Data-Driven Distributionally Robust MPC for Constrained Stochastic Systems

In this letter we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. We conic representable risk, which is useful derive tractable reformulations optimization problems. Specifically, illustrate techniques introduced, utilize risk measures constructed based on data-driven sets, constraining second moment random disturbance. setting, such moment-based lead controllers when combined with affine disturbance feedback. Assumptions constraints are given guarantee The resulting scheme acts as controller little data available and converges certainty equivalent large sample count implies high confidence in estimated moment. This illustrated numerical experiment.