Data-driven output reachability without known system matrices

Develop a data-driven approach to compute output reachable sets for discrete-time linear time-invariant systems using only noisy input-output measurements when all state-space matrices A, B, and C are unknown, i.e., without knowledge of any system matrix.

Background

Existing data-driven reachability methods typically assume knowledge of at least the output matrix C to either reconstruct latent states for reachability or to map outputs back to states for estimation. When C is also unknown, these mechanisms break down, yet this setting is practically relevant when only noisy input-output trajectories are available.

The paper highlights that prior work lacks methods for output reachability directly from input-output data without any system matrix knowledge, identifying this gap as an open problem that motivates their proposed framework.