  In this paper we investigate infinite horizon optimal control problems for
parametrized partial differential equations. We are interested in feedback
control via dynamic programming equations which is well-known to suffer from
the curse of dimensionality. Thus, we apply parametric model order reduction
techniques to construct low-dimensional subspaces with suitable information on
the control problem, where the dynamic programming equations can be
approximated. To guarantee a low number of basis functions, we combine recent
basis generation methods and parameter partitioning techniques. Furthermore, we
present a novel technique to construct nonuniform grids in the reduced domain,
which is based on statistical information. Finally, we discuss numerical
examples to illustrate the effectiveness of the proposed methods for PDEs in
two space dimensions.
