Reduced-Order Bicriterial Optimal Control of Evolution Equations

Abstract

In this thesis, available results from previous master theses for a bicriterial optimal control problem governed by time-independent and a time-dependent convection-diffusion equation, respectively, are extended from the case of two space dimensions to three space dimensions and arising difficulties are investigated. These multiobjective optimal control problems are treated by the Euclidean reference point method and in this thesis, the focus is set on computing Pareto optimal solutions numerically. The step sizes used in the associated algorithm are considered more closely with regard to the speed of convergence for the individual reference point problems. By adapting certain step sizes, considerable improvement is achieved on this matter.Furthermore, POD is employed as a method of model-order reduction while various POD basis strategies are analysed and refined. In particular, a-priori and a-posteriori estimates are applied to construct time efficient and sufficiently accurate strategies to determine the size of the POD basis. As tools to control the POD basis size, basis extensions and basis updates are employed.