Boundary control of a wave equation with in-domain damping

Abstract : This thesis is concerned by the boundary control of the one dimensional wave equation, which can be used to model a string (like a guitar string). The objective is to act at one boundary to control and stabilize the otherboundary which is considered to be an unstable dynamic boundary condition. This thesis suggests answers to both following questions:Consider that the unstable dynamics boundary condition has some unknown parameters. Is a nonlinear adaptive control law still performing efficiently, if the viscous damping taken equal to zero for its design is no longer neglected?How can we take into account the in-domain damping in order to stabilize the wave equation subject to dynamic boundary conditions?This thesis suggests a method to derive a Lyapunov analysis in order to prove the robustness mismatch ofparticular nonlinear adaptive control law as the answer of the first question. Then using infinite dimensionalbackstepping technique we develop feedback control law that exponentially stabilize the considered wave equation.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-01943937
Contributor : Abes Star <>
Submitted on : Tuesday, December 4, 2018 - 11:51:06 AM
Last modification on : Thursday, February 7, 2019 - 1:58:01 PM

File

ROMAN_2018_diffusion.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01943937, version 1

Citation

Christophe Roman. Boundary control of a wave equation with in-domain damping. Computer science. Université Grenoble Alpes, 2018. English. ⟨NNT : 2018GREAT053⟩. ⟨tel-01943937⟩

Share

Metrics

Record views

170

Files downloads

134