A characterization of switched linear control systems with finite L 2 -gain

Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of the L2-gain is equivalent, for a large set of switched linear control systems, to the condition that the generalized spectral radius associated with any minimal realization of the original switched system is smaller than one

Generic controllability properties for the bilinear Schrödinger equation

International audienceIn [15] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schrödinger equation. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schrödinger operator. The aim of this paper is to show that these conditions are generic with respect to the uncontrolled and the controlled potential, denoted respectively by $V$ and $W$. More precisely, we prove that the Schrödinger equation is approximately controllable generically with respect to $W$ when $V$ is fixed and also generically with respect to $V$ when $W$ is fixed and non-constant. The results are obtained by analytic perturbation arguments and through the study of asymptotic properties of eigenfunctions

Adiabatic control of the Schr\"odinger equation via conical intersections of the eigenvalues

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 the latter are conical (as it happens generically). We provide sharp estimates of the relation between the error and the controllability time

Motion planning in quantum control via intersection of eigenvalues

International audienceIn this paper we consider the problem of inducing a transition in a controlled quantum mechanical system whose spectrum loses simplicity for some values of the control. We study the situation in which the Hamiltonian of the system is real, and we are in presence of two controls. In this case, eigenvalue crossings are generically conical. Adiabatic approximation is used to decouple a finite dimensional sub-system from the original one (usually infinite dimensional). The main advantage of this method is that as a byproduct of the controllability result it permits to get an explicit expression of the controls. Moreover it may be used in the case in which the dependence of the Hamiltonian from the controls is non-linear, for which at the moment, no other method works. In this paper we study the basic block of this controllability method, that is a two by two system whose spectrum presents a conical intersection. We show how to control exactly this system with a control strategy that can be slowed down. The possibility of slowing down the control law is essential to obtain an adiabatic decoupling from the rest of the system with an arbitrary precision

The seed laser system of the FERMI free-electron laser: design, performance and near future upgrades

Abstract An important trend in extreme ultraviolet and soft X-ray free-electron laser (FEL) development in recent years has been the use of seeding by an external laser, aimed to improve the coherence and stability of the generated pulses. The high-gain harmonic generation seeding technique was first implemented at FERMI and provided FEL radiation with high coherence as well as intensity and wavelength stability comparable to table-top ultrafast lasers. At FERMI, the seed laser has another very important function: it is the source of external laser pulses used in pump–probe experiments allowing one to achieve a record-low timing jitter. This paper describes the design, performance and operational modes of the FERMI seed laser in both single- and double-cascade schemes. In addition, the planned upgrade of the system to meet the challenges of the upgrade to echo-enabled harmonic generation mode is presented

Characterization of linear switched systems admitting a Barabanov norm

International audienceIn this paper we recall some general properties of extremal and Barabanov norms and we give a necessary and sufficient condition for a finite-dimensional continuoustime linear switched system to admit a Barabanov norm

Controllability of spin-boson systems

In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter