# Iterative learning control of neuronal firing based on FHN and HR models

## TL;DR

This paper introduces a new closed-loop control method to precisely regulate neuronal firing patterns, which could improve treatments for neurological disorders.

## Contribution

A novel iterative learning control framework using PI control for closed-loop neuromodulation is proposed and validated.

## Key findings

- The proposed ILC method outperforms conventional PI control in tracking accuracy and system stability.
- The approach adapts well to different neuronal dynamics, showing potential for robust neural regulation.
- Numerical simulations confirm the effectiveness of the ILC strategy in controlling FHN and HR neuron models.

## Abstract

Neuronal firing patterns are fundamental to neural information processing and functional regulation, with abnormal firing closely linked to a range of neurological disorders. However, existing neuromodulation techniques largely rely on open-loop stimulation strategies, which lack adaptability and fail to provide precise control over neuronal dynamics. To address this limitation, this study introduces a novel iterative learning control (ILC) framework based on proportional-integral (PI) control for closed-loop modulation of neuronal firing patterns. The proposed method is developed and validated using two representative neuron models: the FitzHugh–Nagumo (FHN) and Hindmarsh–Rose (HR) models. A dynamical analysis of these models is conducted, followed by the design and implementation of a PI-based ILC strategy. Numerical simulations demonstrate that the proposed control method significantly outperforms conventional PI control, achieving lower tracking errors, enhanced control accuracy, and improved system stability. Additionally, the ILC approach exhibits strong adaptability to different neuronal dynamics, highlighting its potential for precise and robust regulation in complex neural systems. These findings offer a theoretical basis for advancing closed-loop neuromodulation technologies, with promising implications for applications in neurorehabilitation and the treatment of neurological disorders.