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In this article a stabilizing feedback control is computed for a semilinear parabolic partial differential equation utilizing a nonlinear model predictive (NMPC) method. In each level of the NMPC algorithm the finite time horizon open loop…

Optimization and Control · Mathematics 2014-09-30 Alessandro Alla , Stefan Volkwein

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear parabolic systems on bounded domains. It is shown that the continuous-time boundary feedback applied in a sample-and-hold…

Optimization and Control · Mathematics 2017-01-10 Iasson Karafyllis , Miroslav Krstic

The present paper addresses the topic of boundary output feedback stabilization of parabolic-type equations, governed by linear differential operators which can be diagonalized by the introduction of adequate weighting functions (by means…

Optimization and Control · Mathematics 2023-02-27 Hugo Lhachemi , Ionut Munteanu , Christophe Prieur

We consider the stabilisation of solutions to the Cahn-Hilliard equation towards a given trajectory by means of a finite-dimensional static output feedback mechanism. Exponential stabilisation of the controlled state around the target…

Optimization and Control · Mathematics 2025-05-01 Herbert Egger , Marvin Fritz , Karl Kunisch , Sérgio S. Rodrigues

This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…

Optimization and Control · Mathematics 2026-04-15 Mohamed Ouzahra

We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…

Optimization and Control · Mathematics 2024-01-26 Michael Herty , Ferdinand Thein

Given a nonstationary trajectory of the Navier-Stokes system, a finite-dimensional feedback boundary controller stabilizing locally the system to the given trajectory is derived. Moreover the controller is supported in a given open subset…

Optimization and Control · Mathematics 2015-08-05 Sérgio S. Rodrigues

In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories.…

Optimization and Control · Mathematics 2021-04-06 Axel Kröner , Carlos N. Rautenberg , Sérgio S. Rodrigues

We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be…

Optimization and Control · Mathematics 2021-05-20 Timm Strecker , Ole Morten Aamo , Michael Cantoni

We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…

Optimization and Control · Mathematics 2025-01-24 Michael Herty , Ferdinand Thein

The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial…

Optimization and Control · Mathematics 2023-08-21 Karl Kunisch , Sérgio S. Rodrigues , Daniel Walter

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

We regard anisotropic Maxwell's equations as a boundary control and observation system on a bounded Lipschitz domain. The boundary is split into two parts: one part with perfect conductor boundary conditions and the other where the control…

Analysis of PDEs · Mathematics 2024-04-11 Nathanael Skrepek , Marcus Waurick

We consider the problem of stabilization to zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum. This problem was previously studied in…

Optimization and Control · Mathematics 2018-07-09 Andrey Fursikov , Lyubov Osipova

This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer…

Optimization and Control · Mathematics 2022-08-15 Stephan Gerster , Felix Nagel , Aleksey Sikstel , Giuseppe Visconti

The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…

Optimization and Control · Mathematics 2008-01-31 S. Nikitin

In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…

Analysis of PDEs · Mathematics 2012-11-07 Jonathan Touboul

The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…

Systems and Control · Electrical Eng. & Systems 2020-01-17 Andrea Cristofaro , Francesco Ferrante

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

The stabilizability to trajectories of the Schl\"ogl model is investigated in the norm of the natural state space for strong solutions, which is strictly contained in the standard pivot space of square integrable functions. As actuators a…

Optimization and Control · Mathematics 2022-12-06 Karl Kunisch , Sérgio S. Rodrigues