Backstepping control of a wave PDE with unstable source terms and dynamic boundary

Christophe Roman (1) , Delphine Bresch-Pietri (2) , Eduardo Cerpa (3) , Christophe Prieur (1) , Olivier Sename (4)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 CAS - Centre Automatique et Systèmes
3 Departamento de Matematica, Universidad Tecnica Federico Santa Maria
4 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse

This letter presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation. The control is acting on a Robin's boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.

Domaines: Automatique / Robotique

Christophe Roman, Delphine Bresch-Pietri, Eduardo Cerpa, Christophe Prieur, Olivier Sename. Backstepping control of a wave PDE with unstable source terms and dynamic boundary. IEEE Control Systems Letters, 2018, 2 (3), pp.459-464. ⟨10.1109/LCSYS.2018.2841898⟩. ⟨hal-01815802⟩