Sampled-Data and Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Collocated Sensing and Actuation

TL;DR

This paper develops observer-based sampled-data and event-triggered boundary control methods for reaction-diffusion PDEs, ensuring stability and robustness with minimal control updates, validated through simulations.

Contribution

It introduces novel observer-based boundary control strategies using backstepping for reaction-diffusion PDEs with sampled-data and event-triggered implementations.

Findings

Ensures global exponential stability with small sampling periods.

Guarantees robustness to sampling schedule perturbations.

Establishes minimal dwell-time between control updates.

Abstract

This paper provides observer-based sampled-data and event-triggered boundary control strategies for a class of reaction-diffusion PDEs with collocated sensing and Robin actuation. Infinite-dimensional backstepping design is used as the underlying control approach. It is shown that the continuous-time output feedback boundary control applied in a sample-and-hold fashion ensures global closed-loop exponential stability, provided that the sampling period is sufficiently small. Further, robustness to perturbations of the sampling schedule is guaranteed. For the event-triggered implementation of the continuous-time controller, a dynamic triggering condition is utilized. The triggering condition determines the time instants at which the control input needs to be updated. Under the observer-based event-triggered boundary control, it is shown that there is a minimal dwell-time between two triggering instants independent of initial conditions. Further, the global exponential convergence of the closed-loop system to the equilibrium point is established. A simulation example is provided to validate the theoretical results.