Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control

Christophe Prieur 1 Emmanuel Trélat 2, 3
1 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
3 CaGE - Control And GEometry
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
Abstract : The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system equivalent to a parabolic equation coupled with a transport equation, a prediction-based control is explicitly computed. To do that we decompose the infinite-dimensional system into two parts: one finite-dimensional unstable part, and one stable infinite-dimensional part. An finite-dimensional delay controller is computed for the unstable part, and it is shown that this controller succeeds in stabilizing the whole partial differential equation. The proof is based on a an explicit form of the classical Artstein transformation, and an appropriate Lyapunov function. A numerical simulation illustrate the constructive design method.
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https://hal.archives-ouvertes.fr/hal-01583199
Contributeur : Emmanuel Trélat <>
Soumis le : jeudi 7 septembre 2017 - 13:17:01
Dernière modification le : samedi 9 septembre 2017 - 01:08:50

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  • HAL Id : hal-01583199, version 1
  • ARXIV : 1709.02735

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Christophe Prieur, Emmanuel Trélat. Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control. 2017. <hal-01583199>

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