Type of Publication:  Contribution to a conference collection 
Publication status:  Published 
Author:  Jäkle, Christian; Volkwein, Stefan 
Year of publication:  2020 
Conference:  SON 2020 : International Workshop on Dynamics, Optimization, and Computation : In honor of Michael Dellnitz' 60th birthday, Sep 27, 2021  Oct 1, 2021, Paderborn, Germany 
Published in:  Advances in Dynamics, Optimization and Computation : A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday / Junge, Oliver et al. (ed.).  Cham : Springer, 2020.  (Studies in Systems, Decision and Control ; 304).  pp. 238264.  ISSN 21984182.  eISSN 21984190.  ISBN 9783030512637 
Summary: 
In this chapter the authors consider the numerical treatment of a mixed integer optimal control problem governed by linear convectiondiffusion equations and binary control variables. Using relaxation techniques (introduced by [31] for ordinary differential equations) the original mixedinteger optimal control problem is transferred into a relaxed optimal control problem with no integrality constraints. After an optimal solution to the relaxed problem has been computed, binary admis sible controls are constructed by a sumup rounding technique. This allows us to construct – in an iterative process – binary admissible controls such that the cor responding optimal state and the optimal cost value approximate the original ones with arbitrary accuracy. However, using finite element (FE) methods to discretize the state and adjoint equations yield often to extensive systems which make the frequently calculations timeconsuming. Therefore, a modelorder reduction based on the proper orthogonal decomposition (POD) method is applied. Compared to the FE case, the POD approach yields to a significant acceleration of the CPU times while the error stays sufficiently small.

Subject (DDC):  510 Mathematics 
Bibliography of Konstanz:  Yes 
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JÄKLE, Christian, Stefan VOLKWEIN, 2020. PODbased mixedinteger optimal control of evolution systems. SON 2020 : International Workshop on Dynamics, Optimization, and Computation : In honor of Michael Dellnitz' 60th birthday. Paderborn, Germany, Sep 27, 2021  Oct 1, 2021. In: JUNGE, Oliver, ed. and others. Advances in Dynamics, Optimization and Computation : A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Cham:Springer, pp. 238264. ISSN 21984182. eISSN 21984190. ISBN 9783030512637
@inproceedings{Jakle2020PODba48957.2, title={PODbased mixedinteger optimal control of evolution systems}, year={2020}, number={304}, isbn={9783030512637}, issn={21984182}, address={Cham}, publisher={Springer}, series={Studies in Systems, Decision and Control}, booktitle={Advances in Dynamics, Optimization and Computation : A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday}, pages={238264}, editor={Junge, Oliver}, author={Jäkle, Christian and Volkwein, Stefan} }
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