Verification of Neural Network Control Systems using Symbolic Zonotopes and Polynotopes

TL;DR

This paper introduces a compositional symbolic approach using zonotopes and polynotopes for the verification of neural network control systems, enabling efficient and accurate safety analysis.

Contribution

It proposes a novel inclusion-preserving symbolic dependency modeling framework that combines zonotopes and polynotopes for NNCS verification, with an input partitioning algorithm for sensitivity analysis.

Findings

Achieves low conservatism in verification results

Demonstrates computational efficiency on benchmarks

Provides a scalable approach for complex systems

Abstract

Verification and safety assessment of neural network controlled systems (NNCSs) is an emerging challenge. To provide guarantees, verification tools must efficiently capture the interplay between the neural network and the physical system within the control loop. In this paper, a compositional approach focused on inclusion preserving long term symbolic dependency modeling is proposed for the analysis of NNCSs. First of all, the matrix structure of symbolic zonotopes is exploited to efficiently abstract the input/output mapping of the loop elements through (inclusion preserving) affine symbolic expressions, thus maintaining linear dependencies between interacting blocks. Then, two further extensions are studied. Firstly, symbolic polynotopes are used to abstract the loop elements behaviour by means of polynomial symbolic expressions and dependencies. Secondly, an original input partitioning algorithm takes advantage of symbol preservation to assess the sensitivity of the computed approximation to some input directions. The approach is evaluated via different numerical examples and benchmarks. A good trade-off between low conservatism and computational efficiency is obtained.