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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 1, Pages 39–50
DOI: https://doi.org/10.21538/0134-4889-2020-26-1-39-50
(Mi timm1698)
 

This article is cited in 3 scientific papers (total in 3 papers)

Construction of Solutions to Control Problems for Fractional-Order Linear Systems Based on Approximation Models

M. I. Gomoyunovab, N. Yu. Lukoyanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (243 kB) Citations (3)
References:
Abstract: We consider an optimal control problem for a dynamical system whose motion is described by a linear differential equation with the Caputo fractional derivative of order $\alpha \in (0, 1)$. The time interval of the control process is fixed and finite. The control actions are subject to geometric constraints. The aim of the control is to minimize a given terminal-integral performance index. In order to construct a solution, we develop the following approach. First, from the considered problem, we turn to an auxiliary optimal control problem for a first-order linear system with lumped delays, which approximates the original system. After that, the auxiliary problem is reduced to an optimal control problem for an ordinary differential system. Based on this, we propose a closed-loop scheme of optimal control of the original system that uses the approximating system as a guide. In this scheme, the control in the approximating system is formed with the help of an optimal positional control strategy from the reduced problem. The effectiveness of the developed approach is illustrated by a problem in which the performance index is the norm of the terminal state of the system.
Keywords: optimal control, linear systems, fractional-order derivatives, approximation, time-delay systems, closed-loop control.
Funding agency Grant number
Russian Science Foundation 19-11-00105
This work was supported by RSF (project no. 19-11-00105).
Received: 25.12.2019
Revised: 24.01.2020
Accepted: 27.01.2020
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2021, Volume 313, Issue 1, Pages S73–S82
DOI: https://doi.org/10.1134/S0081543821030093
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 49N05, 34A08
Language: Russian
Citation: M. I. Gomoyunov, N. Yu. Lukoyanov, “Construction of Solutions to Control Problems for Fractional-Order Linear Systems Based on Approximation Models”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 1, 2020, 39–50; Proc. Steklov Inst. Math. (Suppl.), 313, suppl. 1 (2021), S73–S82
Citation in format AMSBIB
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\by M.~I.~Gomoyunov, N.~Yu.~Lukoyanov
\paper Construction of Solutions to Control Problems for Fractional-Order Linear Systems Based on Approximation Models
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 1
\pages 39--50
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\crossref{https://doi.org/10.21538/0134-4889-2020-26-1-39-50}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2021
\vol 313
\issue , suppl. 1
\pages S73--S82
\crossref{https://doi.org/10.1134/S0081543821030093}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85090518080}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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