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Verification and safety assessment of neural network controlled systems(NNCSs) is an emerging challenge. To provide guarantees, verification toolsmust efficiently capture the interplay between the neural network and thephysical system within the control loop. In this paper, a compositionalapproach focused on inclusion preserving long term symbolic dependency modelingis proposed for the analysis of NNCSs. First of all, the matrix structure ofsymbolic zonotopes is exploited to efficiently abstract the input/outputmapping of the loop elements through (inclusion preserving) affine symbolicexpressions, thus maintaining linear dependencies between interacting blocks.Then, two further extensions are studied. Firstly, symbolic polynotopes areused to abstract the loop elements behaviour by means of polynomial symbolicexpressions and dependencies. Secondly, an original input partitioningalgorithm takes advantage of symbol preservation to assess the sensitivity ofthe computed approximation to some input directions. The approach is evaluatedvia different numerical examples and benchmarks. A good trade-off between lowconservatism and computational efficiency is obtained.

Verification of Neural Network Control Systems using Symbolic Zonotopes and Polynotopes