Related papers: Controllability issues for continuous-spectrum sys…
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…
A variety of physically relevant bilinear Schr\"odinger equations are known to be approximately controllable in large times. There are however examples which are approximately controllable in large times, but not in small times. This…
In finite dimensions, controllability of bilinear quantum control systems can be decided quite easily in terms of the "Lie algebra rank condition" (LARC), such that only the systems Lie algebra has to be determined from a set of generators.…
This paper studies the local exact controllability and the local stabilization of the semilinear Schr\"odinger equation posed on a product of $n$ intervals ($n\ge 1$). Both internal and boundary controls are considered, and the results are…
In this work, we study the bilinear optimal stabilization of a non-homogeneous Fokker-Planck equation. We first study the problem of optimal control in a finite-time interval and then focus on the case of the infinite time horizon. We…
In this paper we estimate the minimal controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the controllability time if the image of the control matrix is…
In this work, we investigate the $L^p$- partial null controllability of the abstract semilinear fractional-order differential inclusion with nonlocal conditions. The set of admissible controls is characterized by $u\in L^p(I,U)$,…
The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the…
In this paper we study the bilinear-control problem for the linear and non-linear Schr{\"o}dinger equation with harmonic potential. By the means of different examples, we show how space-time smoothing effects (Strichartz estimates, Kato…
In this work, the null controllability problem for a linear system in $\ell^2$ is considered, where the matrix of a linear operator describing the system is an infinite matrix with $\lambda\in \mathbb R$ on the main diagonal and 1s above…
We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…
In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system.…
We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control. Beauchard and Laurent proved that, under an appropriate non degeneracy assumption, this system is controllable, locally around the ground state, in…
Well-known Bloch equations describe the spin systems (electronic and nuclear) for any scale of time, from transient processes to steady states. Usually in solids T_2 << T_1. The question arises: what are the approximations that should be…
This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss the approximate controllability of…
The $U\rightarrow +\infty$ one-dimensional Hubbard model in an electric field has be exactly solved, with an emphasis on the charge current. It is found that undamped Bloch oscillations extensively exist in the system. Such conclusion has…
Here is considered application of Spin(m) groups in theory of quantum control of chain with spin-1/2 systems. It may be also compared with m-dimensional analogues of Bloch sphere, but has nontrivial distinctions for chain with more than one…
We present sufficient conditions for exact controllability of a semilinear infinite dimensional dynamical system. The system mild solution is formed by a noncompact semigroup and a nonlinear disturbance that does not need to be Lipschitz…
In [15] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schr\"odinger equation. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the…
This paper deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the…