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 - SLR
GIPSA-DA - Département Automatique
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
3 CaGE - Control And GEometry
Inria de Paris, LJLL - Laboratoire Jacques-Louis Lions
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.
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  • HAL Id : hal-01226598, version 1
  • ARXIV : 1511.03030

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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, Elsevier, 2018, 113, pp.9--16. ⟨hal-01226598⟩

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