Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods

We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is correct in a probabilistic sense. The first method recasts the reachability problem as a binary classification problem, using a Gaussian process classifier to represent the reachable set. The quantified uncertainty of the Gaussian process model allows for an adaptive approach to the selection of new sample points. The second method uses a Monte Carlo sampling approach to compute an interval-based approximation of the reachable set. This method comes with a guarantee of probabilistic correctness, and an explicit bound on the number of sample points needed to achieve a desired accuracy and confidence. Each method is illustrated with a numerical example.