  The paper considers constrained linear systems with stochastic additive
disturbances and noisy measurements transmitted over a lossy communication
channel. We propose a model predictive control (MPC) law that minimizes a
discounted cost subject to a discounted expectation constraint. Sensor data is
assumed to be lost with known probability, and data losses are accounted for by
expressing the predicted control policy as an affine function of future
observations, which results in a convex optimal control problem. An online
constraint-tightening technique ensures recursive feasibility of the online
optimization and satisfaction of the expectation constraint without bounds on
the distributions of the noise and disturbance inputs. The cost evaluated along
trajectories of the closed loop system is shown to be bounded by the optimal
predicted cost. A numerical example is given to illustrate these results.
