Robustness of an Adaptive Output Feedback for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping

Christophe Roman 1, 2 Delphine Bresch-Pietri 1 Christophe Prieur 2 Olivier Sename 1
1 GIPSA-SLR - SLR
GIPSA-DA - Département Automatique
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : This paper presents a robustness result for the use of a previously developed adaptive output-feedback controller designed for a pure wave PDE. This one-dimensional wave PDE has a boundary actuation opposite to an unknown anti-damping dynamics boundary. We prove that stabilization is still valid in the case of in-domain viscous damping using a controller designed neglecting the damping, provided that the damping coefficient is small enough. Our robustness proof grounds on the use of an alternative pure wave PDE, neglecting the in-domain damping. We compare these two systems and apply a tailored backstepping transformation to carry out Lyapunov analysis. Numerical simulations show the relevance of our result for drilling applications and illustrate the merits of this control design.
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Communication dans un congrès
American Control Conférence (ACC 2016), Jul 2016, Boston, United States. 2016
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https://hal.archives-ouvertes.fr/hal-01349352
Contributeur : Christophe Roman <>
Soumis le : mercredi 27 juillet 2016 - 12:01:01
Dernière modification le : jeudi 1 décembre 2016 - 21:53:16

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  • HAL Id : hal-01349352, version 1

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Christophe Roman, Delphine Bresch-Pietri, Christophe Prieur, Olivier Sename. Robustness of an Adaptive Output Feedback for an Anti-Damped Boundary Wave PDE in Presence of In-Domain Viscous Damping. American Control Conférence (ACC 2016), Jul 2016, Boston, United States. 2016. <hal-01349352>

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