Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers

Weiming Xiang, Hoang Dung Tran, Joel A. Rosenfeld, Taylor T. Johnson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks. The computation is formulated in the form of a set of manipulations for a union of polytopes. Based on the output reachable set for neural network controllers, the output reachable set for a piecewise linear feedback control system can be estimated iteratively for a given finite-time interval. With the estimated output reachable set, the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set. A numerical example is presented to illustrate the effectiveness of our approach.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1574-1579
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Externally publishedYes
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Conference

Conference2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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    Xiang, W., Tran, H. D., Rosenfeld, J. A., & Johnson, T. T. (2018). Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers. In 2018 Annual American Control Conference, ACC 2018 (pp. 1574-1579). [8431048] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431048