POD-galerkin approximations in PDE-constrained optimization

Proper orthogonal decomposition (POD) is one of the most popular model reduction techniques for nonlinear partial differential equations. It is based on a Galerkin-type approximation, where the POD basis functions contain information from a solution of the dynamical system at pre-specified time instances, so-called snapshots. POD models have been applied very successfully in the area of optimization with PDEs or feedback control laws. Neverthe-less, various issues are still unclear and are currently under research, e.g. timely updates of the snapshot information and error analyses for the POD approximations. © WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.