Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910097849974784 |
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| author | Zhang, Zhen Xie, Peng Wu, Wenyuan Huang, Yanliang Alanwar, Amr |
| author_facet | Zhang, Zhen Xie, Peng Wu, Wenyuan Huang, Yanliang Alanwar, Amr |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees Zhang, Zhen Xie, Peng Wu, Wenyuan Huang, Yanliang Alanwar, Amr Systems and Control 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. |
| title | Transformer-Enhanced Data-Driven Output Reachability with Conformal Coverage Guarantees |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.02173 |