Event-triggered boundary control of the linearized FitzHugh-Nagumo equation

TL;DR

This paper develops an event-triggered boundary control method for the linearized FitzHugh-Nagumo system, achieving exponential stabilization with fewer updates and maintaining stability through backstepping and input-to-state stability analysis.

Contribution

It introduces a novel event-triggered boundary control strategy for the FitzHugh-Nagumo system using backstepping, reducing control updates while ensuring stability.

Findings

Effective stabilization with fewer control updates

Backstepping-based feedback law derived

Numerical simulations confirm stability and efficiency

Abstract

In this paper, we address the exponential stabilization of the linearized FitzHugh-Nagumo system using an event-triggered boundary control strategy. Employing the backstepping method, we derive a feedback control law that updates based on specific triggering rules while ensuring the exponential stability of the closed-loop system. We establish the well-posedness of the system and analyze its input-to-state stability in relation to the deviations introduced by the event-triggered control. Numerical simulations demonstrate the effectiveness of this approach, showing that it stabilizes the system with fewer control updates compared to continuous feedback strategies while maintaining similar stabilization performance.