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Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation

Author

Listed:
  • Stefan Banholzer

    (Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz, Germany;)

  • Giulia Fabrini

    (Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz, Germany;)

  • Lars Grüne

    (Mathematical Institute, University of Bayreuth, D-95440 Bayreuth, Germany)

  • Stefan Volkwein

    (Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz, Germany;)

Abstract

In the present paper, a multiobjective optimal control problem governed by a linear parabolic advection-diffusion-reaction equation is considered. The optimal controls are computed by applying model predictive control (MPC), which is a method for controlling dynamical systems over long or infinite time horizons by successively computing optimal controls over a moving finite time horizon. Numerical experiments illustrate that the proposed solution approach can be successfully applied although some of the assumptions which are necessary to conduct the theoretical analysis cannot be guaranteed for the studied tests.

Suggested Citation

  • Stefan Banholzer & Giulia Fabrini & Lars Grüne & Stefan Volkwein, 2020. "Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:777-:d:357082
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    References listed on IDEAS

    as
    1. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
    2. S. Schäffler & R. Schultz & K. Weinzierl, 2002. "Stochastic Method for the Solution of Unconstrained Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 209-222, July.
    3. Laabidi, Kaouther & Bouani, Faouzi & Ksouri, Mekki, 2008. "Multi-criteria optimization in nonlinear predictive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(5), pages 363-374.
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