Recursively feasible Data-driven Distributionally Robust Model Predictive Control with additive disturbances

TL;DR

This paper introduces a data-driven distributionally robust MPC approach for stochastic systems with unbounded disturbances, ensuring recursive feasibility and chance constraint satisfaction through moment-based ambiguity sets and sample-based confidence guarantees.

Contribution

It presents a novel recursive feasible MPC framework using data-driven ambiguity sets for unbounded disturbances, with theoretical guarantees on chance constraints.

Findings

Performance improvements demonstrated in numerical example

Chance constraint satisfaction achieved with fewer samples

Theoretical bounds on sample size for confidence levels

Abstract

In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly interpolated initial state constraint in combination with a simplified affine disturbance feedback policy. We consider a moment-based ambiguity set with data-driven radius for the second moment of the disturbance, where we derive a minimum number of samples in order to ensure user-given confidence bounds on the chance constraints and closed-loop performance. The paper closes with a numerical example, highlighting the performance gain and chance constraint satisfaction based on different sample sizes.