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

arXiv: https://arxiv.org/abs/1906.04679 · HTML: https://mlsanity.com/paper/1906.04679/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2019.

## Built on by (most cited first, 26 of 26)

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- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)
- [Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach](https://mlsanity.com/paper/2511.09242/) (2025)
- [Adaptive Control of Unknown Linear Switched Systems via Policy Gradient Methods](https://mlsanity.com/paper/2601.03016/) (2026)
- [Symplectic Inductive Bias for Data-Driven Target Reachability in Hamiltonian Systems](https://mlsanity.com/paper/2604.17213/) (2026)
- [Safety-Critical Contextual Control via Online Riemannian Optimization with World Models](https://mlsanity.com/paper/2604.19639/) (2026)
- [Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems](https://mlsanity.com/paper/2606.11596/) (2026)
- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)

## Abstract (arXiv)

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.