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arXiv · 2604.13792

Orthogonal Transformations for Efficient Data-Driven Reachability Analysis

Peng Xie·Amr Alanwar
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Abstract

Data-driven reachability analysis using matrix zonotopes faces a fundamental challenge: the number of generators in the reachable set grows exponentially during propagation, while current order reduction yields overly conservative approximations in data-driven settings. This paper introduces an orthogonal matrix-based framework that appropriately transfers the coordinate system before reducing the generators of the reachable set, dramatically reducing reachable set volumes. By exploiting the factorized structure of data-driven matrix zonotope generators, we develop several efficient algorithms to solve the problem. Numerical experiments demonstrate order-of-magnitude volume reductions compared to traditional methods, while maintaining comparable generator numbers. Our method provides a practical solution to improve precision in data-driven safety verification.

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BibTeXRIS

Peng Xie, Amr Alanwar. 2026-04-15. Orthogonal Transformations for Efficient Data-Driven Reachability Analysis. https://arxiv.org/abs/2604.13792

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