  Fractional-order dynamical systems are used to describe processes that
exhibit temporal long-term memory and power-law dependence of trajectories.
There has been evidence that complex neurophysiological signals like
electroencephalogram (EEG) can be modeled by fractional-order systems. In this
work, we propose a model-based approach for closed-loop Transcranial Magnetic
Stimulation (TMS) to regulate brain activity through EEG data. More precisely,
we propose a model predictive control (MPC) approach with an underlying
fractional-order system (FOS) predictive model. Furthermore, MPC offers, by
design, an additional layer of robustness to compensate for system-model
mismatch, which the more traditional strategies lack. To establish the
potential of our framework, we focus on epileptic seizure mitigation by
computational simulation of our proposed strategy upon seizure-like events. We
conclude by empirically analyzing the effectiveness of our method, and compare
it with event-triggered open-loop strategies.
