A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems
Abstract
Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of Pontryagin's maximum principle is proved. As corollaries, necessary optimality conditions for Caputo-Fabrizio, Atangana-Baleanu and weighted Atangana-Baleanu fractional dynamic optimization problems are trivially obtained. As an application, the weighted generalized fractional problem of the calculus of variations is investigated and a new more general fractional Euler-Lagrange equation is given.
Cite
@article{arxiv.2312.10086,
title = {A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems},
author = {Houssine Zine and El Mehdi Lotfi and Delfim F. M. Torres and Noura Yousfi},
journal= {arXiv preprint arXiv:2312.10086},
year = {2023}
}
Comments
This is a preprint version of the paper published open access in 'Results in Control and Optimization 14 (2024), Art. 100356, 5 pp' [https://doi.org/10.1016/j.rico.2023.100356]