Regret and Conservatism of Distributionally Robust Constrained Stochastic Model Predictive Control

We analyse the conservatism and regret of distributionally robust (DR) stochastic model predictive control (SMPC) when using moment-based ambiguity sets for modeling unknown uncertainties. To quantify the conservatism, we compare the deterministic constraint tightening while taking a DR approach against the optimal tightening when the exact distributions of the stochastic uncertainties are known. Furthermore, we quantify the sub-optimality gap and regret by comparing the performance when the distributions of the stochastic uncertainties are known and unknown. Analysing the accumulated sub-optimality of SMPC due to the lack of knowledge about the true distributions of the uncertainties marks the novel contribution of this work.