POD-Based Bicriterial Optimal Control of Time-Dependent Convection-Diffusion Equations with Basis Update

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2018
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In this thesis we consider a bicriterial optimal control problem governed by the heat equation with a convection term and bilateral control constraints which arise in HVAC operation of building applications. Furthermore, we allow the convection term to be time-dependent and investigate its influence on the optimal control problem. For this purpose, we apply the Euclidean reference point method, which is a special case of the reference point method, in order to transform the bicriterial optimal control problem into a series of scalar-valued optimal control problems. In order to make the computation effort feasible, we apply the proper orthogonal decomposition method (POD) which is a well-known model-order reduction technique. In the context of this thesis, we derive new a-priori estimates for the approximation error in the objective and control space. In our numerical experiments we analyse the results and compare them with the results for the time-independent convection term. Furthermore, new strategies for efficiently updating the POD basis in the optimization process are proposed and tested numerically.

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510 Mathematik
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ISO 690MAKAROV, Eugen, 2018. POD-Based Bicriterial Optimal Control of Time-Dependent Convection-Diffusion Equations with Basis Update [Master thesis]. Konstanz: Universität Konstanz
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@mastersthesis{Makarov2018PODBa-43432,
  year={2018},
  title={POD-Based Bicriterial Optimal Control of Time-Dependent Convection-Diffusion Equations with Basis Update},
  address={Konstanz},
  school={Universität Konstanz},
  author={Makarov, Eugen}
}
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Konstanz, Universität Konstanz, Masterarbeit/Diplomarbeit, 2018
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