Robust synchronization of coupled neural oscillators using the derivative-free nonlinear Kalman Filter

Area of Science:

• Computational Neuroscience
• Control Theory
• Dynamical Systems

Background:

• Coupled neural oscillators, such as the FitzHugh-Nagumo model, are fundamental in understanding neural dynamics.
• Synchronization of these oscillators is crucial for various brain functions.
• Existing control schemes may struggle with disturbances and parametric uncertainties.

Purpose of the Study:

• To develop a robust synchronizing control scheme for coupled FitzHugh-Nagumo neural oscillators.
• To utilize differential flatness theory for model linearization and controller design.
• To incorporate a disturbance observer based on Kalman Filtering for enhanced robustness.

Main Methods:

• Transformation of the coupled neural oscillator model into a linear canonical (Brunovsky) form using differential flatness theory.
• Design of a state feedback controller for synchronization based on the linearized model.
• Implementation of a Kalman Filter-based disturbance observer to estimate and compensate for uncertainties and external disturbances.

Main Results:

• The proposed control scheme successfully synchronizes the membrane voltage variations of two coupled neurons.
• The disturbance observer effectively estimates and compensates for model uncertainties and external perturbations.
• Simulation experiments validate the performance and robustness of the synchronization control loop.

Conclusions:

• Differential flatness theory provides an effective framework for designing synchronizing controllers for neural oscillators.
• Kalman Filtering offers a robust approach for disturbance observation and compensation in neural models.
• The integrated control scheme demonstrates significant potential for applications requiring precise neural synchronization.