Controllability of the 1D Schr\"odinger equation using flatness
Philippe Martin, Lionel Rosier, Pierre Rouchon
TL;DR
This paper demonstrates the exact controllability of the 1D free Schrödinger equation using a flatness approach, providing explicit controls through a parametrization by derivatives of a flat output.
Contribution
It introduces a direct flatness-based method to achieve explicit and regular controls for the Schrödinger equation's controllability.
Findings
Explicit control functions are derived for the Schrödinger equation.
The method achieves controllability in the energy space.
Controls are parametrized by derivatives of a flat output.
Abstract
We derive in a direct way the exact controllability of the 1D free Schr\"odinger 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.
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