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Quasigradient Aiming Strategies in Optimal Control Problems for Time-Delay Systems

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Abstract

We consider an optimal control problem in which the motion of a dynamical system is described by delay differential equations, the initial conditions are determined by a piecewise continuous function, and a Bolza type cost functional is optimized. The construction of positional control strategies is proposed that permits one to obtain piecewise constant approximations to the optimal control. These strategies use quasigradients of the value functional. Strategies are calculated by searching for points of extremum on a finite-dimensional set. The fact that this set can be finite-dimensional is the main result of the paper.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of state order no. 075-01265-22-00 (project no. FEWS-2020-0010).

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620108, Russia

    N. Yu. Lukoyanov & A. R. Plaksin

  2. Udmurt State University, Izhevsk, 426034, Russia

    A. R. Plaksin

Authors
  1. N. Yu. Lukoyanov
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  2. A. R. Plaksin
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Correspondence to N. Yu. Lukoyanov or A. R. Plaksin.

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Translated by V. Potapchouck

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Lukoyanov, N.Y., Plaksin, A.R. Quasigradient Aiming Strategies in Optimal Control Problems for Time-Delay Systems. Diff Equat 58, 1514–1524 (2022). https://doi.org/10.1134/S00122661220110076

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  • DOI: https://doi.org/10.1134/S00122661220110076

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