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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v29.i1.50
pages 40-43

Singularly Perturbed Control with Delay Problem

Vitaliy P. Zholtikov
Odessa National I.I. Mechnikov University
Vladislav V. Efendiev
European University, Uman


A singularly perturbed parametric control problem with a constant delay is considered. A high-order asymptotic approximation of a solution to the initial-value problem is constructed with the help of the A. B. Vasil'eva theorem. Estimates of trajectories and the solution functional of the initial-value problem as well as the asymptotic approximation of the solution are proved.


  1. Vasil'eva, A. B. and Butuzov, V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuchshenii (Asymptotic Methods in the Theory of Singular Perturbations).

  2. Zheltikov, V. P. and Efendiev, V. V., Asymptotic Solution of the Optimal Control Problem of Systems of the Standard Form with Delay.

  3. Plotnikov, V. A., Metod usredneniya v zadachakh upravleniya (Averaging Method in Control Problems).

  4. Shashina, M. K., Some Problems for Singularly-Perturbed Problems With Delayed Argument, In: Trudy po Teorii Differentsial'nykh Uravnenii s Otklonyayushchimisya argumentami (Problems of the Theory of Differential Equations with Divergent Arguments).

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