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Title: Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
Author: Salati, Abubakar Bello
Shamsi, Mostafa
Torres, Delfim F. M.
Keywords: Fractional optimal control
Direct numerical solution
Fractional integration matrix
Trapezoidal and Simpson fractional integral formulas
Issue Date: Feb-2019
Publisher: Elsevier
Abstract: This paper presents three direct methods based on Grünwald–Letnikov, trapezoidal and Simpson fractional integral formulas to solve fractional optimal control problems (FOCPs). At first, the fractional integral form of FOCP is considered, then the fractional integral is approximated by Grünwald–Letnikov, trapezoidal and Simpson formulas in a matrix approach. Thereafter, the performance index is approximated either by trapezoidal or Simpson quadrature. As a result, FOCPs are reduced to nonlinear programming problems, which can be solved by many well-developed algorithms. To improve the efficiency of the presented method, the gradient of the objective function and the Jacobian of constraints are prepared in closed forms. It is pointed out that the implementation of the methods is simple and, due to the fact that there is no need to derive necessary conditions, the methods can be simply and quickly used to solve a wide class of FOCPs. The efficiency and reliability of the presented methods are assessed by ample numerical tests involving a free final time with path constraint FOCP, a bang-bang FOCP and an optimal control of a fractional-order HIV-immune system.
Peer review: yes
DOI: 10.1016/j.cnsns.2018.05.011
ISSN: 1007-5704
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Appears in Collections:CIDMA - Artigos
SCG - Artigos

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