A certified reduced basis method for parametrized elliptic optimal control problems∗. (7th April 2014)

• Record Type: Journal Article
• Authors: Kärcher, Mark; Grepl, Martin A.
• Is Part Of: ESAIM. Volume 20:Number 2(2014:Apr.)
• Page Start: 416
• Page End: 441
• Publication Date: 2014-04-07
• Subjects: Optimal control, -- reduced basis method, -- a posteriori error estimation, -- model order reduction, -- parameter-dependent systems; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013069
• Languages: English
• ISSNs: 1292-8119

Abstract

Abstract : In this paper, we employ the reduced basis method as a surrogate model for the solution 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 assumption 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.