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

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.