Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917903546187776 |
|---|---|
| author | Koudohode, Florent Bekiaris-Liberis, Nikolaos |
| author_facet | Koudohode, Florent Bekiaris-Liberis, Nikolaos |
| contents | We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay, we reformulate the problem as an actuated transport PDE coupled with the original reaction-diffusion PDE. Then, we design a quantized predictor-based feedback mechanism that employs a dynamic switching strategy to adjust the quantization range and error over time. The stability of the closed-loop system is proven properly combining backstepping with a small-gain approach and input-to-state stability techniques, for deriving estimates on solutions, despite the quantization effect and the system's instability. We also extend this result to the input quantization case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization Koudohode, Florent Bekiaris-Liberis, Nikolaos Systems and Control Analysis of PDEs We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay, we reformulate the problem as an actuated transport PDE coupled with the original reaction-diffusion PDE. Then, we design a quantized predictor-based feedback mechanism that employs a dynamic switching strategy to adjust the quantization range and error over time. The stability of the closed-loop system is proven properly combining backstepping with a small-gain approach and input-to-state stability techniques, for deriving estimates on solutions, despite the quantization effect and the system's instability. We also extend this result to the input quantization case. |
| title | Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization |
| topic | Systems and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2501.15924 |