  This paper is concerned with the problem of Model Predictive Control and
Rolling Horizon Control of discrete-time systems subject to possibly unbounded
random noise inputs, while satisfying hard bounds on the control inputs. We use
a nonlinear feedback policy with respect to noise measurements and show that
the resulting mathematical program has a tractable convex solution in both
cases. Moreover, under the assumption that the zero-input and zero-noise system
is asymptotically stable, we show that the variance of the state, under the
resulting Model Predictive Control and Rolling Horizon Control policies, is
bounded. Finally, we provide some numerical examples on how certain matrices in
the underlying mathematical program can be calculated off-line.
