  We provide a solution to the problem of receding horizon control for
stochastic discrete-time systems with bounded control inputs and imperfect
state measurements. For a suitable choice of control policies, we show that the
finite-horizon optimization problem to be solved on-line is convex and
successively feasible. Due to the inherent nonlinearity of the feedback loop, a
slight extension of the Kalman filter is exploited to estimate the state
optimally in mean-square sense. We show that the receding horizon
implementation of the resulting control policies renders the state of the
overall system mean-square bounded under mild assumptions. Finally, we discuss
how some of the quantities required by the finite-horizon optimization problem
can be computed off-line, reducing the on-line computation, and present some
numerical examples.
