mlsanityData to 7 Oct 2026

Data-Driven Reachability Analysis from Noisy Data

arXiv 2105.07229 ↗First posted 15 May 2021eess.SY cs.LG cs.SYcited by 14

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Abstract (arXiv)

We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and, under the assumption of Lipschitz continuity, to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and comparisons are made between algorithms.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 21 of its 57 references that are in the map. First posted on arXiv 15 May 2021.

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21 of 57 references.

References · 21

  1. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 150
  2. 2019Formulas for Data-driven Control: Stabilization, Optimality and Robustnesscited by 40
  3. 2019A Tutorial on Concentration Bounds for System Identificationcited by 19
  4. 2019Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysiscited by 14
  5. 2019Data informativity: a new perspective on data-driven analysis and controlcited by 14
  6. 2019Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methodscited by 14
  7. 2021Data-Driven Reachability Analysis with Christoffel Functionscited by 12
  8. 2020Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Samplingcited by 11
  9. 2020Data-Driven Reachability Analysis Using Matrix Zonotopescited by 11
  10. 2020From noisy data to feedback controllers: non-conservative design via a matrix S-lemmacited by 9
  11. 2020Combining Prior Knowledge and Data for Robust Controller Designcited by 9
  12. 2019Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended versioncited by 8
9 more
  1. 2019Robust Adaptive Model Predictive Control: Performance and Parameter Estimationcited by 7
  2. 2020On-The-Fly Control of Unknown Smooth Systems from Limited Datacited by 6
  3. 2021Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guaranteescited by 6
  4. 2019Robust data-driven state-feedback designcited by 5
  5. 2020Verifying dissipativity properties from noise-corrupted input-state datacited by 4
  6. 2020Provably robust verification of dissipativity properties from datacited by 3
  7. 2021Robust Data-Driven Predictive Control using Reachability Analysiscited by 3
  8. 2020Dissipativity verification with guarantees for polynomial systems from noisy input-state datacited by 2
  9. 2017Simulation-based reachability analysis for nonlinear systems using componentwise contraction propertiescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 1; 2023: 2; 2024: 2; 2025: 3; 2026: 4.

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  1. 2023Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inferencecited by 9
  2. 2025Safe LLM-Controlled Robots with Formal Guarantees via Reachability Analysiscited by 7
  3. 2023Data-driven Reachability using Christoffel Functions and Conformal Predictioncited by 6
  4. 2021Formal Verification of Unknown Dynamical Systems via Gaussian Process Regressioncited by 5
  5. 2022Safe Reinforcement Learning using Data-Driven Predictive Controlcited by 4
  6. 2024Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shiftcited by 4
  7. 2025Pick-to-Learn for Systems and Control: Data-driven Synthesis with State-of-the-art Safety Guaranteescited by 4
  8. 2024Pedestrian Motion Prediction Using Transformer-based Behavior Clustering and Data-Driven Reachability Analysiscited by 1
  9. 2025Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopescited by 1
  10. 2021Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemicscited by 0
  11. 2026Data-Driven Reachability Analysis via Diffusion Models with PAC Guaranteescited by 0
  12. 2026Data-driven Reachable Set Estimation with Tunable Adversarial and Wasserstein Distributional Guaranteescited by 0
2 more
  1. 2026Matrix Zonotopic Attention: A Context-Adaptive Value Projection for Set Transformerscited by 0
  2. 2026Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysiscited by 0