Offline Uncertainty Sampling in Data-driven Stochastic MPC

TL;DR

This work develops a data-driven stochastic MPC framework for unknown LTI systems with measurement noise by leveraging Willems' fundamental lemma and offline uncertainty sampling to handle chance constraints. By constructing a data-driven predicted trajectory from a single persistently exciting data sequence and performing offline constraint sampling, the method yields a deterministic, reduced set of constraints and a robust first-step constraint to guarantee recursive feasibility. Theoretical guarantees ensure closed-loop chance constraint satisfaction with confidence level $\beta$ and robust input feasibility, while simulations show improved performance and feasibility over purely robust DD-MPC, particularly at higher noise levels. The approach lowers online computational load and enables safe operation near constraint boundaries in data-limited settings, with future work including extensions to additive disturbances and stability analysis.

Abstract

In this work, we exploit an offline-sampling based strategy for the constrained data-driven predictive control of an unknown linear system subject to random measurement noise. The strategy uses only past measured, potentially noisy data in a non-parametric system representation and does not require any prior model identification. The approximation of chance constraints using uncertainty sampling leads to efficient constraint tightening. Under mild assumptions, robust recursive feasibility and closed-loop constraint satisfaction is shown. In a simulation example, we provide evidence for the improved control performance of the proposed control scheme in comparison to a purely robust data-driven predictive control approach.

Figures (2)

• Figure 1: Comparison between the proposed method and the robust method by berberich2020robust: trajectories of 10 runs with noisy data and online measurements for the noise bound $= 0.002$. Constraints are shown in dotted black lines.
• Figure 2: Boxplots of the total trajectory cost $J_{\text{tot}}$ for both the proposed method and the robust approach berberich2020robust in different noise scenarios. Note that the robust approach is infeasible for noise bound $= 0.01$ and $= 0.1$.