Distributionally Robust Stochastic MPC under Disturbance-Affine Feedback Policies

TL;DR

This paper introduces a disturbance-affine distributionally robust MPC framework that improves control performance and reduces conservatism compared to traditional tube-based approaches by leveraging Wasserstein ambiguity sets.

Contribution

It develops a novel DA-DR MPC method with a tractable quadratic program, demonstrating enhanced feasibility, stability, and performance over existing methods.

Findings

DA-DR MPC outperforms tube-based MPC in initial feasible sets.

The proposed method achieves better average performance.

It effectively reduces state variance in control tasks.

Abstract

This study addresses the stochastic Model Predictive Control (MPC) problem for linear time-invariant systems subjected to unknown disturbance distributions. By leveraging the most recent disturbance data, we construct a set of distributions with similar statistical properties contained within a Wasserstein ball, thereby accounting for the worst-case impacts on constraint satisfaction. Numerous MPC strategies, particularly tube-based approaches, have been extensively studied under the Wasserstein ambiguity set, but these methods often introduce conservatism and can limit control performance. Unlike tube-based approaches, we adopt a disturbance-affine control strategy, which introduces additional control degrees of freedom. We begin by developing the Disturbance-Affine Distributionally Robust (DA-DR) MPC framework, subsequently reformulating the control problem into a tractable quadratic programming formulation. Furthermore, we establish the recursive feasibility and stability of the proposed MPC scheme. Finally, we present comprehensive theoretical analysis and simulation results, demonstrating the superiority of the DA-DR MPC over tube-based MPC in initial feasible sets, average performance, and state variance control.