Data-Driven Model Predictive Control With Stability and Robustness Guarantees

TLDR

The authors propose a robust data‑driven model predictive control scheme for linear time‑invariant systems. The scheme employs an implicit behavioral model built from past input‑output data, requiring only an initial trajectory and a bound on system order, and incorporates a slack‑variable regularization to handle bounded output noise. The authors prove that the nominal data‑driven MPC is exponentially stable without noise, and that the robust variant achieves practical exponential stability in the presence of bounded measurement noise, providing the first theoretical closed‑loop analysis for such a purely data‑driven scheme.

Abstract

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant 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 multistep 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.