research-article

Synthesizing barrier certificates using neural networks

Authors:

Zhiming LiuAuthors Info & Claims

HSCC '20: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

Article No.: 25, Pages 1 - 11

https://doi.org/10.1145/3365365.3382222

Published: 22 April 2020 Publication History

Abstract

This paper presents an approach of safety verification based on neural networks for continuous dynamical systems which are modeled as a system of ordinary differential equations. We adopt the deductive verification methods based on barrier certificates. These are functions over the states of the dynamical system with certain constraints the existence of which entails the safety of the system under consideration. We propose to represent the barrier function by neural networks and provide a comprehensive synthesis framework. In particular, we devise a new type of activation functions, i.e., Bent-ReLU, for the neural networks; we provide sampling based approaches to generate training sets and formulate the loss functions for neural network training which can capture the essence of barrier certificate; we also present practical methods to check a learnt candidate barrier certificate against the criteria of barrier certificates as a formal guarantee. We implement our approaches via proof-of-concept experiments with encouraging results.

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Cited By

Chen DLin WDing Z(2025)A Learner-Refiner Framework for Barrier Certificate GenerationMathematics10.3390/math1305084813:5(848)Online publication date: 4-Mar-2025
https://doi.org/10.3390/math13050848
Bajelani Mvan Heusden K(2024)Data-Driven Safety Filter: An Input-Output Perspective2024 American Control Conference (ACC)10.23919/ACC60939.2024.10644850(5106-5112)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10644850
Edwards APeruffo AAbate A(2024)Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical ModelsProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3651398(1-10)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3651398
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Synthesizing barrier certificates using neural networks

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cover image ACM Conferences

HSCC '20: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control

April 2020

324 pages

ISBN:9781450370189

DOI:10.1145/3365365

Program Chairs:
Aaron Ames
California Institute of Technology
,
Sanjit A. Seshia
University of California, Berkeley
,
Publications Chair:
Jyotirmoy Deshmukh
University of Southern California

Copyright © 2020 ACM.

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Badge change: Article originally badged under Version 1.0 guidelines https://www.acm.org/publications/policies/artifact-review-badging

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Published: 22 April 2020

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National Natural Science Foundation of China
Birkbeck BEI School Project (ARTEFACT)
Guangdong Science and Technology Department grant
China's Fundamental Research Funds for the Central Universities
Capacity Development Grant of Southwest University
Basic Science and Frontier Technology Research Program of Chongqing

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HSCC '20: 23rd ACM International Conference on Hybrid Systems: Computation and Control

April 22 - 24, 2020

New South Wales, Sydney, Australia

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Overall Acceptance Rate 153 of 373 submissions, 41%

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Cited By

Chen DLin WDing Z(2025)A Learner-Refiner Framework for Barrier Certificate GenerationMathematics10.3390/math1305084813:5(848)Online publication date: 4-Mar-2025
https://doi.org/10.3390/math13050848
Bajelani Mvan Heusden K(2024)Data-Driven Safety Filter: An Input-Output Perspective2024 American Control Conference (ACC)10.23919/ACC60939.2024.10644850(5106-5112)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10644850
Edwards APeruffo AAbate A(2024)Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical ModelsProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3651398(1-10)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3651398
Jin CMa XRen TLin WDing Z(2024)Safe Controller Synthesis for Nonlinear Systems Using Bayesian Optimization Enhanced Reinforcement LearningProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3650137(1-10)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3650137
Zhao HLiu BDehbi LXie HYang ZQian H(2024)Polynomial Neural Barrier Certificate Synthesis of Hybrid Systems via Counterexample GuidanceIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2024.344722643:11(3756-3767)Online publication date: Nov-2024
https://doi.org/10.1109/TCAD.2024.3447226
Anand MMurali VTrivedi AZamani M(2024)Verification of Hyperproperties for Dynamical Systems via Barrier CertificatesIEEE Transactions on Automatic Control10.1109/TAC.2024.338444869:10(6920-6934)Online publication date: Oct-2024
https://doi.org/10.1109/TAC.2024.3384448
Zhang HNiu LClark APoovendran R(2024)Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attacks2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10610491(9901-9907)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10610491
Tayal MZhang HJagtap PClark AKolathaya S(2024)Learning a Formally Verified Control Barrier Function in Stochastic Environment2024 IEEE 63rd Conference on Decision and Control (CDC)10.1109/CDC56724.2024.10886052(4098-4104)Online publication date: 16-Dec-2024
https://doi.org/10.1109/CDC56724.2024.10886052
Samanipour PPoonawala H(2024)Invariant set estimation for piecewise affine dynamical systems using piecewise affine barrier functionEuropean Journal of Control10.1016/j.ejcon.2024.10111580(101115)Online publication date: Nov-2024
https://doi.org/10.1016/j.ejcon.2024.101115
Sheikhi SMehmood UBak SSmolka SStoller S(2024)The black-box simplex architecture for runtime assurance of multi-agent CPSInnovations in Systems and Software Engineering10.1007/s11334-024-00553-6Online publication date: 21-Mar-2024
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