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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

We introduce a novel Lyapunov function for stabilization of linear Vlasov--Fokker--Planck type equations with stiff source term. Contrary to existing results relying on transport properties to obtain stabilization, we present results based…

Optimization and Control · Mathematics 2020-02-12 Michael Herty , Shi Jin , Yuhua Zhu

A boundary feedback stabilisation problem of non-uniform linear hyperbolic systems of balance laws with additive disturbance is discussed. A continuous and a corresponding discrete Lyapunov function is defined. Using an…

Optimization and Control · Mathematics 2020-06-09 Mapundi Kondwani Banda , Gediyon Weldegiyorgis

The stabilization of nonautonomous parabolic equations is achieved by feedback inputs tuning a finite number of actuators, where it is assumed that the input is subject to a time delay. To overcome destabilizing effects of the time delay,…

Optimization and Control · Mathematics 2025-11-21 Karl Kunisch , Sérgio S. Rodrigues

This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an…

Optimization and Control · Mathematics 2019-04-22 Matthieu Barreau , Frédéric Gouaisbaut , Alexandre Seuret

In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is…

Optimization and Control · Mathematics 2022-03-25 Yusen Meng , Hongyinping Feng

The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…

Optimization and Control · Mathematics 2024-04-09 B. Hassoun , R. Al-Saphory , S. Hassan

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

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping…

Analysis of PDEs · Mathematics 2017-06-02 Varga K. Kalantarov , Edriss S. Titi

In this article, we develop a fully discrete numerical scheme for the one-dimensional (1D) and two-dimensional (2D) viscous Burgers equations with nonlinear Neumann boundary feedback control. The temporal discretization employs a…

Numerical Analysis · Mathematics 2026-02-03 Shishu Pal Singh , Sudeep Kundu

This paper presents a global stabilization result of the viscous Burgers' equation with the memory term by applying Neumann boundary feedback control laws. We construct suitable feedback control inputs using the control Lyapunov functional…

Optimization and Control · Mathematics 2026-02-03 Shishu Pal Singh , Sudeep Kundu

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 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 present a computational study of a simple finite-dimensional feedback control algorithm for stabilizing solutions of infinite-dimensional dissipative evolution equations such as reaction-diffusion systems, the Navier-Stokes equations and…

Analysis of PDEs · Mathematics 2017-07-11 Evelyn Lunasin , Edriss S. Titi

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

Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to systems with deterministic and…

Systems and Control · Electrical Eng. & Systems 2022-02-17 Andrey Polyakov , Miroslav Krstic

This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…

Analysis of PDEs · Mathematics 2022-08-31 Nicolas Vanspranghe , Francesco Ferrante , Christophe Prieur

The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…

Analysis of PDEs · Mathematics 2007-05-23 Jinqiao Duan , Andrei V. Fursikov

In this paper, we focus on the rapid boundary stabilization of 1D nonlinear parabolic equations via the modal decomposition method. The nonlinear term is assumed to satisfy certain local Lipschitz continuity and global growth conditions.…

Analysis of PDEs · Mathematics 2025-10-07 Yu Xiao , Can Zhang

The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…

Systems and Control · Electrical Eng. & Systems 2021-04-22 Sebastian A. Nugroho , Suyash C. Vishnoi , Ahmad F. Taha , Christian G. Claudel