Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Bilinear Control of Schrödinger PDEs

  • Karine BeauchardEmail author
  • Pierre Rouchon
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_12


This entry is an introduction to modern issues about controllability of Schrödinger PDEs with bilinear controls. This model is pertinent for a quantum particle, controlled by an electric field. We review recent developments in the field, with discrimination between exact and approximate controllabilities, in finite or infinite time. We also underline the variety of mathematical tools used by various teams in the last decade. The results are illustrated on several classical examples.


Approximate controllability Global exact controllability Local exact controllability Quantum particles Schrödinger equation Small-time controllability 
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The authors were partially supported by the “Agence Nationale de la Recherche” (ANR), Projet Blanc EMAQS number ANR-2011-BS01-017-01.


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© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.CNRS, CMLSEcole PolytechniquePalaiseauFrance
  2. 2.Centre Automatique et SystmesMines ParisTechParis Cedex 06France