}
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