  Optimal control problems driven by evolutionary partial differential
equations arise in many industrial applications and their numerical solution is
known to be a challenging problem. One approach to obtain an optimal feedback
control is via the Dynamic Programming principle. Nevertheless, despite many
theoretical results, this method has been applied only to very special cases
since it suffers from the curse of dimensionality. Our goalis to mitigate this
crucial obstruction developing a new version of dynamic programming algorithms
based on a tree structure and exploiting the compact representation of the
dynamical systems based on tensors notations via a model reduction approach.
Here, we want to show how this algorithm can be constructed for general
nonlinear control problems and to illustrate its performances on a number of
challenging numerical tests. Our numerical results indicate a large decrease in
memory requirements, as well as computational time, for the proposed problems.
Moreover, we prove the convergence of the algorithm and give some hints on its
implementation
