7,103 research outputs found
Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability
The aim of this work is to study the controllability of the bilinear
Schr\"odinger equation on compact graphs. In particular, we consider the
equation (BSE) in the Hilbert space
, with being a compact graph. The
Laplacian is equipped with self-adjoint boundary conditions, is a
bounded symmetric operator and with . We
provide a new technique leading to the global exact controllability of the
(BSE) in with . Afterwards, we introduce the
"energetic controllability", a weaker notion of controllability useful when the
global exact controllability fails. In conclusion, we develop some applications
of the main results involving for instance star graphs
- …