# Data-Driven Model Predictive Control with Stability and Robustness Guarantees

## TL;DR

This paper introduces a robust data-driven MPC method for linear systems that guarantees stability and robustness without requiring system identification, using only measured trajectories and behavioral systems theory.

## Contribution

It presents the first theoretical analysis of stability and robustness guarantees for a simple, purely data-driven MPC scheme without prior system identification.

## Key findings

- Proves exponential stability of the nominal scheme without noise.
- Develops a robust scheme with practical stability under measurement noise.
- Provides theoretical guarantees for closed-loop properties of data-driven MPC.

## Abstract

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant (LTI) systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input-output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multi-step fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.