  The computation of feedback control using Dynamic Programming equation is a
difficult task due the curse of dimensionality. The tree structure algorithm is
one the methods introduced recently that mitigate this problem. The method
computes the value function avoiding the construction of a space grid and the
need for interpolation techniques using a discrete set of controls. However,
the computation of the control is strictly linked to control set chosen in the
computation of the tree. Here, we extend and complete the method selecting a
finer control set in the computation of the feedback. This requires to use an
interpolation method for scattered data which allows us to reconstruct the
value function for nodes not belonging to the tree. The effectiveness of the
method is shown via a numerical example.
