Data-Driven Reachability Analysis from Noisy Data

15 May 2021  ·  Amr Alanwar, Anne Koch, Frank Allgöwer, Karl Henrik Johansson ·

We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different type 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 accuracy comparisons are made between algorithms.

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