  We investigate model predictive control (MPC) formulations for linear systems
subject to i.i.d. stochastic disturbances with bounded support and chance
constraints. Existing stochastic MPC formulations with closed-loop guarantees
can be broadly classified in two separate frameworks: i) using robust
techniques; ii) feasibility preserving algorithms. We investigate two
particular MPC formulations representative for these two frameworks called
robust-stochastic MPC and indirect feedback stochastic MPC. We provide a
qualitative analysis, highlighting intrinsic limitations of both approaches in
different edge cases. Then, we derive a unifying stochastic MPC framework that
naturally includes these two formulations as limit cases. This qualitative
analysis is complemented with numerical results, showcasing the advantages and
limitations of each method.
