Adaptive Boundary Control of the Kuramoto-Sivashinsky Equation Under Intermittent Sensing
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913807090057216 |
|---|---|
| author | Belhadjoudja, Mohamed Camil Maghenem, Mohamed Witrant, Emmanuel Prieur, Christophe |
| author_facet | Belhadjoudja, Mohamed Camil Maghenem, Mohamed Witrant, Emmanuel Prieur, Christophe |
| contents | We study in this paper boundary stabilization, in the L2 sense, of the perturbed Kuramoto-Sivashinsky (KS) equation subject to intermittent sensing. We assume that we measure the state on a given spatial subdomain during certain time intervals, while we measure the state on the remaining spatial subdomain during the remaining time intervals. We assign a feedback law at the boundary of the spatial domain and force to zero the value of the state at the junction of the two subdomains. Throughout the study, the equation's destabilizing coefficient is assumed to be unknown and possibly space dependent but bounded. As a result, adaptive boundary controllers are designed under different assumptions on the perturbation. In particular, we guarantee input-to-state stability (ISS) when an upperbound on the perturbation's size is known. Otherwise, only global uniform ultimate boundedness (GUUB) is guaranteed. In contrast, when the state is measured at every spatial point all the time (full state measurement), convergence to an arbitrarily-small neighborhood of the origin is guaranteed, even if the perturbation's maximal size is unknown. Numerical simulations are performed to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Boundary Control of the Kuramoto-Sivashinsky Equation Under Intermittent Sensing Belhadjoudja, Mohamed Camil Maghenem, Mohamed Witrant, Emmanuel Prieur, Christophe Systems and Control Analysis of PDEs We study in this paper boundary stabilization, in the L2 sense, of the perturbed Kuramoto-Sivashinsky (KS) equation subject to intermittent sensing. We assume that we measure the state on a given spatial subdomain during certain time intervals, while we measure the state on the remaining spatial subdomain during the remaining time intervals. We assign a feedback law at the boundary of the spatial domain and force to zero the value of the state at the junction of the two subdomains. Throughout the study, the equation's destabilizing coefficient is assumed to be unknown and possibly space dependent but bounded. As a result, adaptive boundary controllers are designed under different assumptions on the perturbation. In particular, we guarantee input-to-state stability (ISS) when an upperbound on the perturbation's size is known. Otherwise, only global uniform ultimate boundedness (GUUB) is guaranteed. In contrast, when the state is measured at every spatial point all the time (full state measurement), convergence to an arbitrarily-small neighborhood of the origin is guaranteed, even if the perturbation's maximal size is unknown. Numerical simulations are performed to illustrate our results. |
| title | Adaptive Boundary Control of the Kuramoto-Sivashinsky Equation Under Intermittent Sensing |
| topic | Systems and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2403.18055 |