  Dynamic Programming is bedeviled by the "curse of dimensionality", which is
intensified by the expectations over the process noise. In this paper we
present a Monte Carlo-based sampling of the state-space and an interpolation
procedure of the resulting value function dependent on the process noise
density in a "self-approximating" fashion. Proof of almost sure convergence is
presented. The proposed sampling and interpolation algorithm alleviates the
burden of gridding of Dynamic Programming and avoids the construction of a
piecewise constant value function over the grid. The sampling nature, and the
interpolation procedure of this approach make it adequate to deal with
probabilistic constraints.

Systems and Control;Systems and Control