  The Dynamic Programming approach allows to compute a feedback control for
nonlinear problems, but suffers from the curse of dimensionality. The
computation of the control relies on the resolution of a nonlinear PDE, the
Hamilton-Jacobi-Bellman equation, with the same dimension of the original
problem. Recently, a new numerical method to compute the value function on a
tree structure has been introduced. The method allows to work without a
structured grid and avoids any interpolation.
  Here, we aim to test the algorithm for nonlinear two dimensional PDEs. We
apply model order reduction to decrease the computational complexity since the
tree structure algorithm requires to solve many PDEs. Furthermore, we prove an
error estimate which guarantees the convergence of the proposed method.
Finally, we show efficiency of the method through numerical tests.
