Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2019

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

Résumé

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

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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. SIAM Journal on Control and Optimization, 2019, 57 (2), pp.1390-1412. ⟨10.1137/17M1117653⟩. ⟨hal-01311421⟩
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