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

TL;DR

This paper introduces a novel data-driven control policy for uncertain linear systems that improves computational efficiency and solution quality in distributionally robust mixed-integer control problems using Wasserstein metric-based ambiguity sets.

Contribution

The paper proposes the DR-LCP method, a new lifted control policy that provides high-quality approximate solutions for distributionally robust mixed-integer control with theoretical performance guarantees.

Findings

DR-LCP outperforms existing methods in numerical experiments.

Theoretical analysis shows tight non-asymptotic bounds.

Method applies to a broad class of Wasserstein ambiguity sets.

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.