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

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-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 languageEnglish
Title of host publicationNonlinear Physical Science
PublisherSpringer Science and Business Media Deutschland GmbH
Pages131-146
Number of pages16
DOIs
Publication statusPublished - 2022

Publication series

NameNonlinear 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

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