Data-Driven Reachability Analysis From Noisy Data

Amr Alanwar, Anne Koch, Frank Allgower, Karl Henrik Johansson

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish
Pages (from-to)3054-3069
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - 1 May 2023
Externally publishedYes


  • Constrained zonotope
  • discrete-time systems
  • reachability analysis
  • robustness
  • zonotope


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