Event-triggered boundary control of constant-parameter reaction-diffusion PDEs: a small-gain approach

TL;DR

This paper introduces an event-triggered boundary control method for reaction-diffusion PDEs that guarantees stability and minimal sampling intervals using a small-gain approach, validated by simulations.

Contribution

It presents a novel event-triggered boundary control strategy for reaction-diffusion PDEs employing a small-gain framework, ensuring stability and minimal inter-trigger times.

Findings

Existence of a minimal dwell-time between triggers

Guarantee of well-posedness and exponential stability

Validation through simulation example

Abstract

This paper deals with an event-triggered boundary control of constant-parameters reaction-diffusion PDE systems. The approach relies on the emulation of backstepping control along with a suitable triggering condition which establishes the time instants at which the control value needs to be sampled/updated. In this paper, it is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial condition) between two triggering times and furthermore the well-posedness and global exponential stability are guaranteed. The analysis follows small-gain arguments and builds on recent papers on sampled-data control for this kind of PDE. A simulation example is presented to validate the theoretical results.