Distributionally robust uncertainty quantification via data-driven stochastic optimal control

This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances uncertain distribution. Uncertainty about the is usually described via ambiguity sets probability measures or distributions. Typically, requires knowledge underlying dynamics and as such challenging. Relying on a fundamental lemma from data-driven framework polynomial chaos expansions, we propose an approach reformulate distributionally robust with conic programs in finite-dimensional vector space. We show how construct these previously recorded data relax program numerically tractable convex appropriate sampling The efficacy our method illustrated numerical example.