Related papers: Approximate Controllability of the Two Trapped Ion…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
The article considers a two-level open quantum system, whose evolution is governed by the Gorini--Kossakowski--Lindblad--Sudarshan master equation with Hamiltonian and dissipation superoperator depending, correspondingly, on piecewise…
This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…
We study the exact controllability, by a reduced number of controls, of coupled cascade systems of PDE's and the existence of exact insensitizing controls for the scalar wave equation. We give a necessary and sufficient condition for the…
In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis…
In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schr\"odinger equation with two controls between two states…
In [14] Duca and Nersesyan proved a small-time controllability property of nonlinear Schr\"odinger equations on a d-dimensional torus $\mathbb{T}^d$. In this paper we study a similar property, in the linear setting, starting from a closed…
In this paper we present a constructive method to control the bilinear Schr\"odinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
Reparable systems are systems that are characterized by their ability to undergo maintenance actions when failures occur. These systems are often described by transport equations, all coupled through an integro-differential equation. In…
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…
Here is investigated the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schr\"odinger equation perturbed by a linear multiplicative Wiener process. The existence of…
In this paper, we prove an approximate controllability result for the linearized Boussinesq system around a fluid at rest, in a two dimensional channel, when the control acts only on the temperature, through the upper boundary.
We consider N independent quantum particles, in an infinite square potential well coupled to an external laser field. These particles are modelled by a system of linear Schr\"odinger equations on a bounded interval. This is a bilinear…
We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with…
We propose a method to establish the rapid stabilization of the bilinear Schr\"odinger control system and its linearized system, and the finite time stabilization of the linearized system using the Grammian operators. The analysis of the…
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
Quantum-optical techniques allow for generating controllable spin-spin interactions between ions, making trapped ions an ideal quantum simulator of Heisenberg chains. A single parameter, the detuning of the Raman coupling, allows to switch…
In this paper we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term. We analyze the existence, uniqueness and regularity of pointwise strong solutions in a bidimensional domain. We…
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…