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Related papers: Feedback stabilization of a 1D linear reaction-dif…

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We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…

Optimization and Control · Mathematics 2015-11-11 Delphine Bresch-Pietri , Christophe Prieur , Emmanuel Trélat

This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…

Optimization and Control · Mathematics 2020-12-29 Hugo Lhachemi , Christophe Prieur

This paper studies the design of a finite-dimensional output feedback controller for the stabilization of a reaction-diffusion equation in the presence of a sector nonlinearity in the boundary input. Due to the input nonlinearity, classical…

Optimization and Control · Mathematics 2022-07-13 Hugo Lhachemi , Christophe Prieur

Here we deal with the stabilization problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into…

Optimization and Control · Mathematics 2021-07-19 Ionut Munteanu

This paper addresses the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs with delayed boundary measurement. The output takes the form of a either Dirichlet or Neumann trace. The output delay can be arbitrarily…

Optimization and Control · Mathematics 2021-06-28 Hugo Lhachemi , Christophe Prieur

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

Optimization and Control · Mathematics 2024-01-22 Dandan Guan , Jie Qi , Mamadou Diagne

This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output…

Optimization and Control · Mathematics 2021-06-01 Hugo Lhachemi , Robert Shorten

This paper provides global exponential stabilization results by means of boundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial Differential Equations (PDEs) with nonlinearities of superlinear growth. The class of…

Optimization and Control · Mathematics 2019-03-26 Iasson Karafyllis , Miroslav Krstic

An explicit output-feedback boundary feedback law is introduced that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an $n$-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only…

Optimization and Control · Mathematics 2015-11-23 Rafael Vazquez , Miroslav Krstic

In this paper, a delay compensation design method based on PDE backstepping is developed for a two-dimensional reaction-diffusion partial differential equation (PDE) with bilateral input delays. The PDE is defined in a rectangular domain,…

Optimization and Control · Mathematics 2023-07-10 Dandan Guan , Yanmei Chen , Jie Qi , Linglong Du

This paper investigates the output feedback boundary control of reaction-diffusion equations with either distributed or boundary measurement by means of a finite-dimensional observer. A constructive method dealing with the design of…

Optimization and Control · Mathematics 2021-08-25 Hugo Lhachemi , Christophe Prieur

This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the…

Optimization and Control · Mathematics 2022-07-13 Hugo Lhachemi , Christophe Prieur

The general context of this work is the feedback control of an infinite-dimensional system so that the closed-loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically,…

Optimization and Control · Mathematics 2021-08-18 Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat

This paper investigates the output feedback setpoint regulation control of a reaction-diffusion equation by means of boundary control. The considered reaction-diffusion plant may be open-loop unstable. The proposed control strategy consists…

Optimization and Control · Mathematics 2021-12-10 Hugo Lhachemi , Christophe Prieur

This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in…

Optimization and Control · Mathematics 2020-04-20 Imene Aicha Djebour , Takéo Takahashi , Julie Valein

This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a…

Optimization and Control · Mathematics 2020-03-17 Hugo Lhachemi , Robert Shorten

This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…

Optimization and Control · Mathematics 2021-08-18 Hugo Lhachemi , Christophe Prieur , Robert Shorten

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general…

Optimization and Control · Mathematics 2020-07-07 Andrii Mironchenko , Christophe Prieur , Fabian Wirth

This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…

Optimization and Control · Mathematics 2023-10-19 Constantinos Kitsos , Emilia Fridman

We investigate a nonlinear parabolic partial differential equation whose boundary conditions contain a single control input. This model describes a chemical reaction of the type ``$A \to $ product'', occurring in a dispersed flow tubular…

Analysis of PDEs · Mathematics 2025-11-07 Yevgeniia Yevgenieva , Alexander Zuyev , Peter Benner
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