Observer-based Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs

TL;DR

This paper develops an observer-based event-triggered boundary control method for reaction-diffusion PDEs, ensuring minimal update intervals, stability, and convergence using boundary measurements and backstepping techniques.

Contribution

It introduces a novel event-triggered control scheme for reaction-diffusion PDEs that guarantees stability with minimal control updates based on boundary measurements.

Findings

Ensures a minimal dwell-time between control updates.

Proves global exponential stability of the closed-loop system.

Validates the approach with a simulation example.

Abstract

This paper presents an observer-based event-triggered boundary control strategy for a class of reaction-diffusion PDEs with Robin actuation. The observer only requires boundary measurements. The control approach consists of a backstepping output feedback boundary controller, derived using estimated states, and a dynamic triggering condition, which determines the time instants at which the control input needs to be updated. It is shown that under the proposed observer-based event-triggered boundary control approach, there is a minimal dwell-time between two triggering instants independent of initial conditions. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to the equilibrium point are established. A simulation example is provided to validate the theoretical developments.