Constraint tightening to non-conservatively guarantee recursive feasibilityand stability in Stochastic Model Predictive Control is addressed. Stabilityand feasibility requirements are considered separately, highlighting thedifference between existence of a solution and feasibility of a suitable, apriori known candidate solution. Subsequently, a Stochastic Model PredictiveControl algorithm which unifies previous results is derived, leaving thedesigner the option to balance an increased feasible region against guaranteedbounds on the asymptotic average performance and convergence time. Besidestypical performance bounds, under mild assumptions, we prove asymptoticstability in probability of the minimal robust positively invariant setobtained by the unconstrained LQ-optimal controller. A numerical example,demonstrating the efficacy of the proposed approach in comparison withclassical, recursively feasible Stochastic MPC and Robust MPC, is provided.
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