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We investigate model predictive control (MPC) formulations for linear systemssubject to i.i.d. stochastic disturbances with bounded support and chanceconstraints. Existing stochastic MPC formulations with closed-loop guaranteescan be broadly classified in two separate frameworks: i) using robusttechniques; ii) feasibility preserving algorithms. We investigate twoparticular MPC formulations representative for these two frameworks calledrobust-stochastic MPC and indirect feedback stochastic MPC. We provide aqualitative analysis, highlighting intrinsic limitations of both approaches indifferent edge cases. Then, we derive a unifying stochastic MPC framework thatnaturally includes these two formulations as limit cases. This qualitativeanalysis is complemented with numerical results, showcasing the advantages andlimitations of each method.

On stochastic MPC formulations with closed-loop guarantees: Analysis and a unifying framework