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Avtomatika i Telemekhanika, 2020, Issue 12, Pages 82–99
DOI: https://doi.org/10.31857/S0005231020120053
(Mi at15616)
 

Topical issue (end)

Construction of confidence absorbing sets using statistical methods

A. I. Kibzun, S. V. Ivanov

Moscow Aviation Institute (National Research University), Moscow, Russia
Full-text PDF (254 kB) (1)
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Abstract: In this paper, the problem of constructing the confidence absorbing set is considered as follows: find the set of initial positions of a system for which at a terminal time instant a loss function will not exceed some fixed level with a given probability. The dependence of the system's state at the terminal time instant on its initial position is assumed to be a known random function. An approach to construct outer and inner approximations of the confidence absorbing set is proposed. In the first stage, deterministic inner and outer approximations are obtained. Then, these approximations are refined for a certain finite set of initial positions of the system using sample estimates. The sample size sufficient to construct the approximations is estimated. The latter estimate is improved for the case of a star-shaped loss function. An algorithm for constructing approximations of the confidence absorbing set in the two-dimensional case is developed. The resulting approximations are used in a production planning problem.
Keywords: stochastic programming, confidence absorbing set, probability function, quantile function.
Funding agency Grant number
Russian Foundation for Basic Research 18-07-00617_а
19-07-00436_а
A.I. Kibzun acknowledges the support of the Russian Foundation for Basic Research, project no. 18-07-00617 A. S.V. Ivanov acknowledges the support of the Russian Foundation for Basic Research, project no. 19-07-00436 A.
Presented by the member of Editorial Board: B. M. Miller

Received: 02.03.2020
Revised: 18.05.2020
Accepted: 09.07.2020
English version:
Automation and Remote Control, 2020, Volume 81, Issue 12, Pages 2206–2219
DOI: https://doi.org/10.1134/S000511792012005X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. I. Kibzun, S. V. Ivanov, “Construction of confidence absorbing sets using statistical methods”, Avtomat. i Telemekh., 2020, no. 12, 82–99; Autom. Remote Control, 81:12 (2020), 2206–2219
Citation in format AMSBIB
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\paper Construction of confidence absorbing sets using statistical methods
\jour Avtomat. i Telemekh.
\yr 2020
\issue 12
\pages 82--99
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\crossref{https://doi.org/10.31857/S0005231020120053}
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\transl
\jour Autom. Remote Control
\yr 2020
\vol 81
\issue 12
\pages 2206--2219
\crossref{https://doi.org/10.1134/S000511792012005X}
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  • https://www.mathnet.ru/eng/at/y2020/i12/p82
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:34
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