Event-triggered gain scheduling of reaction-diffusion PDEs

TL;DR

This paper introduces an event-triggered gain scheduling method for boundary stabilization of reaction-diffusion PDEs, ensuring stability and avoiding Zeno behavior through state-dependent mechanisms.

Contribution

It develops a novel event-triggered control scheme for reaction-diffusion PDEs with time- and space-varying coefficients, guaranteeing stability and well-posedness.

Findings

Stability of the closed-loop system is proven under event-triggered gain updates.

Event-triggered mechanisms prevent Zeno behavior in the control scheme.

Numerical simulations validate the effectiveness of the proposed approach.

Abstract

This paper deals with the problem of boundary stabilization of 1D reaction-diffusion PDEs with a time- and space- varying reaction coefficient. The boundary control design relies on the backstepping approach. The gains of the boundary control are scheduled under two suitable event-triggered mechanisms. More precisely, gains are computed/updated on events according to two state-dependent event-triggering conditions: static-based and dynamic-based conditions, under which, the Zeno behavior is avoided and well-posedness as well as exponential stability of the closed-loop system are guaranteed. Numerical simulations are presented to illustrate the results.