Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees
This addresses safety-critical control problems for systems with unknown dynamics, though it is incremental as it builds on existing reachability and conformal prediction techniques.
The paper tackles output reachability analysis for linear time-invariant systems with unknown parameters using only noisy measurements, achieving deterministic containment guarantees and distribution-free coverage via a Transformer-enhanced method validated on a five-dimensional system.
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.