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Open AccessArticle

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

1
Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz, Germany;
2
Mathematical Institute, University of Bayreuth, D-95440 Bayreuth, Germany
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(5), 777; https://doi.org/10.3390/math8050777
Received: 9 March 2020 / Revised: 9 April 2020 / Accepted: 28 April 2020 / Published: 12 May 2020
(This article belongs to the Special Issue Recent Trends in Multiobjective Optimization and Optimal Control)
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. View Full-Text
Keywords: multiobjectice optimization; multiobjective optimal control; model predictive control; evolution problems; advection-diffusion equations multiobjectice optimization; multiobjective optimal control; model predictive control; evolution problems; advection-diffusion equations
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MDPI and ACS Style

Banholzer, S.; Fabrini, G.; Grüne, L.; Volkwein, S. Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation. Mathematics 2020, 8, 777.

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