# Formulas for Data-driven Control: Stabilization, Optimality and Robustness

arXiv: https://arxiv.org/abs/1903.06842 · HTML: https://mlsanity.com/paper/1903.06842/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2019.

## Built on by (most cited first, 30 of 47)

- [Uncovering mesa-optimization algorithms in Transformers](https://mlsanity.com/paper/2309.05858/) (2023)
- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [On the sample complexity of stabilizing linear dynamical systems from data](https://mlsanity.com/paper/2203.00474/) (2022)
- [Symbolic Abstractions From Data: A PAC Learning Approach](https://mlsanity.com/paper/2104.13901/) (2021)
- [Policy Gradient Adaptive Control for the LQR: Indirect and Direct Approaches](https://mlsanity.com/paper/2505.03706/) (2025)
- [Robust Data-Driven Predictive Control using Reachability Analysis](https://mlsanity.com/paper/2103.14110/) (2021)
- [Context-aware controller inference for stabilizing dynamical systems from scarce data](https://mlsanity.com/paper/2207.11049/) (2022)
- [Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]](https://mlsanity.com/paper/2303.17618/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Offline Reinforcement Learning via Inverse Optimization](https://mlsanity.com/paper/2502.20030/) (2025)
- [Data-Driven Linear Koopman Embedding for Networked Systems: Model-Predictive Grid Control](https://mlsanity.com/paper/2206.01272/) (2022)
- [An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problem](https://mlsanity.com/paper/2303.17819/) (2023)
- [The Neuron as a Direct Data-Driven Controller](https://mlsanity.com/paper/2401.01489/) (2024)
- [Controller Synthesis from Noisy-Input Noisy-Output Data](https://mlsanity.com/paper/2402.02588/) (2024)
- [Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noise](https://mlsanity.com/paper/2406.00234/) (2024)
- [Fading memory and the convolution theorem](https://mlsanity.com/paper/2408.07386/) (2024)
- [Predictive Monitoring of Black-Box Dynamical Systems](https://mlsanity.com/paper/2412.16564/) (2024)
- [Linear Dynamics meets Linear MDPs: Closed-Form Optimal Policies via Reinforcement Learning](https://mlsanity.com/paper/2508.17185/) (2025)
- [Analysis and Detectability of Offline Data Poisoning Attacks on Linear Dynamical Systems](https://mlsanity.com/paper/2211.08804/) (2022)
- [On the Hardness of Learning to Stabilize Linear Systems](https://mlsanity.com/paper/2311.11151/) (2023)
- [Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient](https://mlsanity.com/paper/2403.05367/) (2024)
- [A New Perspective On AI Safety Through Control Theory Methodologies](https://mlsanity.com/paper/2506.23703/) (2025)
- [Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach](https://mlsanity.com/paper/2508.13241/) (2025)
- [A Secure Learning Control Strategy via Dynamic Camouflaging for Unknown Dynamical Systems under Attacks](https://mlsanity.com/paper/2102.00573/) (2021)
- [Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems](https://mlsanity.com/paper/2102.09111/) (2021)
- [Discrete fully probabilistic design: towards a control pipeline for the synthesis of policies from examples](https://mlsanity.com/paper/2112.11210/) (2021)
- [Efficient Reinforcement Learning Through Trajectory Generation](https://mlsanity.com/paper/2211.17249/) (2022)
- [LMI-based Data-Driven Robust Model Predictive Control](https://mlsanity.com/paper/2303.04777/) (2023)
- [Data-Driven Adversarial Online Control for Unknown Linear Systems](https://mlsanity.com/paper/2308.08138/) (2023)
- [MR-ARL: Model Reference Adaptive Reinforcement Learning for Robustly Stable On-Policy Data-Driven LQR](https://mlsanity.com/paper/2402.14483/) (2024)

## Abstract (arXiv)

In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.