# Controller design for robust invariance from noisy data

arXiv: https://arxiv.org/abs/2007.13181 · HTML: https://mlsanity.com/paper/2007.13181/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Robust Data-Driven Predictive Control using Reachability Analysis](https://mlsanity.com/paper/2103.14110/) (2021)
- [Data-Driven Motion Planning for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2508.00154/) (2025)
- [Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systems](https://mlsanity.com/paper/2505.09734/) (2025)
- [SAFE--MA--RRT: Multi-Agent Motion Planning with Data-Driven Safety Certificates](https://mlsanity.com/paper/2509.04413/) (2025)

## Abstract (arXiv)

For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design a linear feedback controller that guarantees robust invariance of a given polyhedral set of the state in the presence of disturbances. The main result is a necessary and sufficient condition for the existence of such a controller, and amounts to the solution of a linear program. The benefits of large and rich data sets for the solution of the problem are discussed. A numerical example about a simplified platoon of two vehicles illustrates the method.