Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes

TL;DR

This paper introduces a set-based verification method using constrained zonotopes to ensure the safety of neural feedback control systems, applicable to both linear and nonlinear models, with demonstrated efficiency and accuracy.

Contribution

It proposes a novel constrained zonotope-based approach for exact and over-approximated reachable set computation and safety verification in neural feedback systems.

Findings

Method accurately verifies safety in linear neural feedback systems.

Approach extends to nonlinear models with promising results.

Comparison shows improved efficiency over existing methods.

Abstract

Artificial neural networks have recently been utilized in many feedback control systems and introduced new challenges regarding the safety of such systems. This paper considers the safe verification problem for a dynamical system with a given feedforward neural network as the feedback controller by using a constrained zonotope-based approach. A novel set-based method is proposed to compute both exact and over-approximated reachable sets for neural feedback systems with linear models, and linear program-based sufficient conditions are presented to verify whether the trajectories of such a system can avoid unsafe regions represented as constrained zonotopes. The results are also extended to neural feedback systems with nonlinear models. The computational efficiency and accuracy of the proposed method are demonstrated by two numerical examples where a comparison with state-of-the-art methods is also provided.