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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
References:
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:
    1. A. S. Kirsanova, “Relaksatsionnye kolebaniya v modeli vetroenergeticheskoi ustanovki Dare”, Vestn. SamU. Estestvennonauchn. ser., 30:1 (2024), 31–39  mathnet  crossref
    2. O. B. Tsekhan, “Kompozitnyi nablyudatel lineinoi nestatsionarnoi singulyarno vozmuschennoi sistemy s kvazidifferentsiruemymi koeffitsientami”, Avtomat. i telemekh., 2024, no. 4, 31–54  mathnet  crossref
    3. O. B. Tsekhan, “Composite Observer of a Linear Time-Varying Singularly Perturbed System with Quasidifferentiable Coefficients”, ARC, 85:4 (2024), 373  crossref
    4. A. I. Kalinin, L. I. Lavrinovich, “Asymptotic method for solving the problem of transition process optimization in a three-tempo singularly perturbed system”, Dokl. Akad. nauk, 68:3 (2024), 183  crossref
    5. O. B. Tsekhan, “Composite Observer of a Linear Time-Varying Singularly Perturbed System with Quasidifferentiable Coefficients”, Autom Remote Control, 85:4 (2024), 341  crossref
    6. Galina Kurina, Springer Proceedings in Physics, 315, Proceedings of the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024), Volume 2, 2024, 220  crossref
    7. Galina Kurina, 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT), 2024, 2536  crossref
    8. O. B. Tsekhan, “Rasscheplyayuschee preobrazovanie lineinoi nestatsionarnoi singulyarno vozmuschennoi sistemy s postoyannym zapazdyvaniem v uravnenii medlennoi peremennoi”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 236, VINITI RAN, M., 2024, 49–71  mathnet  crossref
    9. G. A. Kurina, N. T. Hoai, “Zero-Order Asymptotics for the Solution of One Type of Singularly Perturbed Linear–Quadratic Control Problems in the Critical Case”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S154–S169  mathnet  crossref  crossref  mathscinet  isi  elib
    10. A. R. Danilin, A. A. Shaburov, “Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S69–S77  mathnet  crossref  crossref  mathscinet  isi  elib
    11. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S85–S97  mathnet  crossref  crossref  mathscinet  elib
    12. V. A. Sobolev, “Decomposition of singularly perturbed optimal tracking problems with a given reference trajectory”, J. Appl. Industr. Math., 17:3 (2023), 640–650  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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