Towards data-driven stochastic predictive control

TL;DR

This paper introduces a novel data-driven stochastic predictive control method for LTI systems with unbounded disturbances, utilizing a stochastic fundamental lemma and polynomial chaos expansions to ensure stability and feasibility.

Contribution

It extends data-driven predictive control to stochastic systems by developing a stochastic fundamental lemma and a surrogate optimal control problem with stability guarantees.

Findings

Demonstrates effectiveness through numerical examples

Provides conditions for recursive feasibility and stability

Handles unbounded process disturbances with different distributions

Abstract

Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this paper, we propose a data-driven stochastic predictive control scheme for LTI systems subject to possibly unbounded additive process disturbances. Based on a stochastic extension of the fundamental lemma and leveraging polynomial chaos expansions, we construct a data-driven surrogate Optimal Control Problem (OCP). Moreover, combined with an online selection strategy of the initial condition of the OCP, we provide sufficient conditions for recursive feasibility and for stability of the proposed data-driven predictive control scheme. Finally, two numerical examples illustrate the efficacy and closed-loop properties of the proposed scheme for process disturbances governed by different distributions.