Obstruction to the bilinear control of the Gross-Pitaevskii equation: an example with an unbounded potential

Thomas Chambrion (1, 2, 3) , Laurent Thomann (2, 1)

1 EDP - Equations aux dérivées partielles
2 IECL - Institut Élie Cartan de Lorraine
3 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

In 1982, Ball, Marsden, and Slemrod proved an obstruction to the controllability of linear dynamics with a bounded bilinear control term. This note presents an example of nonlinear dynamics with respect to the state for which this obstruction still holds while the control potential is not bounded.

Mots clés: Gross-Pitaevskii equation; Nonlinear control system; controllability; bilinear control

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Thomas Chambrion, Laurent Thomann. Obstruction to the bilinear control of the Gross-Pitaevskii equation: an example with an unbounded potential. 2019. ⟨hal-02063308v1⟩