# Robust Data-Driven Predictive Control using Reachability Analysis

arXiv: https://arxiv.org/abs/2103.14110 · HTML: https://mlsanity.com/paper/2103.14110/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 25 Mar 2021.

## Builds on (most cited first, 15 of 15)

- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [Data informativity: a new perspective on data-driven analysis and control](https://mlsanity.com/paper/1908.00468/) (2019)
- [Distributionally Robust Chance Constrained Data-enabled Predictive Control](https://mlsanity.com/paper/2006.01702/) (2020)
- [Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis](https://mlsanity.com/paper/1901.01780/) (2019)
- [Data-Driven Reachability Analysis Using Matrix Zonotopes](https://mlsanity.com/paper/2011.08472/) (2020)
- [Robust data-driven state-feedback design](https://mlsanity.com/paper/1909.04314/) (2019)
- [Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees](https://mlsanity.com/paper/2101.10784/) (2021)
- [Data-Driven LQR Control Design](https://mlsanity.com/paper/1807.03263/) (2018)
- [Verifying dissipativity properties from noise-corrupted input-state data](https://mlsanity.com/paper/2004.07270/) (2020)
- [Controller design for robust invariance from noisy data](https://mlsanity.com/paper/2007.13181/) (2020)
- [Provably robust verification of dissipativity properties from data](https://mlsanity.com/paper/2006.05974/) (2020)
- [Robust MPC for Linear Systems with Parametric and Additive Uncertainty: A Novel Constraint Tightening Approach](https://mlsanity.com/paper/2007.00930/) (2020)
- [On the relationship between data-enabled predictive control and subspace predictive control](https://mlsanity.com/paper/2011.13868/) (2020)

## Built on by (most cited first, 3 of 3)

- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Safe Reinforcement Learning using Data-Driven Predictive Control](https://mlsanity.com/paper/2211.11027/) (2022)
- [Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics](https://mlsanity.com/paper/2111.04704/) (2021)

## Abstract (arXiv)

We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.