Orthogonal Transformations for Efficient Data-Driven Reachability Analysis

TL;DR

This paper presents an orthogonal transformation framework that significantly reduces the volume of data-driven reachable sets in matrix zonotope analysis, enhancing precision in safety verification.

Contribution

It introduces a novel orthogonal matrix-based approach that transfers coordinate systems to reduce reachable set volumes efficiently in data-driven analysis.

Findings

Achieves order-of-magnitude volume reductions compared to traditional methods.

Maintains comparable generator numbers while improving accuracy.

Provides a practical solution for data-driven safety verification.

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.