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POD-Based Economic Optimal Control of Heat-Convection Phenomena

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Numerical Methods for Optimal Control Problems

Part of the book series: Springer INdAM 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.

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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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Authors and Affiliations

  1. University of Konstanz, Department of Mathematics and Statistics, Konstanz, Germany

    Luca Mechelli & Stefan Volkwein

Authors
  1. Luca Mechelli
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  2. Stefan Volkwein
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Corresponding author

Correspondence to Luca Mechelli .

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Editors and Affiliations

  1. Department of Mathematics, Sapienza University of Rome, Roma, Italy

    Maurizio Falcone

  2. Department of Mathematics & Physics, Roma Tre University, Rome, Italy

    Roberto Ferretti

  3. Mathematical Institut, Universität Bayreuth, Bayreuth, Bayern, Germany

    Lars Grüne

  4. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA

    William M. McEneaney

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Mechelli, L., Volkwein, S. (2018). POD-Based Economic Optimal Control of Heat-Convection Phenomena. In: Falcone, M., Ferretti, R., Grüne, L., McEneaney, W. (eds) Numerical Methods for Optimal Control Problems. Springer INdAM Series, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-01959-4_4

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