ar X iv : 0 90 5 . 34 47 v 1 [ m at h . O C ] 2 1 M ay 2 00 9 On convex problems in chance - constrained stochastic model predictive control ⋆

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then reformulated in terms of probabilistic constraints. It is shown that, for a suitable parametrization of the control policy, a wide class of the resulting optimization problems are convex, or admit reasonable convex approximations.