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

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.

Mots clés

Goh-transform Optimal control Semigroup theory Optimization in complex Banach spaces Second-order optimality conditions Partial differential equations Bilinear control systems Schrödinger equation

Domaines

Optimisation et contrôle [math.OC] Mathématiques [math]

Fichier principal

ABK_2016_v1.pdf (359.98 Ko)

Origine : Fichiers produits par l'(les) auteur(s)

Axel Kröner : Connectez-vous pour contacter le contributeur

https://hal.science/hal-01311421

Soumis le : mercredi 4 mai 2016-11:35:14

Dernière modification le : jeudi 1 février 2024-14:24:52

Archivage à long terme le : mardi 15 novembre 2016-20:16:00

Dates et versions

hal-01311421 , version 1 (04-05-2016)

Identifiants

HAL Id : hal-01311421 , version 1
DOI : 10.1137/17M1117653

Citer

Maria Soledad Aronna, Joseph Frédéric Bonnans, Axel Kröner. Optimal control of PDEs in a complex space setting; application to the Schrödinger equation. SIAM Journal on Control and Optimization, 2019, 57 (2), pp.1390-1412. ⟨10.1137/17M1117653⟩. ⟨hal-01311421⟩

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