  In this paper we propose an output-feedback Model Predictive Control (MPC)
algorithm for linear discrete-time systems affected by a possibly unbounded
additive noise and subject to probabilistic constraints. In case the noise
distribution is unknown, the chance constraints on the input and state
variables are reformulated by means of the Chebyshev - Cantelli inequality. The
recursive feasibility of the proposed algorithm is guaranteed and the
convergence of the state to a suitable neighbor of the origin is proved under
mild assumptions. The implementation issues are thoroughly addressed showing
that, with a proper choice of the design parameters, its computational load can
be made similar to the one of a standard stabilizing MPC algorithm. Two
examples are discussed in details, with the aim of providing an insight on the
performance achievable by the proposed control scheme.
