Reachable Set Estimation and Verification for Neural Network Models of Nonlinear Dynamic Systems

Weiming Xiang, Diego Manzanas Lopez, Patrick Musau, Taylor T. Johnson

Research output: Chapter in Book/Report/Conference proceedingChapter

23 Scopus citations


Neural networks have been widely used to solve complex real-world problems. Due to the complex, nonlinear, non-convex nature of neural networks, formal safety and robustness guarantees for the behaviors of neural network systems are crucial for their applications in safety-critical systems. In this paper, the reachable set estimation and safety verification problems for Nonlinear Autoregressive-Moving Average (NARMA) models in the forms of neural networks are addressed. The neural networks involved in the model are a class of feed-forward neural networks called Multi-Layer Perceptrons (MLPs). By partitioning the input set of an MLP into a finite number of cells, a layer-by-layer computation algorithm is developed for reachable set estimation of each individual cell. The union of estimated reachable sets of all cells forms an over-approximation of the reachable set of the MLP. Furthermore, an iterative reachable set estimation algorithm based on reachable set estimation for MLPs is developed for NARMA models. The safety verification can be performed by checking the existence of non-empty intersections between unsafe regions and the estimated reachable set. Several numerical examples are provided to illustrate the approach.

Original languageEnglish (US)
Title of host publicationUnmanned System Technologies
Number of pages22
StatePublished - 2019
Externally publishedYes

Publication series

NameUnmanned System Technologies
ISSN (Print)2523-3734
ISSN (Electronic)2523-3742


  • NARMA Model
  • Nonlinear Autoregressive Moving Average (NARMA)
  • Reachable Set
  • Safety Verification
  • Safety Verification Problem

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Networks and Communications
  • Automotive Engineering


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