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Singularly Perturbed Problems with Multi-Tempo Fast Variables

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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.

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ACKNOWLEDGMENTS

The authors express their deep gratitude to the referees of the article for providing useful information as well as to A.V. Vlakhova, N.V. Voropaeva, A.R. Danilin, M.G. Dmitriev, Yu.E. Gliklikh, V.G. Zadorozhnii, A.I. Kalinin, O.O. Kovrizhnykh, A.S. Kostenko, K.N. Kudryavtsev, D.A. Makarov, M.E. Semenov, N.T. Hoai, O.B. Tsekhan, and G. Marinoschi for helpful discussions.

Funding

The work of the first author was financially supported by the Russian Science Foundation, project no. 21-11-00202.

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  1. Voronezh State University, Voronezh, 394018, Russia

    G. A. Kurina

  2. Federal Research Center “Informatics and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    G. A. Kurina

  3. Atos IT Solutions and Services, Voronezh, 394026, Russia

    M. A. Kalashnikova

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Kurina, G.A., Kalashnikova, M.A. Singularly Perturbed Problems with Multi-Tempo Fast Variables. Autom Remote Control 83, 1679–1723 (2022). https://doi.org/10.1134/S00051179220110017

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