Sampling-based Stochastic Data-driven Predictive Control under Data Uncertainty - Extended Version

TL;DR

This paper introduces a data-driven predictive control method for linear systems with uncertainties, using a novel disturbance parameterization and sampling-based chance constraint approximation to ensure stability and constraint satisfaction.

Contribution

It proposes a stochastic control scheme that does not require exact disturbance data, extending Willems' lemma for data-driven predictors under uncertainty.

Findings

Demonstrates recursive feasibility and stability in simulations

Achieves constraint satisfaction without exact disturbance data

Shows efficiency of the control scheme in a numerical example

Abstract

We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems' fundamental lemma and requires only a single persistently exciting input-output data trajectory. Compared to current state-of-the-art approaches, we do not rely on availability of exact disturbance data. Instead, we leverage a novel parameterization of the unknown disturbance data considering consistency with the measured data and the system class. This allows for deterministic approximation of the chance constraints in a sampling-based fashion. A robust constraint on the first predicted step enables recursive feasibility, closed-loop constraint satisfaction, and robust asymptotic stability in expectation under standard assumptions. A numerical example demonstrates the efficiency of the proposed control scheme.