Backstepping Observer Based-Control for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping

Christophe Roman (1, 2) , Delphine Bresch-Pietri (2) , Eduardo Cerpa (3) , Christophe Prieur (1) , Olivier Sename (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
3 UTFSM - Universidad Tecnica Federico Santa Maria [Valparaiso]

This paper presents a backstepping control design for a one-dimensional wave PDE with in-domain viscous damping , subject to a dynamical anti-damped boundary condition. Its main contribution is the design of an observer-based control law which stabilizes the wave PDE velocity, using only boundary mesurements. Numerical simulations on an oil-inspired example show the relevance of our result and illustrate the merits of this control design.

Mots clés: Exponential stabilisation; Source terms; Observer based control; Wave equation; Boundary control of PDEs; Infinite Dimensional Systems; Backstepping control design

Domaines: Automatique / Robotique

Christophe Roman, Delphine Bresch-Pietri, Eduardo Cerpa, Christophe Prieur, Olivier Sename. Backstepping Observer Based-Control for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping. CDC 2016 - 55th IEEE Conference on Decision and Control, ieee, Dec 2016, Las Vegas, NV, United States. ⟨hal-01413025v2⟩