Data-Driven Distributionally Robust Bounds for Stochastic Model Predictive Control

We present a distributionally robust stochastic model predictive control scheme for linear discrete-time systems subject to unbounded additive disturbance. We consider joint chance constraints over the task horizon for both the states and inputs. For settings where distributional information is unavailable and only few samples of the disturbance are accessible, we devise a tube MPC formulation where we synthesize ambiguous tubes in the Wasserstein metric. These tubes are used for constraint tightening around the nominal system and are based on the synthesis of bounds that encompass a given probability mass of the error distribution despite distributional ambiguity. The method is tested on a building temperature control problem.