Periodic Event-Triggered Boundary Control for Enhancing Neuron Growth with Actuation at the Soma

Core Concepts

The authors introduce a periodic event-triggered control (PETC) mechanism to enhance the practical implementation of a backstepping-based boundary control law for regulating axon growth in neurons. The PETC approach updates the control input aperiodically while evaluating the triggering condition periodically, which is well-suited for standard time-sliced actuators like Chondroitinase ABC (ChABC) used in neuron regeneration therapies.

Abstract

The content presents a model for tubulin-driven axon growth, which is described by a coupled moving boundary partial differential equation (PDE) and ordinary differential equations (ODEs). The authors first introduce a continuous-time boundary control law based on the backstepping method that locally exponentially stabilizes the system. To address the practical challenges in implementing the continuous-time control law, the authors then propose a periodic event-triggered control (PETC) mechanism. The PETC approach evaluates the triggering condition periodically but updates the control input aperiodically, which is more suitable for standard time-sliced actuators like ChABC used in neuron regeneration therapies. The key aspects of the PETC design include: Deriving a novel triggering condition that ensures the system remains locally exponentially stable and prevents Zeno behavior. Establishing an upper bound on the continuous-time event trigger between two periodic examinations, which is explicitly derived as the sampling period. Proving the local exponential convergence of the closed-loop system in the L2-norm sense under the PETC framework. Numerical simulations are provided to confirm the theoretical findings and demonstrate the performance of the PETC approach compared to the continuous-time event-triggered control (CETC) and the continuous control law.

Stats

The authors use the following key parameters and metrics in their analysis: Tubulin diffusivity (D) Tubulin velocity (a) Tubulin degradation constant (g) Growth ratio (lc) Reaction rate of microtubules production (rg) Equilibrium tubulin concentration in the cone (c∞) Lumped parameter (rg)

Quotes

"Periodic event-triggering control (PETC) and self-triggered control are proposed in [35] and [36], respectively, for a class of reaction diffusion PDEs." "The PETC improves the practical implementation of the control law because it can be applied to standard time-sliced actuators (like ChABC) for axon growth."

Key Insights Distilled From

Periodic Event-Triggered Boundary Control of Neuron Growth with Actuation at Soma

by Cenk Demir,M... at arxiv.org 05-01-2024

https://arxiv.org/pdf/2404.19206.pdf

Deeper Inquiries

How can the PETC approach be extended to handle more complex neuron growth models, such as those involving multiple interacting PDEs or nonlinear dynamics

The PETC approach can be extended to handle more complex neuron growth models by adapting the periodic event-triggering mechanism to accommodate the additional complexities. For models involving multiple interacting PDEs, the triggering conditions can be designed to account for the dynamics of each PDE and their interactions. This may involve developing a more sophisticated triggering function that considers the state variables of all PDEs and their impact on the overall system behavior. By incorporating these additional dynamics into the triggering mechanism, the PETC approach can effectively regulate the growth of neurons in complex models. In cases where nonlinear dynamics are present in the neuron growth model, the PETC framework can be enhanced by incorporating nonlinear control strategies. Nonlinear event-triggered control laws can be designed to handle the nonlinearities in the system and ensure stability and convergence. By utilizing nonlinear control techniques, such as feedback linearization or adaptive control, the PETC approach can effectively manage the complexities introduced by nonlinear dynamics in neuron growth models. Additionally, advanced control algorithms, such as model predictive control or sliding mode control, can be integrated into the PETC framework to address the challenges posed by nonlinear dynamics.

What are the potential limitations or drawbacks of the PETC approach compared to other control strategies, and how can they be addressed

One potential limitation of the PETC approach compared to other control strategies is the need to carefully design the triggering mechanism to ensure system stability and performance. The periodic evaluation of the triggering function may introduce delays in the control action, which can impact the system's response time. To address this limitation, the triggering conditions can be optimized to minimize the delay while maintaining stability. By fine-tuning the parameters of the triggering function and adjusting the sampling rate, the PETC approach can mitigate the effects of delays and improve the overall control performance. Another drawback of the PETC approach is the sensitivity to parameter variations and uncertainties in the system. Changes in the system parameters or external disturbances can affect the triggering mechanism and lead to suboptimal control performance. To overcome this limitation, robust control techniques, such as robust event-triggered control or adaptive event-triggered control, can be implemented within the PETC framework. These methods can enhance the system's robustness to uncertainties and variations, ensuring reliable control in the presence of disturbances.

Can the PETC framework be applied to other biological or medical applications beyond neuron growth, where practical implementation challenges exist for continuous-time control laws

The PETC framework can be applied to other biological or medical applications beyond neuron growth where practical implementation challenges exist for continuous-time control laws. One such application is drug delivery systems, where precise control over drug administration is crucial for effective treatment. By implementing the PETC approach in drug delivery systems, the dosage of medication can be regulated based on specific triggering conditions, optimizing drug release and minimizing side effects. The periodic event-triggering mechanism can ensure efficient drug delivery while conserving resources and reducing unnecessary dosing. Furthermore, the PETC framework can be utilized in prosthetic devices to enhance their functionality and usability. By integrating event-triggered control strategies into prosthetics, such as robotic limbs or neural interfaces, the devices can respond to user commands more efficiently and accurately. The periodic evaluation of control inputs can improve the device's performance while conserving energy and prolonging battery life. This application of PETC in prosthetics demonstrates its versatility in addressing practical implementation challenges in various medical and biological systems.