Fourier-Gegenbauer Pseudospectral Method for Solving Periodic Higher-Order Fractional Optimal Control Problems
Abstract
In [1], we inaugurated a new area of optimal control (OC) theory that we called "periodic fractional OC theory," which was developed to find optimal ways to periodically control a fractional dynamic system. The typical mathematical formulation in this area includes the class of periodic fractional OC problems (PFOCPs), which can be accurately solved numerically for a fractional order {\alpha} in the range 0 < {\alpha} < 1 using Fourier collocation at equally spaced nodes and Fourier and Gegenbauer quadratures. In this study, we extend this earlier work to cover periodic higher-order fractional OC problems (PHFOCPs) of any positive non-integer fractional order {\alpha}.
Cite
@article{arxiv.2305.00458,
title = {Fourier-Gegenbauer Pseudospectral Method for Solving Periodic Higher-Order Fractional Optimal Control Problems},
author = {Kareem T. Elgindy},
journal= {arXiv preprint arXiv:2305.00458},
year = {2023}
}
Comments
7 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2304.04454; text overlap with arXiv:2304.14061