New probabilistic zonotope method refines disturbance models from data

A team of researchers from multiple institutions has proposed a novel data-driven reachability analysis framework for linear systems using probabilistic zonotopes (PZs). The method addresses a critical gap in existing approaches: traditional reachability analysis requires a precisely known disturbance model (either purely deterministic or purely stochastic), but real-world systems often have only a conservative prior. The new framework refines this prior using real trajectory data by separating two types of uncertainty: realized disturbances that act along the collected trajectory and determine the size of the data-consistent model set, and aleatory disturbances that enter as future additive uncertainty during propagation.

The core technical contribution is a constrained-PZ calculus that absorbs the stochastic constraints into an equivalent representation, removes infeasible latent directions, and reduces stochastic covariance. The refined disturbance proxies are then fed into a linear program that learns the smallest translated and scaled copy of the prior disturbance set that contains all proxy confidence sets while remaining nested in the prior. Numerical experiments demonstrate that the pipeline produces deterministic, high-probability reachable sets with formal containment guarantees that are substantially tighter than those from standard methods, making it particularly relevant for safety-critical applications like autonomous vehicle control and robotics.