Title data
Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Efficient MPC for parabolic PDEs with goal oriented error estimation.
Bayreuth
,
2020
.  26 p.
Official URL:
Project information
Project title: 
Project's official title  Project's id 

Specialized Adaptive Algorithms for Model Predictive Control of PDEs  GR 1569/171  Specialized Adaptive Algorithms for Model Predictive Control of PDEs  SCHI 1379/51 

Project financing: 
Deutsche Forschungsgemeinschaft

Abstract in another language
We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context. To this end, we present a truncated cost functional as objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity. This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.
Further data
Item Type: 
Preprint, postprint

Keywords: 
Model predictive control; goal oriented error estimation; adaptive numerical discretization; partial differential equations

Subject classification: 
Mathematics Subject Classification Code: 35Q93, 65N30, 65M50, 49K40

Institutions of the University: 
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics)  Univ.Prof. Dr. Lars Grüne Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics  Univ.Prof. Dr. Anton Schiela Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields 
Result of work at the UBT: 
Yes 
DDC Subjects: 
500 Science > 510 Mathematics 
Date Deposited: 
03 Aug 2020 09:27 
Last Modified: 
03 Aug 2020 09:27 
URI: 
https://eref.unibayreuth.de/id/eprint/56267 