Finite-dimensional predictor-based feedback stabilization of a 1D linear reaction-diffusion equation with boundary input delay
Optimization and Control
2015-11-11 v1
Abstract
We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport equation. We prove that this is possible to stabilize (in H 1 norm) this process by means of an explicit predictor-based feedback control that is designed from a finite-dimensional subsystem. The implementation is very simple and efficient and is based on standard tools of pole-shifting. Our feedback acts on the system as a finite-dimensional predictor. We compare our approach with the backstepping method.
Cite
@article{arxiv.1511.03030,
title = {Finite-dimensional predictor-based feedback stabilization of a 1D linear reaction-diffusion equation with boundary input delay},
author = {Delphine Bresch-Pietri and Christophe Prieur and Emmanuel Trélat},
journal= {arXiv preprint arXiv:1511.03030},
year = {2015}
}