Event-Triggered Control of Neuron Growth with Actuation at Soma

TL;DR

This paper presents a novel dynamic event-triggered control strategy for regulating neuron axon growth by controlling tubulin concentration at the soma, ensuring stability and avoiding Zeno behavior through Lyapunov analysis.

Contribution

It introduces a new event-triggering mechanism for neuron growth control using boundary actuation and PDE backstepping, with stability guarantees.

Findings

Ensures minimum dwell-time to prevent Zeno behavior.

Proves local stability of the closed-loop system.

Demonstrates effectiveness through numerical simulations.

Abstract

We introduce a dynamic event-triggering mechanism for regulating the axonal growth of a neuron. We apply boundary actuation at the soma (the part of a neuron that contains the nucleus) and regulate the dynamics of tubulin concentration and axon length. The control law is formulated by applying a Zero-Order Hold (ZOH) to a continuous-time controller which guides the axon to reach the desired length. The proposed dynamic event-triggering mechanism determines the specific time instants at which control inputs are sampled from the continuous-time control law. We establish the existence of a minimum dwell-time between two triggering times that ensures avoidance of Zeno behavior. Through employing the Lyapunov analysis with PDE backstepping, we prove the local stability of the closed-loop system in $L_2$-norm, initially for the target system, and subsequently for the original system. The effectiveness of the proposed method is showcased through numerical simulations.