Model order reduction techniques for the optimal control of parabolic partial differential equations with control and state constraints

Abstract

In this thesis linear-quadratic optimal control problems for dynamical systems modeled by parabolic partial differential equations with control and state constraints are observed. Different model order reduction techniques basing on a spectral method called proper orthogonal decomposition are analyzed and both a-priori and a-posteriori error bounds are developed to quantify the arising model reduction errors efficiently. Iterative solution techniques for the coupled nonlinear optimality equations are proposed and an associated convergence analysis is provided. The theoretical findings are visualized by numerical tests which illustrate both the advantages and limits of the introduced model reduction strategies.