  This paper presents a new approach to Model Predictive Control for
environments where essential, discrete variables are partially observed. Under
this assumption, the belief state is a probability distribution over a finite
number of states. We optimize a \textit{control-tree} where each branch assumes
a given state-hypothesis. The control-tree optimization uses the probabilistic
belief state information. This leads to policies more optimized with respect to
likely states than unlikely ones, while still guaranteeing robust constraint
satisfaction at all times. We apply the method to both linear and non-linear
MPC with constraints. The optimization of the \textit{control-tree} is
decomposed into optimization subproblems that are solved in parallel leading to
good scalability for high number of state-hypotheses. We demonstrate the
real-time feasibility of the algorithm on two examples and show the benefits
compared to a classical MPC scheme optimizing w.r.t. one single hypothesis.
