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In this paper, we study the null and approximate controllability of a class of fully nonlocal coupled stochastic reaction--convection--diffusion systems. The system consists of two forward stochastic parabolic equations driven by general…

Optimization and Control · Mathematics 2026-03-31 Abdellatif Elgrou , Federica Gregorio , Abdelaziz Rhandi

The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…

Optimization and Control · Mathematics 2010-03-31 Xu Zhang

In this paper, we study the problem of controllability of Schr\"odinger equation. We prove that the system is exactly controllable in infinite time to any position. The proof is based on an inverse mapping theorem for multivalued functions.…

Analysis of PDEs · Mathematics 2011-10-07 Vahagn Nersesyan , Hayk Nersisyan

In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of…

Analysis of PDEs · Mathematics 2013-07-09 Camille Laurent

We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schr\"odinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability,…

Optimization and Control · Mathematics 2013-02-19 Ugo Boscain , Marco Caponigro , Mario Sigalotti

In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…

Analysis of PDEs · Mathematics 2024-03-14 Said Boulite , Abdellatif Elgrou , Lahcen Maniar , Omar Oukdach

In this paper we prove an approximate controllability result for the bilinear Schr\"odinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schr\"odinger operator than those…

Optimization and Control · Mathematics 2013-02-14 Ugo Boscain , Marco Caponigro , Thomas Chambrion , Mario Sigalotti

Strichartz estimates, well-posedness theory and long time behavior for (nonlinear) Schr\"odinger equations on waveguide manifolds $\mathbb{R}^m \times \mathbb{T}^n$ are intensively studied in recent decades while the corresponding control…

Analysis of PDEs · Mathematics 2025-02-20 Jingrui Niu , Zehua Zhao

The aim of this work is to study the controllability of the Schr\"odinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-\Delta u(t)~~~~~\text{ on }\Omega(t) \tag{$\ast$} \end{equation} with Dirichlet boundary conditions,…

Analysis of PDEs · Mathematics 2022-11-28 Alessandro Duca , Romain Joly , Dmitry Turaev

The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…

Optimization and Control · Mathematics 2014-05-29 Haisen Zhang , Xu Zhang

This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…

Optimization and Control · Mathematics 2016-12-09 Qi Lu , Xu Zhang

The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…

Optimization and Control · Mathematics 2022-09-21 Liangying Chen , Qi Lü

We consider a system described by a controlled bilinear Schr{\"o}dinger equation with three external inputs. We provide a constructive method to approximately steer the system from a given energy level to a superposition of energy levels…

Optimization and Control · Mathematics 2015-02-25 Paolo Mason , Francesca Chittaro

The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…

Optimization and Control · Mathematics 2018-12-27 Hélène Frankowska , Xu Zhang

This paper deals with a stochastic optimal feedback control problem for the controlled stochastic partial differential equations. More precisely, we establish the existence of stochastic optimal feedback control for the controlled…

Probability · Mathematics 2025-01-07 Gaofeng Zong

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…

Probability · Mathematics 2015-05-13 S. Bonaccorsi , F. Confortola , E. Mastrogiacomo

We prove the approximate controllability of a bilinear Schr\"odinger equation modelling a two trapped ions system. A new spectral decoupling technique is introduced, which allows to analyze the controllability of the infinite-dimensional…

Optimization and Control · Mathematics 2014-12-10 Esteban Paduro , Mario Sigalotti

We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear…

Optimization and Control · Mathematics 2015-05-13 Karine Beauchard , Jean-Michel Coron , Pierre Rouchon

We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their…

Mathematical Physics · Physics 2024-07-11 Aitor Balmaseda , Davide Lonigro , Juan Manuel Pérez-Pardo

A control problem with terminal overdetermination is considered for the higher order nonlinear Schr\"odinger equation on a bounded interval. The boundary condition on the space derivative is chosen as the control. Results on global…

Analysis of PDEs · Mathematics 2023-12-07 Andrei V. Faminskii