Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach

Weiming Xiang, Hoang Dung Tran, Xiaodong Yang, Taylor T. Johnson

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped with neural network components at various stages of sensing and control. This article addresses the reachable set estimation and safety verification problems for dynamical systems embedded with neural network components serving as feedback controllers. The closed-loop system can be abstracted in the form of a continuous-time sampled-data system under the control of a neural network controller. First, a novel reachable set computation method in adaptation to simulations generated out of neural networks is developed. The reachability analysis of a class of feedforward neural networks called multilayer perceptrons (MLPs) with general activation functions is performed in the framework of interval arithmetic. Then, in combination with reachability methods developed for various dynamical system classes modeled by ordinary differential equations, a recursive algorithm is developed for over-approximating the reachable set of the closed-loop system. The safety verification for neural network control systems can be performed by examining the emptiness of the intersection between the over-approximation of reachable sets and unsafe sets. The effectiveness of the proposed approach has been validated with evaluations on a robotic arm model and an adaptive cruise control system.

Original languageEnglish (US)
Article number9093970
Pages (from-to)1821-1830
Number of pages10
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number5
StatePublished - May 2021


  • Neural network control systems
  • reachability
  • safety verification
  • simulation

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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