Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees

TL;DR

This paper introduces a Transformer-augmented method for output reachability analysis of linear systems with unknown parameters, providing deterministic guarantees and distribution-free coverage using conformal prediction.

Contribution

It combines set-based propagation with Transformer-based decoding and conformal prediction to improve reachability analysis under uncertainty.

Findings

Validated on a 5D system with multiple unknown observation matrices.

Achieved distribution-free coverage guarantees at per-step and trajectory levels.

Reduced conservatism in set propagation through Transformer-based decoding.

Abstract

This paper considers output reachability analysis for linear time-invariant systems with unknown state-space matrices and unknown observation map, given only noisy input-output measurements. The Cayley--Hamilton theorem is applied to eliminate the latent state algebraically, producing an autoregressive input-output model whose parameter uncertainty is enclosed in a matrix zonotope. Set-valued propagation of this model yields output reachable sets with deterministic containment guarantees under a bounded aggregated residual assumption. The conservatism inherent in the lifted matrix-zonotope product is then mitigated by a decoder-only Transformer trained on labels obtained through directional contraction of the formal envelope via an exterior non-reachability certificate. Split conformal prediction restores distribution-free coverage at both per-step and trajectory levels without access to the true reachable-set hull. The framework is validated on a five-dimensional system with multiple unknown observation matrices.