Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case

An algorithm is proposed for solving the problem of analytical constructing of an optimal fractional-order regulator (OFOR) in the general case. By inscribing the extended functional, the corresponding fractional order Euler-Lagrange equation is determined. Then, using the Mittag-Leffler function, a...

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Main Authors:	Fikret Aliev, Nihan Aliev, Nargiz Safarova, Yegana Mamedova
Format:	Article
Language:	English
Published:	Shahid Chamran University of Ahvaz 2021-04-01
Series:	Journal of Applied and Computational Mechanics
Subjects:	fractional derivative analytical construction of controllers hamiltonian matrix fundamental matrix mittag-leffler function ‎euler-lagrange equation‎
Online Access:	https://jacm.scu.ac.ir/article_16462_7b8d482401be8a8a0685cd87afcbbc01.pdf

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spelling	doaj-cfb5291acd3e4a57b97dd2d028c403372021-02-04T16:51:02ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362021-04-017297097610.22055/jacm.2021.35130.257216462Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General CaseFikret Aliev0Nihan Aliev1Nargiz Safarova2Yegana Mamedova3Institute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan‎Institute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan‎Institute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan‎Institute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan‎An algorithm is proposed for solving the problem of analytical constructing of an optimal fractional-order regulator (OFOR) in the general case. By inscribing the extended functional, the corresponding fractional order Euler-Lagrange equation is determined. Then, using the Mittag-Leffler function, a fundamental solution to the corresponding Hamiltonian system is constructed. It is shown that to obtain an analogue of the analytical construction of AM Letov's regulators, the order of the fractional derivatives must be a rational number, the denominator and numerator of which are odd numbers. Numerical illustrative examples are provided.https://jacm.scu.ac.ir/article_16462_7b8d482401be8a8a0685cd87afcbbc01.pdffractional derivativeanalytical construction of controllershamiltonian matrixfundamental matrixmittag-leffler function‎euler-lagrange equation‎
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Fikret Aliev Nihan Aliev Nargiz Safarova Yegana Mamedova
spellingShingle	Fikret Aliev Nihan Aliev Nargiz Safarova Yegana Mamedova Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case Journal of Applied and Computational Mechanics fractional derivative analytical construction of controllers hamiltonian matrix fundamental matrix mittag-leffler function ‎euler-lagrange equation‎
author_facet	Fikret Aliev Nihan Aliev Nargiz Safarova Yegana Mamedova
author_sort	Fikret Aliev
title	Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case
title_short	Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case
title_full	Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case
title_fullStr	Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case
title_full_unstemmed	Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case
title_sort	solution of the problem of analytical construction of optimal ‎regulators for a fractional order oscillatory system in the ‎general case
publisher	Shahid Chamran University of Ahvaz
series	Journal of Applied and Computational Mechanics
issn	2383-4536 2383-4536
publishDate	2021-04-01
description	An algorithm is proposed for solving the problem of analytical constructing of an optimal fractional-order regulator (OFOR) in the general case. By inscribing the extended functional, the corresponding fractional order Euler-Lagrange equation is determined. Then, using the Mittag-Leffler function, a fundamental solution to the corresponding Hamiltonian system is constructed. It is shown that to obtain an analogue of the analytical construction of AM Letov's regulators, the order of the fractional derivatives must be a rational number, the denominator and numerator of which are odd numbers. Numerical illustrative examples are provided.
topic	fractional derivative analytical construction of controllers hamiltonian matrix fundamental matrix mittag-leffler function ‎euler-lagrange equation‎
url	https://jacm.scu.ac.ir/article_16462_7b8d482401be8a8a0685cd87afcbbc01.pdf
work_keys_str_mv	AT fikretaliev solutionoftheproblemofanalyticalconstructionofoptimalregulatorsforafractionalorderoscillatorysysteminthegeneralcase AT nihanaliev solutionoftheproblemofanalyticalconstructionofoptimalregulatorsforafractionalorderoscillatorysysteminthegeneralcase AT nargizsafarova solutionoftheproblemofanalyticalconstructionofoptimalregulatorsforafractionalorderoscillatorysysteminthegeneralcase AT yeganamamedova solutionoftheproblemofanalyticalconstructionofoptimalregulatorsforafractionalorderoscillatorysysteminthegeneralcase
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Solution of the Problem of Analytical Construction of Optimal ‎Regulators for a Fractional Order Oscillatory System in the ‎General Case

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