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Related papers: Stabilization of a Wave-Heat Cascade System

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Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupling cascade term. This is done by deriving an observability…

Optimization and Control · Mathematics 2025-06-13 Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat

This paper solves the problem of output feedback stabilization for a cascade of N heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar…

Optimization and Control · Mathematics 2025-06-13 Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat

We study boundary controllability of one-dimensional coupled hyperbolic-parabolic cascades, focusing on the fine structure of reachable sets. The main model is a wave-heat cascade in which a boundary control acts on the wave equation and…

Optimization and Control · Mathematics 2026-01-27 Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat

We study the output feedback exponential stabilization for a 1-d wave PDE with dynamic boundary. With only one measurement, we construct an infinite-dimensional state observer to trace the state and design an estimated state based…

Optimization and Control · Mathematics 2021-05-04 Zhan-Dong Mei

We study the output feedback exponential stabilization of a one-dimensional unstable wave equation, where the boundary input, given by the Neumann trace at one end of the domain, is the sum of the control input and the total disturbance.…

Optimization and Control · Mathematics 2017-06-08 Hua-Cheng Zhou , George Weiss

This paper addresses the problem of feedback stabilization of a cascade of two heat equations that are coupled in the boundary conditions, the input being a boundary control for the first component of the cascade. Two distinct control input…

Optimization and Control · Mathematics 2025-06-13 Hugo Lhachemi , Christophe Prieur , Emmanuel Trélat

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 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

This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance.…

Optimization and Control · Mathematics 2017-06-08 Hua-Cheng Zhou , George Weiss

We consider the strong stabilization of small amplitude gravity water waves in a two dimensional rectangular domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a…

Analysis of PDEs · Mathematics 2020-03-24 Pei Su , Marius Tucsnak , George Weiss

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

In this paper, we analyze the output stabilization problem for cascaded nonlinear ODE with $1-d$ heat diffusion equation affected by both in-domain and boundary perturbations. We assume that the only available part of states is the first…

Optimization and Control · Mathematics 2025-02-04 Abdallah Ben Abdallah , Mohsen Dlala

In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundary conditions: Dirichlet- Dirichlet and Dirichlet-Neumann. In…

Optimization and Control · Mathematics 2025-10-07 Patricio Guzmán , Agustín Huerta , Hugo Parada

This paper investigates the output feedback stabilization of parabolic equation with Lipschitz nonlinearity over general multidimensional domain using spectral geometry theories. First, a novel nonlinear observer is designed, and the error…

Optimization and Control · Mathematics 2026-01-21 Kai Liu , Hua-Cheng Zhou , Zhong-Jie Han , Xiangyang Peng

In this paper, we are concerned with the state feedback stabilization of ODE-PDE cascade systems governed by a linear ordinary differential equation and the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to the…

Analysis of PDEs · Mathematics 2018-01-04 Habib Ayadi

In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control.…

Optimization and Control · Mathematics 2026-05-12 Zhan-Dong Mei , Lan-Xi Tang

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 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

In this paper, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an anti-stable stochastic heat equation with Neumann boundary actuation and unknown boundary…

Optimization and Control · Mathematics 2022-01-04 Ze-Hao Wu , Hua-Cheng Zhou , Feiqi Deng , Bao-Zhu Guo
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