  We present a stochastic model predictive control (MPC) method for linear
discrete-time systems subject to possibly unbounded and correlated additive
stochastic disturbance sequences. Chance constraints are treated in analogy to
robust MPC using the concept of probabilistic reachable sets for constraint
tightening. We introduce an initialization of each MPC iteration which is
always recursively feasibility and thereby allows that chance constraint
satisfaction for the closed-loop system can readily be shown. Under an i.i.d.
zero mean assumption on the additive disturbance, we furthermore provide an
average asymptotic performance bound. Two examples illustrate the approach,
highlighting feedback properties of the novel initialization scheme, as well as
the inclusion of time-varying, correlated disturbances in a building control
setting.
