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POD-Based Economic Optimal Control of Heat-Convection Phenomena

  • Luca MechelliEmail author
  • Stefan Volkwein
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 29)

Abstract

In the setting of energy efficient building operation, an optimal boundary control problem governed by the heat equation with a convection term is considered together with bilateral control and state constraints. The aim is to keep the temperature in a prescribed range with the least possible heating cost. In order to gain regular Lagrange multipliers a Lavrentiev regularization for the state constraints is utilized. The regularized optimal control problem is solved by a primal-dual active set strategy (PDASS) which can be interpreted as a semismooth Newton method and, therefore, has a superlinear rate of convergence. To speed up the PDASS a reduced-order approach based on proper orthogonal decomposition (POD) is applied. An a-posteriori error analysis ensures that the computed (suboptimal) POD solutions are sufficiently accurate. Numerical test illustrates the efficiency of the proposed strategy.

Keywords

Convection-diffusion equation Optimal control State constraints Primal-dual active set strategy Model order reduction 

Notes

Acknowledgements

The authors gratefully acknowledge support by the German Science Fund DFG grant VO 1658/4-1 Reduced-Order Methods for Nonlinear Model Predictive Control.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of KonstanzDepartment of Mathematics and StatisticsKonstanzGermany

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