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

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.

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Automatique / Robotique

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Christophe Prieur : Connectez-vous pour contacter le contributeur

https://hal.science/hal-01815802

Soumis le : jeudi 14 juin 2018-15:27:23

Dernière modification le : mercredi 18 décembre 2024-10:11:52

Archivage à long terme le : samedi 15 septembre 2018-14:21:01

Dates et versions

hal-01815802 , version 1 (14-06-2018)

Identifiants

HAL Id : hal-01815802 , version 1
DOI : 10.1109/LCSYS.2018.2841898

Citer

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⟩

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