# Event-triggered gain scheduling of reaction-diffusion PDEs

arXiv: https://arxiv.org/abs/2005.13945 · HTML: https://mlsanity.com/paper/2005.13945/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2020.

## Built on by (most cited first, 2 of 2)

- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation](https://mlsanity.com/paper/2401.02511/) (2024)

## Abstract (arXiv)

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.