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Related papers: Exact Controllability of linear KP-I equation

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This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…

Optimization and Control · Mathematics 2026-05-26 Liying Sun , Xiaohan Wang , Yongyi Yu

The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [25]. However, the proof is by contradiction arguments and the value of the observability constant remains unknown,…

Analysis of PDEs · Mathematics 2019-11-12 Joachim Krieger , Shengquan Xiang

We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in presence of quasi-linear perturbations, namely nonlinearities containing up to three…

Analysis of PDEs · Mathematics 2017-03-08 Pietro Baldi , Giuseppe Floridia , Emanuele Haus

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 is devoted to the controllability of linear systems of two coupled parabolic equations when the coupling involves a space dependent first order term. This system is set on an bounded interval, and the first equation is controlled…

Analysis of PDEs · Mathematics 2017-01-20 Michel Duprez

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…

Optimization and Control · Mathematics 2019-06-11 Xiuchun Bi , Jingrui Sun , Jie Xiong

This paper is devoted to prove the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We consider the case where the coupling matrix A…

Analysis of PDEs · Mathematics 2019-02-26 S. Avdonin , L. de Teresa

For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We…

Optimization and Control · Mathematics 2017-10-24 Rabah Rabah , Grigory Sklyar , Pavel Yu. Barkhayev , Pavel Barkhayev , Grzegorz Szkibiel

The aim of this paper is to study the null controllability of a class of quasilinear parabolic equations. In a first step we prove that the associated linear parabolic equations with non-constant diffusion coefficients are approximately…

Analysis of PDEs · Mathematics 2023-09-28 Nicolae Cindea , Geoffrey Lacour

We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…

Optimization and Control · Mathematics 2021-01-14 S. A. Belbas

In this paper, we study approximate and exact controllability of the linear difference equation $x(t) = \sum\_{j=1}^N A\_j x(t - \Lambda\_j) + B u(t)$ in $L^2$, with $x(t) \in \mathbb C^d$ and $u(t) \in \mathbb C^m$, using as a basic tool a…

Optimization and Control · Mathematics 2019-11-11 Yacine Chitour , Guilherme Mazanti , Mario Sigalotti

This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…

Optimization and Control · Mathematics 2015-10-15 Mouhamadou Dath , Philippe Jouan

We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…

Analysis of PDEs · Mathematics 2021-12-03 Catalin-George Lefter , Elena-Alexandra Melnig

Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…

Optimization and Control · Mathematics 2012-04-17 Zbigniew Bartosiewicz

The paper is devoted to the exact controllability of a system of coupled abstract wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman type condition and give a description of the…

Analysis of PDEs · Mathematics 2020-01-06 Veli Shakhmurov

In this paper we deal with the controllability problem for some Sobolev type equations. We show that the equations cannot be driven to zero if the control region is strictly supported within the domain. Nevertheless, we also prove that it…

Analysis of PDEs · Mathematics 2024-02-02 F. W. Chaves-Silva , Diego A. Souza

This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…

Optimization and Control · Mathematics 2013-10-22 Qi Lü

We prove exact controllability for quasi-linear Hamiltonian Schr\"odinger equations on tori of dimension greater or equal then two. The result holds true for sufficiently small initial conditions satisfying natural minimal regularity…

Analysis of PDEs · Mathematics 2023-03-20 Felice Iandoli , Jingrui Niu

In this article we study the internal controllability of 1D linear hyperbolic balance laws when the number of controls is equal to the number of state variables. The controls are supported in space in an arbitrary open subset. Our main…

Optimization and Control · Mathematics 2024-10-22 Long Hu , Guillaume Olive

This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…

Optimization and Control · Mathematics 2025-06-19 David Ohlin , Richard Pates , Murat Arcak