Robust stability analysis of a simple data-driven model predictive control approach

TL;DR

This paper presents a simple, data-driven model predictive control scheme that guarantees exponential stability for noise-free data and practical stability with noisy measurements, using only one input-output trajectory.

Contribution

It introduces a straightforward data-driven MPC approach based on behavioral systems theory that avoids terminal ingredients and ensures stability with minimal data requirements.

Findings

Ensures exponential stability with noise-free data and long prediction horizon.

Proves practical exponential stability under noisy measurements.

Demonstrates effectiveness through a numerical example.

Abstract

In this paper, we provide a theoretical analysis of closed-loop properties of a simple data-driven model predictive control (MPC) scheme. The formulation does not involve any terminal ingredients, thus allowing for a simple implementation without (potential) feasibility issues. The proposed approach relies on an implicit description of linear time-invariant systems based on behavioral systems theory, which only requires one input-output trajectory of an unknown system. For the nominal case with noise-free data, we prove that the data-driven MPC scheme ensures exponential stability for the closed loop if the prediction horizon is sufficiently long. Moreover, we analyze the robust data-driven MPC scheme for noisy output measurements for which we prove closed-loop practical exponential stability. The advantages of the presented approach are illustrated with a numerical example.