An Efficient Operational Matrix Technique for Variable-Order Fractional Optimal Control Problems

H. Hassani; J. A. Tenreiro Machado; Z. Avazzadeh

doi:10.1007/978-981-16-4169-5_8

An Efficient Operational Matrix Technique for Variable-Order Fractional Optimal Control Problems

H. Hassani^*
, J. A. Tenreiro Machado
, Z. Avazzadeh

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Chapter in Book or Report/Conference proceeding › Chapter › peer-review

Abstract

This chapter considers a class of variable-order fractional optimal control problems (V-FOCP). An optimization method based on the generalized polynomials (GP) for solving V-FOCP is proposed. The solution of the problem is expanded in terms of the GP with some free coefficients (FC) and control parameters (CP). The FC and CP are obtained optimally by minimizing the error of the approximate solution. Furthermore, a new variable-order fractional operational matrix (V-FOM) in the Caputo sense for the GP is derived. The efficiency and accuracy of the method are demonstrated with some examples.

Original language	English
Title of host publication	Nonlinear Physical Science
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	131-146
Number of pages	16
DOIs	https://doi.org/10.1007/978-981-16-4169-5_8
Publication status	Published - 2022

Publication series

Name	Nonlinear Physical Science
ISSN (Print)	1867-8440
ISSN (Electronic)	1867-8459

Keywords

Control parameters
Free coefficients
Generalized polynomials
Variable-order fractional operational matrix
Variable-order fractional optimal control problems

Access to Document

10.1007/978-981-16-4169-5_8

Cite this

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abstract = "This chapter considers a class of variable-order fractional optimal control problems (V-FOCP). An optimization method based on the generalized polynomials (GP) for solving V-FOCP is proposed. The solution of the problem is expanded in terms of the GP with some free coefficients (FC) and control parameters (CP). The FC and CP are obtained optimally by minimizing the error of the approximate solution. Furthermore, a new variable-order fractional operational matrix (V-FOM) in the Caputo sense for the GP is derived. The efficiency and accuracy of the method are demonstrated with some examples.",

keywords = "Control parameters, Free coefficients, Generalized polynomials, Variable-order fractional operational matrix, Variable-order fractional optimal control problems",

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An Efficient Operational Matrix Technique for Variable-Order Fractional Optimal Control Problems. / Hassani, H.; Tenreiro Machado, J. A.; Avazzadeh, Z.
Nonlinear Physical Science. Springer Science and Business Media Deutschland GmbH, 2022. p. 131-146 (Nonlinear Physical Science).

Research output: Chapter in Book or Report/Conference proceeding › Chapter › peer-review

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AB - This chapter considers a class of variable-order fractional optimal control problems (V-FOCP). An optimization method based on the generalized polynomials (GP) for solving V-FOCP is proposed. The solution of the problem is expanded in terms of the GP with some free coefficients (FC) and control parameters (CP). The FC and CP are obtained optimally by minimizing the error of the approximate solution. Furthermore, a new variable-order fractional operational matrix (V-FOM) in the Caputo sense for the GP is derived. The efficiency and accuracy of the method are demonstrated with some examples.

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KW - Free coefficients

KW - Generalized polynomials

KW - Variable-order fractional operational matrix

KW - Variable-order fractional optimal control problems

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An Efficient Operational Matrix Technique for Variable-Order Fractional Optimal Control Problems

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