Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets

Nabile Boussaid (1) , Marco Caponigro (2) , Thomas Chambrion (3, 4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 M2N - Modélisation mathématique et numérique
3 IECL - Institut Élie Cartan de Lorraine
4 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

We consider a linear Schrödinger equation with an unbounded bilinear control term. The control term is the derivative of function with bounded variations (impulsive control). Well-posedness results and regularity of the associated propagators follow from classical theory from Kato. As a byproduct, one obtains a topological obstruction to exact controllability of the system in the spirit of the results of Ball, Marsden and Slemrod.

Domaines: Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets. 2019 IEEE 58th Conference on Decision and Control (CDC), Dec 2019, Nice, France. ⟨10.1109/CDC40024.2019.9029277⟩. ⟨hal-02747636⟩