2 research outputs found
Efficient finite dimensional approximations for the bilinear Schrodinger equation with bounded variation controls
This the text of a proceeding accepted for the 21st International Symposium
on Mathematical Theory of Networks and Systems (MTNS 2014). We present some
results of an ongoing research on the controllability problem of an abstract
bilinear Schrodinger equation. We are interested by approximation of this
equation by finite dimensional systems. Assuming that the uncontrolled term
has a pure discrete spectrum and the control potential is in some sense
regular with respect to we show that such an approximation is possible.
More precisely the solutions are approximated by their projections on finite
dimensional subspaces spanned by the eigenvectors of . This approximation is
uniform in time and in the control, if this control has bounded variation with
a priori bounded total variation. Hence if these finite dimensional systems are
controllable with a fixed bound on the total variation of the control then the
system is approximatively controllable. The main outcome of our analysis is
that we can build solutions for low regular controls such as bounded variation
ones and even Radon measures
Total Variation of the Control and Energy of Bilinear Quantum Systems
Abstract — In the present note, we give two examples of bilinear quantum systems showing good agreement between the total variation of the control and the variation of the energy of solutions, with bounded or unbounded coupling term. The corresponding estimates in terms of the total variation of the control appear to be optimal. I