Avtomatika i Telemekhanika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Avtomat. i Telemekh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Avtomatika i Telemekhanika, 2022, Issue 11, Pages 3–61
DOI: https://doi.org/10.31857/S0005231022110010 (Mi at15860) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Surveys

Singularly perturbed problems with multi-tempo fast variables

G. A. Kurinaab, M. A. Kalashnikovac

a Federal Research Center “Informatics and Control,” Russian Academy of Sciences, Moscow, 119333 Russia
b Voronezh State University, Voronezh, 394018 Russia
c Atos IT Solutions and Services, Voronezh, 394026 Russia
Full-text PDF (498 kB) First page Citations (12)
References:
PDF
HTML
DOI: https://doi.org/10.31857/S0005231022110010
Abstract: The article contains a survey of publications studying problems characterized by the presence of fast variables with various rates of change (time scales). We consider the passage to the limit from the solution of a perturbed problem to the solution of a degenerate one, asymptotic solutions of initial and boundary value problems, stability and controllability, asymptotic solutions of optimal control problems, and problems with “hidden” multi-tempo variables. In addition, problems with control constraints, game problems, and stochastic systems are given. The last section presents practical problems with multi-tempo fast motions.
Keywords: singular perturbation, multi-tempo fast variables, asymptotic expansion, control problem.
Funding agency Grant number
Russian Science Foundation 21-11-00202
The work of the first author was financially supported by the Russian Science Foundation, project no. 21-11-00202.
Presented by the member of Editorial Board: N. Kuznetsov

Received: 12.12.2021
Revised: 25.05.2022
Accepted: 28.07.2022
English version:
Automation and Remote Control, 2022, Volume 83, Issue 11, Pages 1679–1723
DOI: https://doi.org/10.1134/S00051179220110017
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. A. Kurina, M. A. Kalashnikova, “Singularly perturbed problems with multi-tempo fast variables”, Avtomat. i Telemekh., 2022, no. 11, 3–61; Autom. Remote Control, 83:11 (2022), 1679–1723
Citation in format AMSBIB
\Bibitem{KurKal22}
\by G.~A.~Kurina, M.~A.~Kalashnikova
\paper Singularly perturbed problems with multi-tempo fast variables
\jour Avtomat. i Telemekh.
\yr 2022
\issue 11
\pages 3--61
\mathnet{http://mi.mathnet.ru/at15860}
\crossref{https://doi.org/10.31857/S0005231022110010}
\edn{https://elibrary.ru/KDWMLX}
\transl
\jour Autom. Remote Control
\yr 2022
\vol 83
\issue 11
\pages 1679--1723
\crossref{https://doi.org/10.1134/S00051179220110017}
Linking options:
  • https://www.mathnet.ru/eng/at15860
  • https://www.mathnet.ru/eng/at/y2022/i11/p3
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Avtomatika i Telemekhanika
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025