  This paper presents two stochastic model predictive control methods for
linear time-invariant systems subject to unbounded additive uncertainties. The
new methods are developed by formulating the chance constraints into
deterministic form, which are treated in analogy with robust constraints, by
using the probabilistic reachable set. Firstly, the probabilistically
resolvable time-varying tube-based stochastic model predictive control
algorithm is designed by employing the time-varying probabilistic reachable
sets as the tubes. Secondly, by utilizing the probabilistic positively
invariant set, the probabilistically resolvable constant tube-based stochastic
model predictive control algorithm is developed by employing the constantly
tightened constraints in the entire prediction horizons. In addition, to
enhance the feasibility of the algorithms, the soft constraints are imposed to
the state initializations. The algorithm feasibility and closed-loop stability
results are provided. The efficacy of the approaches are demonstrated by means
of numerical simulations.
