Data-Driven Reachability Analysis from Noisy Data

TL;DR

This paper introduces data-driven algorithms for computing over-approximated reachable sets directly from noisy data, applicable to linear, polynomial, and nonlinear systems, with theoretical guarantees and practical validation.

Contribution

It presents novel reachability algorithms that operate directly on noisy data without requiring explicit system models, extending to nonlinear systems with theoretical guarantees.

Findings

Algorithms successfully compute over-approximated reachable sets from noisy data.

The methods are validated through numerical examples and real experiments.

Comparisons show trade-offs between conservativeness and computational cost.

Abstract

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.