@article{Abuasbeh2026, 
author = {Kinda Abuasbeh and Meraa Arab},
title = {Data-driven variable-order fractional control for grid resilience: A hybrid Caputo-Hadamard framework validated with US power system data},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {5492-5531},
keywords = {fractional-order control, variable-order systems, power grid resilience, data-driven control, adaptive control},
url = {https://www.sciopen.com/article/10.3934/math.2026227},
doi = {10.3934/math.2026227},
abstract = {The rapid integration of inverter-based renewable resources poses significant challenges to power systems' stability and resilience. This paper presents a data-driven variable-order fractional control framework that enhances grids' resilience through adaptive memory management. The proposed controller employs a hybrid Caputo-Hadamard structure, in which the fractional order    α  (  t  ) adapts in real time occording to wide-area frequency measurements. The Caputo component captures short-memory transient dynamics associated with power electronic responses, while the Hadamard component represents long-memory logarithmic effects arising from variability in the load and renewable generation. Rigorous stability analysis establishes Mittag-Leffler stability under bounded order variation and Ulam-Hyers practical stability, ensuring robustness against modeling uncertainties and numerical discretization errors. Numerical validation using realistic US power system data from Pennsylvania-New Jersey-Maryland (PJM)  Interconnection, California Independent System Operator (CAISO), National Renewable Energy Laboratory (NREL), and Frequency Monitoring Network (FNET/GridEye) demonstrates consistently improved performance compared with integer-order and fixed-order fractional controllers, including up to    67  % reduction in voltage overshoot and    72  % reduction in the duration of rate of change of frequency violations  under compound disturbance scenarios. The proposed framework provides a mathematically rigorous and practically viable approach for adaptive control in renewable-rich power systems, aligning with ongoing grid modernization efforts that seek to balance fast transient response with long-term  stability in the system.}
}