In this talk, we consider the efficient and reliable solution of distributed optimal control problems governed by parametrized elliptic partial differential equations involving constraints on the control. The reduced basis method is used as a low-dimensional surrogate model to solve the optimal control problem. To this end, we introduce reduced basis spaces not only for the state and adjoint variable but also for the distributed control variable and propose rigorous error bounds for the error in the optimal control. The reduced basis optimal control problem and associated a posteriori error bounds can be efficiently evaluated in an offline-online computational procedure, thus making our approach relevant in the many-query or real-time context. We present numerical results for a model problem to show the validity of our approach.
|Number of pages||2|
|Publication status||Published - 1 Feb 2015|
|Event||8th Vienna International Conference on Mathematical Modelling, MATHMOD 2015 - Vienna University of Technology, Vienna, Austria|
Duration: 18 Feb 2015 → 20 Feb 2015
Conference number: 8
Bibliographical noteFunding Information:
This work was supported by the Excellence Initiative of the provides sharper error bounds that mimic the convergence German★ federal and state governments and the German Research The methodology in Zhang et al. (2014) not only (i) G★ eTrmhiasnwfoedrkerawlaasndsusptpaotretegdovebrynmtheentsExacnedlletnhceeGIenrimtiaatnivRe eosefatrhche The methodology in Zhang et al. (2014) not only (i) Foundation through Grant GSC 111. rartoeviodfesthsehaRrBperapeprrorxibmoautnidons,thbautmalismoic(iit)hedocoesnvseorgaetnacne FoeurmndaantiofendethrarlouagnhdGstraatnet gGoSvCern1m11e.nts and the German Research provides sharper error bounds that mimic the convergence German federal and state governments and the German Research rate of the RB approximation, but also (ii) does so at an FFoouunnddaattiioonn throughthrough GGrraanntt GSCGSC 111.111. rate of the RB approximation, but also (ii) does so at an Foundation through Grant GSC 111. Copyright © 2015, IFAC 719 C2405-8963 opyright ©© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.2015, IFAC 719 CPoeepry rreigvihetw © u 2n0d1er5 ,r eIFspAoCnsibility of International Federation of Automat7i1c 9Control. Copyright © 2015, IFAC 719
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