  Constraint tightening to non-conservatively guarantee recursive feasibility
and stability in Stochastic Model Predictive Control is addressed. Stability
and feasibility requirements are considered separately, highlighting the
difference between existence of a solution and feasibility of a suitable, a
priori known candidate solution. Subsequently, a Stochastic Model Predictive
Control algorithm which unifies previous results is derived, leaving the
designer the option to balance an increased feasible region against guaranteed
bounds on the asymptotic average performance and convergence time. Besides
typical performance bounds, under mild assumptions, we prove asymptotic
stability in probability of the minimal robust positively invariant set
obtained by the unconstrained LQ-optimal controller. A numerical example,
demonstrating the efficacy of the proposed approach in comparison with
classical, recursively feasible Stochastic MPC and Robust MPC, is provided.
