Data-Driven Reachability Analysis Using Matrix Perturbation Theory
For practitioners of data-driven reachability analysis, this work offers a more scalable and accurate method for real-time applications.
The paper introduces a matrix zonotope perturbation framework for data-driven reachability analysis, using matrix perturbation theory to bound noise-induced distortions. The proposed method is substantially faster than standard constrained matrix zonotope approaches while producing less conservative reachable sets than existing matrix zonotope methods.
We propose a matrix zonotope perturbation framework that leverages matrix perturbation theory to characterize how noise-induced distortions alter the dynamics within sets of models. The framework derives interpretable Cai-Zhang bounds for matrix zonotopes (MZs) and extends them to constrained matrix zonotopes (CMZs). Motivated by this analysis and the computational burden of CMZ-based reachable-set propagation, we introduce a coefficient-space approximation in which the constrained coefficient space of the CMZ is over-approximated by an unconstrained zonotope. Replacing CMZ-constrained-zonotope (CZ) products with unconstrained MZ-zonotope multiplication yields a simpler and more scalable reachable-set update. Experimental results demonstrate that the proposed method is substantially faster than the standard CMZ approach while producing reachable sets that are less conservative than those obtained with existing MZ-based methods, advancing practical, accurate, and real-time data-driven reachability analysis.