Controllability of the 1D Schrödinger equation using flatness
Authors: Philippe Martin, Lionel Rosier, Pierre Rouchon, Automatica, Vol. 91, pp.208-216, May 2018, DOI: 10.1016/j.automatica.2018.01.005
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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.
BibTeX:
@Article{,
author = {Philippe Martin, Lionel Rosier, Pierre Rouchon},
title = {Controllability of the 1D Schrödinger equation using flatness},
journal = {Automatica},
volume = {91},
pages = {208–216},
year = {2018},
abstract = {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.},
keywords = {Partial differential equations; Schrödinger equation; Boundary control; Exact controllability; Motion planning; Flatness},}
Download PDF
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.
BibTeX:
@Article{,
author = {Philippe Martin, Lionel Rosier, Pierre Rouchon},
title = {Controllability of the 1D Schrödinger equation using flatness},
journal = {Automatica},
volume = {91},
pages = {208–216},
year = {2018},
abstract = {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.},
keywords = {Partial differential equations; Schrödinger equation; Boundary control; Exact controllability; Motion planning; Flatness},}