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This paper contrasts recursive state space models and direct multi-steppredictors for linear predictive control. We provide a tutorial exposition forboth model structures to solve the following problems: 1. stochastic optimalcontrol; 2. system identification; 3. stochastic optimal control based on theestimated model. Throughout the paper, we provide detailed discussions of thebenefits and limitations of these two model parametrizations for predictivecontrol and highlight the relation to existing works. Additionally, we derive anovel (partially tight) constraint tightening for stochastic predictive controlwith parametric uncertainty in the multi-step predictor.

State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?