  In this paper infinite horizon optimal control problems for nonlinear
high-dimensional dynamical systems are studied. Nonlinear feedback laws can be
computed via the value function characterized as the unique viscosity solution
to the corresponding Hamilton-Jacobi-Bellman (HJB) equation which stems from
the dynamic programming approach. However, the bottleneck is mainly due to the
curse of dimensionality and HJB equations are only solvable in a relatively
small dimension. Therefore, a reduced-order model is derived for the dynamical
system and for this purpose the method of proper orthogonal decomposition (POD)
is used. The resulting errors in the HJB equations are estimated by an a-priori
error analysis, which suggests a new sampling strategy for the POD method.
Numerical experiments illustrates the theoretical findings.
