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Related papers: Insensitizing controls for stochastic parabolic eq…

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One proves that the linear and semilinear stochastic parabolic equations with a multiplicative noise with a finite number of modes are exactly null controllable.

Analysis of PDEs · Mathematics 2011-06-14 Viorel Barbu

Let $u$ be the solution to the following stochastic evolution equation (1) du(t,x)& = &A u(t,x) dt + B \sigma(u(t,x)) dL(t),\quad t>0; u(0,x) = x taking values in an Hilbert space $\HH$, where $L$ is a $\RR$ valued L\'evy process, $A:H\to…

Probability · Mathematics 2015-07-06 Erika Hausenblas , Paul Andre Razafimandimby

In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…

Optimization and Control · Mathematics 2020-12-11 Jean-Michel Coron , Hoai-Minh Nguyen

We prove existence and uniqueness of the invariant measure and exponential mixing in the total-variation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions…

Probability · Mathematics 2022-09-21 Vahagn Nersesyan , Renaud Raquépas

We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…

Numerical Analysis · Mathematics 2021-09-28 Peter Benner , Tony Stillfjord , Christoph Trautwein

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

This paper deals with the null controllability of a coupled parabolic system, which is Kuramoto-Sivashinsky-Korteweg-de Vries equation coupled with heat equation through first order derivative. More precisely, we prove the null…

Analysis of PDEs · Mathematics 2022-05-20 Manish Kumar , Subrata Majumdar

This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…

Optimization and Control · Mathematics 2010-09-08 Peter Hokayem , Debasish Chatterjee , John Lygeros

This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…

Optimization and Control · Mathematics 2024-03-15 Areefa Khatoon , Abdur Raheem , Asma Afreen

The aim of this paper is to perform a Stackelberg strategy to control parabolic equations. We have one control, \textit{the leader}, that is responsible for a null controllability property; additionally, we have a control \textit{the…

Optimization and Control · Mathematics 2016-10-20 Víctor Hernández-Santamaría , Luz de Teresa

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 study the controllability results of impulsive neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are…

Probability · Mathematics 2016-02-19 El Hassan Lakhel

In this paper, the boundary flex control problem of non stationary equation governing the coupled mass and heat flow of a viscous incompressible fluid in a generalized Boussinesq approximation by assuming that viscosity and heat…

Analysis of PDEs · Mathematics 2012-07-18 Gol Kim

A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation,…

Analysis of PDEs · Mathematics 2015-03-12 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on a phase-field model of grain boundary motion, proposed in…

Analysis of PDEs · Mathematics 2020-10-05 Shodai Kubota , Ryota Nakayashiki , Ken Shirakawa

Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…

Optimization and Control · Mathematics 2020-06-02 Domènec Ruiz-Balet , Enrique Zuazua

This work serves as a continuation of our preceding paper [28]. In that study, we presented a separable variable method to derive the Lebeau-Robbiano spectral inequality for a specific degenerate parabolic equation and subsequently employed…

Optimization and Control · Mathematics 2026-05-19 Donghui Yang , Mengze Gu , Baozhu Guo , Ghadir Shokor

In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…

Optimization and Control · Mathematics 2015-01-07 Kenichi Fujishiro

The paper deals with the controllability of a degenerate beam equation. In particular, we assume that the left end of the beam is fixed, while a suitable control $f$ acts on the right end of it. As a first step we prove the existence of a…

Analysis of PDEs · Mathematics 2023-02-14 Alessandro Camasta , Genni Fragnelli

This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Ming Li , Fan Liu , Yifeng Xiong , Jie Xu , Tao Liu