Orthogonal Transformations for Efficient Data-Driven Reachability Analysis
For researchers in safety verification and reachability analysis, this method provides a practical solution to improve precision in data-driven settings.
Data-driven reachability analysis using matrix zonotopes suffers from exponential growth of generators and overly conservative approximations. This paper introduces an orthogonal matrix-based framework that reduces reachable set volumes by orders of magnitude while maintaining comparable generator numbers.
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.