Optimal control of PDEs in a complex space setting; application to the Schrödinger equation

Abstract : In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state equation is the Schrödinger one, with pointwise constraints on the "bilinear'" control. We derive first and second order optimality conditions and address in particular the case that the control enters the state equation and cost function linearly.
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https://hal.archives-ouvertes.fr/hal-01311421
Contributor : Axel Kröner <>
Submitted on : Wednesday, May 4, 2016 - 11:35:14 AM
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  • HAL Id : hal-01311421, version 1

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Maria Soledad Aronna, Joseph Frédéric Bonnans, Axel Kröner. Optimal control of PDEs in a complex space setting; application to the Schrödinger equation. [Research Report] INRIA. 2016. ⟨hal-01311421⟩

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