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

Makarov, Eugen

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

Files

Makarov_2-l0r8dud5l8z37.pdf(2.61 MB)

Date

2018

Publication type

Diploma thesis

Publication status

Published

Abstract

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.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

MAKAROV, Eugen, 2018. POD-Based Bicriterial Optimal Control of Time-Dependent Convection-Diffusion Equations with Basis Update [Master thesis]. Konstanz: Universität Konstanz

BibTex

@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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University note

Konstanz, Universität Konstanz, Master thesis, 2018