On the numerical solution of optimal control problems via Bell polynomials basis

We present a new numerical approach to solve the optimal control problems (OCPs) with a quadratic performance index. Our method is based on the Bell polynomials basis. The properties of Bell polynomials are explained. We also introduce the operational matrix of derivative for Bell polynomials. The c...

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Main Authors:	Mohammad Reza Dadashi, Ahmad Reza Haghighi, Fahimeh Soltanian, Ayatollah Yari
Format:	Article
Language:	English
Published:	Ferdowsi University of Mashhad 2020-09-01
Series:	Iranian Journal of Numerical Analysis and Optimization
Subjects:	optimal control problems bell polynomial best approximation operational matrix of derivative
Online Access:	https://ijnao.um.ac.ir/article_25532_3dcd2d47781d63e23e2eceb7b075d9e0.pdf

id	doaj-a4265f0fc2b1488fb2b58a780f4d8f9a
record_format	Article
spelling	doaj-a4265f0fc2b1488fb2b58a780f4d8f9a2021-02-17T10:32:40ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692020-09-0110219722110.22067/ijnao.v10i2.8688425532On the numerical solution of optimal control problems via Bell polynomials basisMohammad Reza Dadashi0Ahmad Reza Haghighi1Fahimeh Soltanian2Ayatollah Yari3Department of Mathematics, Payame Noor University, Tehran, Iran.Department of Mathematics, Technical and Vocational University, Tehran, Iran.Department of Mathematics, Payame Noor University, Tehran, Iran.Department of Mathematics, Payame Noor University, Tehran, Iran.We present a new numerical approach to solve the optimal control problems (OCPs) with a quadratic performance index. Our method is based on the Bell polynomials basis. The properties of Bell polynomials are explained. We also introduce the operational matrix of derivative for Bell polynomials. The chief feature of this matrix is reducing the OCPs to an optimization problem. Finally, we discuss the convergence of the new technique and present some illustrative examples to show the effectiveness and applicability of the proposed scheme. Comparison of the proposed method with other previous methods shows that this method is accurate.https://ijnao.um.ac.ir/article_25532_3dcd2d47781d63e23e2eceb7b075d9e0.pdfoptimal control problemsbell polynomialbest approximationoperational matrix of derivative
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mohammad Reza Dadashi Ahmad Reza Haghighi Fahimeh Soltanian Ayatollah Yari
spellingShingle	Mohammad Reza Dadashi Ahmad Reza Haghighi Fahimeh Soltanian Ayatollah Yari On the numerical solution of optimal control problems via Bell polynomials basis Iranian Journal of Numerical Analysis and Optimization optimal control problems bell polynomial best approximation operational matrix of derivative
author_facet	Mohammad Reza Dadashi Ahmad Reza Haghighi Fahimeh Soltanian Ayatollah Yari
author_sort	Mohammad Reza Dadashi
title	On the numerical solution of optimal control problems via Bell polynomials basis
title_short	On the numerical solution of optimal control problems via Bell polynomials basis
title_full	On the numerical solution of optimal control problems via Bell polynomials basis
title_fullStr	On the numerical solution of optimal control problems via Bell polynomials basis
title_full_unstemmed	On the numerical solution of optimal control problems via Bell polynomials basis
title_sort	on the numerical solution of optimal control problems via bell polynomials basis
publisher	Ferdowsi University of Mashhad
series	Iranian Journal of Numerical Analysis and Optimization
issn	2423-6977 2423-6969
publishDate	2020-09-01
description	We present a new numerical approach to solve the optimal control problems (OCPs) with a quadratic performance index. Our method is based on the Bell polynomials basis. The properties of Bell polynomials are explained. We also introduce the operational matrix of derivative for Bell polynomials. The chief feature of this matrix is reducing the OCPs to an optimization problem. Finally, we discuss the convergence of the new technique and present some illustrative examples to show the effectiveness and applicability of the proposed scheme. Comparison of the proposed method with other previous methods shows that this method is accurate.
topic	optimal control problems bell polynomial best approximation operational matrix of derivative
url	https://ijnao.um.ac.ir/article_25532_3dcd2d47781d63e23e2eceb7b075d9e0.pdf
work_keys_str_mv	AT mohammadrezadadashi onthenumericalsolutionofoptimalcontrolproblemsviabellpolynomialsbasis AT ahmadrezahaghighi onthenumericalsolutionofoptimalcontrolproblemsviabellpolynomialsbasis AT fahimehsoltanian onthenumericalsolutionofoptimalcontrolproblemsviabellpolynomialsbasis AT ayatollahyari onthenumericalsolutionofoptimalcontrolproblemsviabellpolynomialsbasis
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On the numerical solution of optimal control problems via Bell polynomials basis

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