Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization
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| Název: | Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization |
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| Autoři: | Koudohode Florent(http://users.isc.tuc.gr/~fkoudohode), Μπεκιαρης-Λυμπερης Νικολαος(http://users.isc.tuc.gr/~nlimperis), Bekiaris-Liberis Nikolaos(http://users.isc.tuc.gr/~nlimperis) |
| Zdroj: | 2025 American Control Conference (ACC) |
| Publication Status: | Preprint |
| Informace o vydavateli: | IEEE, 2025. |
| Rok vydání: | 2025 |
| Témata: | Mathematics - Analysis of PDEs, Backstepping, Quantization, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Reaction-diffusion PDE, Analysis of PDEs (math.AP) |
| Popis: | 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. Accepted for presentation at 2025 American Control Conference (ACC), DENVER, Colorado, USA |
| Druh dokumentu: | Article Conference object |
| Popis souboru: | application/pdf |
| DOI: | 10.23919/acc63710.2025.11108079 |
| DOI: | 10.48550/arxiv.2501.15924 |
| Přístupová URL adresa: | http://arxiv.org/abs/2501.15924 http://purl.tuc.gr/dl/dias/732B793A-39DE-4326-B071-34FBD8635A3F |
| Rights: | STM Policy #29 CC BY NC ND |
| Přístupové číslo: | edsair.doi.dedup.....eb245b126c90e92ea058fee79f5520f6 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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.<br />Accepted for presentation at 2025 American Control Conference (ACC), DENVER, Colorado, USA |
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| DOI: | 10.23919/acc63710.2025.11108079 |