Fractional-Order Model Predictive Control for Neurophysiological Cyber-Physical Systems: A Case Study using Transcranial Magnetic Stimulation

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.