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Journal Articles SIAM Journal on Control and Optimization Year : 2009

Local exact controllability and stabilizability of the nonlinear Schrödinger equation on a bounded interval

Abstract

This paper studies the exact controllability and the stabilization of the cubic Schrödinger equation posed on a bounded interval. Both internal and boundary controls are considered, and the results are given first in a periodic setting, and next with Dirichlet (resp., Neumann) boundary conditions. It is shown that the systems with either an internal control or a boundary control are locally exactly controllable in the classical Sobolev space Hs for any s ≥ 0. It is also shown that the systems with an internal stabilization are locally exponentially stabilizable in Hs for any s ≥ 0.
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Dates and versions

hal-00600889 , version 1 (16-06-2011)

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Lionel Rosier, Bing-Yu Zhang. Local exact controllability and stabilizability of the nonlinear Schrödinger equation on a bounded interval. SIAM Journal on Control and Optimization, 2009, 48 (2), pp.972-992. ⟨10.1137/070709578⟩. ⟨hal-00600889⟩
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