2023/09/29 by Cenk Demir, Demir, Cenk, Shumon Koga +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Cellular Mechanics and Interactions #Mathematical Biology Tumor Growth #Gene Regulatory Network Analysis
paper · pdf · doi:10.48550/arxiv.2310.00131
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 L2-norm, initially for the target system, and subsequently for the original system. The effectiveness of the proposed method is showcased through numerical simulations.