Data-Driven Reachability Analysis from Noisy Data
This work addresses the challenge of reachability analysis for control and verification in scenarios where system models are unavailable, offering a data-driven approach that is incremental in extending existing methods to handle noisy data.
The paper tackles the problem of computing reachable sets directly from noisy data without a known system model, proposing algorithms for linear, polynomial, and nonlinear systems with theoretical guarantees for over-approximation and demonstrating applicability through numerical examples and real experiments.
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.