Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties

TL;DR

This paper introduces a Gaussian process-based statistical verification method for stochastic nonlinear systems with uncertainties, enabling efficient prediction and active sampling to improve accuracy and confidence in system performance assessments.

Contribution

It presents a novel GP regression framework with a variance-based confidence metric and active sampling algorithms for simulation-efficient verification of uncertain nonlinear systems.

Findings

Active sampling reduces prediction error by up to 35%.

The variance metric effectively identifies low-confidence regions.

Framework successfully predicts system performance across uncertainties.

Abstract

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the proposed framework constructs a GP regression model and predicts the system's performance over the entire set of possible uncertainties. Included in the framework is a new metric to estimate the confidence in those predictions based on the variance of the GP's cumulative distribution function. This variance-based metric forms the basis of active sampling algorithms that aim to minimize prediction error through careful selection of simulations. In three case studies, the new active sampling algorithms demonstrate up to a 35% improvement in prediction error over other approaches and are able to correctly identify regions with low prediction confidence through the variance metric.