Sample-Free Safety Assessment of Neural Network Controllers via Taylor Methods

TL;DR

This paper introduces a method for safety assessment of neural network controllers in safety-critical systems by combining Taylor polynomial approximations, domain splitting, and polynomial bounding to rigorously analyze system outcomes.

Contribution

It develops a novel approach that embeds neural networks into dynamical systems and uses Taylor methods for rigorous safety verification, addressing trust issues in neural network controllers.

Findings

Enables rigorous safety bounds for neural network controllers.

Efficiently analyzes large state spaces through automatic domain splitting.

Provides a framework for safety-critical system verification with neural networks.

Abstract

In recent years, artificial neural networks have been increasingly studied as feedback controllers for guidance problems. While effective in complex scenarios, they lack the verification guarantees found in classical guidance policies. Their black-box nature creates significant concerns regarding trustworthiness, limiting their adoption in safety-critical spaceflight applications. This work addresses this gap by developing a method to assess the safety of a trained neural network feedback controller via automatic domain splitting and polynomial bounding. The methodology involves embedding the trained neural network into the system's dynamical equations, rendering the closed-loop system autonomous. The system flow is then approximated by high-order Taylor polynomials, which are subsequently manipulated to construct polynomial maps that project state uncertainties onto an event manifold. Automatic domain splitting ensures the polynomials are accurate over their relevant subdomains, whilst also allowing an extensive state-space to be analysed efficiently. Utilising polynomial bounding techniques, the resulting event values may be rigorously constrained and analysed within individual subdomains, thereby establishing bounds on the range of possible closed-loop outcomes from using such neural network controllers and supporting safety assessment and informed operational decision-making in real-world missions.