Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization

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 cou...

Full description

Saved in:
Bibliographic Details
Main Authors Koudohode, Florent, Bekiaris-Liberis, Nikolaos
Format Journal Article
LanguageEnglish
Published 27.01.2025
Subjects
Computer Science - Systems and Control
Mathematics - Analysis of PDEs
Online AccessGet full text
DOI10.48550/arxiv.2501.15924

Cover

More Information
Summary: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.
DOI:10.48550/arxiv.2501.15924