Rapid stabilization for a wave equation with boundary disturbance
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911194072219648 |
|---|---|
| author | Guzmán, Patricio Huerta, Agustín Parada, Hugo |
| author_facet | Guzmán, Patricio Huerta, Agustín Parada, Hugo |
| contents | In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundary conditions: Dirichlet- Dirichlet and Dirichlet-Neumann. In both cases, we design a feedback law, located at the same place as the unknown disturbance, that forces the exponential decay of the energy for any desired decay rate while suppressing the effects of the unknown disturbance. For the feedback design, we employ the backstepping method, Lyapunov techniques and the sign multivalued operator. The well-posedness of the closed-loop system, which is a differential inclusion, is shown with the maximal monotone operator theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rapid stabilization for a wave equation with boundary disturbance Guzmán, Patricio Huerta, Agustín Parada, Hugo Optimization and Control Systems and Control Analysis of PDEs In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundary conditions: Dirichlet- Dirichlet and Dirichlet-Neumann. In both cases, we design a feedback law, located at the same place as the unknown disturbance, that forces the exponential decay of the energy for any desired decay rate while suppressing the effects of the unknown disturbance. For the feedback design, we employ the backstepping method, Lyapunov techniques and the sign multivalued operator. The well-posedness of the closed-loop system, which is a differential inclusion, is shown with the maximal monotone operator theory. |
| title | Rapid stabilization for a wave equation with boundary disturbance |
| topic | Optimization and Control Systems and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04893 |