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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.
For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control systems, th
In this paper we present necessary and sufficient conditions to guarantee the existence of invariant cones, for semigroup actions, in the space of the $k$-fold exterior product. As consequence we establish a necessary and sufficient condition for con
In this paper we present an extension to the case of $L^1$-controls of a famous result by Ball--Marsden--Slemrod on the obstruction to the controllability of bilinear control systems in infinite dimensional spaces.
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty allows us to prove the existence of minimizers of
A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the control field,