Data-Driven Distributionally Robust Mixed-Integer Control through Lifted Control Policy

Abstract: This paper investigates the finite-horizon distributionally robust mixed-integer control (DRMIC) of uncertain linear systems. However, deriving an optimal causal feedback control policy to this DRMIC problem is computationally formidable for most ambiguity sets. To address the computational challenge, we propose a novel distributionally robust lifted control policy (DR-LCP) method to derive a high-quality approximate solution to this DRMIC problem for a rich class of Wasserstein metric-based ambiguity sets, including the Wasserstein ambiguity set and its variants. In theory, we analyze the asymptotic performance and establish a tight non-asymptotic bound of the proposed method. In numerical experiments, the proposed DR-LCP method empirically demonstrates superior performance compared with existing methods in the literature.