Controllability of the 1D Schrödinger equation using flatness

Philippe Martin (1) , Lionel Rosier (2) , Pierre Rouchon (1, 3)

1 CAS - Centre Automatique et Systèmes
2 CAOR - Centre de Robotique
3 QUANTIC - QUANTum Information Circuits

We derive in a direct way the exact controllability of the 1D Schrödinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in parametrizing the solution and the control by the derivatives of a “flat output”. This provides an explicit and very regular control achieving the exact controllability in the energy space.

Mots clés: Schrödinger equation; Partial differential equations; Boundary control; Exact controllability; Motion planning; Flatness

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Sciences de l'ingénieur [physics]; Automatique / Robotique

Philippe Martin, Lionel Rosier, Pierre Rouchon. Controllability of the 1D Schrödinger equation using flatness. Automatica, 2018, 91, pp.208 - 216. ⟨10.1016/j.automatica.2018.01.005⟩. ⟨hal-01769227⟩