  We design receding horizon control strategies for stochastic discrete-time
linear systems with additive (possibly) unbounded disturbances, while obeying
hard bounds on the control inputs. We pose the problem of selecting an
appropriate optimal controller on vector spaces of functions and show that the
resulting optimization problem has a tractable convex solution. Under the
assumption that the zero-input and zero-noise system is asymptotically stable,
we show that the variance of the state is bounded when enforcing hard bounds on
the control inputs, for any receding horizon implementation. Throughout the
article we provide several examples that illustrate how quantities needed in
the formulation of the resulting optimization problems can be calculated
off-line, as well as comparative examples that illustrate the effectiveness of
our control strategies.
