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Bilinear Control of Schrödinger PDEs

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Encyclopedia of Systems and Control

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Abstract

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.

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Author information

Authors and Affiliations

  1. CNRS, CMLS, Ecole Polytechnique, 91120, Palaiseau, France

    Karine Beauchard

  2. Centre Automatique et Systmes, Mines ParisTech, 60 Bd Saint-Michel, 75272, Paris Cedex 06, France

    Pierre Rouchon

Authors
  1. Karine Beauchard
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  2. Pierre Rouchon
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Corresponding author

Correspondence to Karine Beauchard .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2013 Springer-Verlag London

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Beauchard, K., Rouchon, P. (2013). Bilinear Control of Schrödinger PDEs. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_12-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_12-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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