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Optimal Feedback in a Linear–Quadratic Optimal Control Problem for a Fractional-Order System

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Abstract

For a dynamical system described by a linear differential equation with a Caputo fractional derivative, we consider an optimal control problem of minimizing a quadratic terminal–integral performance functional. We propose and justify the construction of optimal feedback (optimal control synthesis) that generates the corresponding optimal control for any initial state of the system.

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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. 075-01483-23-00, 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

    M. I. Gomoyunov & N. Yu. Lukoyanov

  2. Udmurt State University, Izhevsk, 426034, Russia

    M. I. Gomoyunov

Authors
  1. M. I. Gomoyunov
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  2. N. Yu. Lukoyanov
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Corresponding authors

Correspondence to M. I. Gomoyunov or N. Yu. Lukoyanov.

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Translated by V. Potapchouck

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Gomoyunov, M.I., Lukoyanov, N.Y. Optimal Feedback in a Linear–Quadratic Optimal Control Problem for a Fractional-Order System. Diff Equat 59, 1117–1129 (2023). https://doi.org/10.1134/S0012266123080104

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  • DOI: https://doi.org/10.1134/S0012266123080104

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