Name: Stabilization of an unstable reaction-diffusion PDE with input delay despite state and input quantization
Keywords: 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)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Conference object 08 Jul 2025Embargo end date: 01 Jan 2025Publisher:IEEEJournal:2025 American Control Conference (ACC)Funded by:EC | C-NORA

Authors: Koudohode Florent(http://users.isc.tuc.gr/~fkoudohode); 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);

doi: 10.23919/acc63710.2025.11108079 , 10.48550/arxiv.2501.15924

arXiv: http://arxiv.org/abs/2501.15924

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

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Abstract

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

Related Organizations

Technical University of Crete
Greece

Keywords

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)

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