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Preprint-No.: <   341   >   Published in: May 2012   PDF-File: IGPM341_k.pdf
Title:A Certified Reduced Basis Method for Parametrized Elliptic Optimal Control Problems
Authors:Mark Kärcher and Martin A. Grepl
In this paper, we employ the reduced basis method as a surrogate model for the solu- tion of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the as- sumption of affine parameter dependence, the reduced order optimal control problem and the proposed bounds can be efficiently evaluated in an offline-online computational procedure. Numerical results are presented to confirm the validity of our approach.
Keywords:optimal control, reduced basis method, a posteriori error estimation, model order reduction, parameter–dependent systems
DOI: 10.1051/cocv/2013069
Publication:Control, optimisation and calculus of variations : COCV = Contrôle, optimisation et calcul des variations
20(2), 416-441 (2014)