  We deal with the convergence of the value function of an approximate control
problem with uncertain dynamics to the value function of a nonlinear optimal
control problem. The assumptions on the dynamics and the costs are rather
general and we assume to represent uncertainty in the dynamics by a probability
distribution. The proposed framework aims to describe and motivate some
model-based Reinforcement Learning algorithms where the model is probabilistic.
We also show some numerical experiments which confirm the theoretical results.
