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

TL;DR

This paper introduces two probabilistic, data-driven methods for estimating reachable sets in control systems, leveraging Gaussian process classification and Monte Carlo sampling to provide guarantees on accuracy and confidence.

Contribution

It proposes novel, probabilistic approaches for reachable set estimation using Gaussian processes and Monte Carlo methods, with formal guarantees and adaptive sampling strategies.

Findings

Gaussian process classifier effectively models reachable sets with uncertainty quantification.

Monte Carlo method provides interval-based reachable set approximation with probabilistic correctness.

Both methods demonstrate practical applicability through numerical examples.

Abstract

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.