POD-Based Multiobjective Optimal Control of Time-Variant Heat Phenomena
In the present paper, a multiobjective optimal control problem governed by a heat equation with time-dependent convection term and bilateral control constraints is considered. For computing Pareto optimal points and approximating the Pareto front, the reference point method is applied. As this method transforms the multiobjective optimal control problem into a series of scalar optimization problems, the method of proper orthogonal decomposition (POD) is introduced as an approach for model-order reduction. New strategies for efficiently updating the POD basis in the optimization process are proposed and tested numerically.
S. Banholzer gratefully acknowledges support by the German DFG-Priority Program 1962 and by the Landesgraduiertenförderung of Baden-Württemberg.
- 1.S. Banholzer, POD-Based Bicriterial Optimal Control of Convection-Diffusion Equations, Master thesis, University of Konstanz, Department of Mathematics and Statistics, 2017, see http://nbn-resolving.de/ urn:nbn:de:bsz:352-0-421545
- 3.R. Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Volume 5: Evolution Problems I (Springer, Berlin, 2000)Google Scholar
- 7.M. Gubisch, S. Volkwein, Proper orthogonal decomposition for linear-quadratic optimal control, in Model Reduction and Approximation: Theory and Algorithms, ed. by P. Benner, A. Cohen, M. Ohlberger, K. Willcox (SIAM, Philadelphia, 2017), pp. 5–66Google Scholar
- 9.K. Miettinen, Nonlinear Multiobjective Optimization. International Series in Operations Research and Management Science (Springer, Berlin, 1998)Google Scholar
- 10.S. Peitz, S. Oder-Blöbaum, M. Dellnitz, Multiobjective optimal control methods for fluid flow using reduced order modeling, in 24th Congress of Theoretical and Applied Mechanics (ICTAM), Montreal, Canada, 21–26 August 2016, see http://arxiv.org/pdf/1510.05819v2.pdf
- 11.C. Romaus, J. Böcker, K. Witting, A. Seifried, O. Znamenshchykov, Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors, in IEEE Energy Conversion Congress and Exposition, San Jose, 2009, pp. 1640–1647Google Scholar