Finite-dimensional predictor-based feedback stabilization of a 1D linear reaction-diffusion equation with boundary input delay

Delphine Bresch-Pietri (1) , Christophe Prieur (2) , Emmanuel Trélat (3, 4, 5)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
3 CaGE - Control And GEometry
4 SU - Sorbonne Université
5 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Domaines: Optimisation et contrôle [math.OC]

Delphine Bresch-Pietri, Christophe Prieur, Emmanuel Trélat. Finite-dimensional predictor-based feedback stabilization of a 1D linear reaction-diffusion equation with boundary input delay. Systems and Control Letters, 2018, 113, pp.9--16. ⟨10.1016/j.sysconle.2017.12.007⟩. ⟨hal-01226598v1⟩