Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems
Abstract
We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo fractional-orders derivatives. We establish continuity and differentiability of the state solutions with respect to perturbed trajectories. Then, we state and prove a Pontryagin maximum principle for incommensurate Caputo fractional optimal control problems. Finally, we give an example, illustrating the applicability of our Pontryagin maximum principle.
Cite
@article{arxiv.2310.08604,
title = {Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems},
author = {Faical Ndairou and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:2310.08604},
year = {2023}
}
Comments
This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', at [https://doi.org/10.3390/math11194218]. Cite this paper as: F. Nda\"{\i}rou and D.F.M. Torres, Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems, Mathematics 11 (2023), no. 19, Art. 4218, 12 pp