research-article

FOSSIL: a software tool for the formal synthesis of lyapunov functions and barrier certificates using neural networks

Authors:

Alessandro Abate,

Mirco Giacobbe,

Andrea PeruffoAuthors Info & Claims

HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control

Article No.: 24, Pages 1 - 11

https://doi.org/10.1145/3447928.3456646

Published: 19 May 2021 Publication History

Abstract

This paper accompanies FOSSIL: a software tool for the synthesis of Lyapunov functions and of barrier certificates (or functions) for dynamical systems modelled as differential equations. Lyapunov functions are formal certificates for stability analysis, whereas barrier functions are formal certificates for the safety of dynamical models. FOSSIL is sound and automatic thanks to a counterexample-guided inductive synthesis loop. This method exploits the flexibility of candidate functions generated by training neural network templates, the formal assertions provided by a verifier (namely, an SMT solver), and finally new procedures to ease the exchange of information between the two mentioned components. We endow the tool with features of usability, scalability, and robustness---all of which are showcased on benchmarks.

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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
Liu CTse CHuang MWu ZHan HYang J(2025)Design-Oriented Transient Stability Analysis of Grid-Connected Converters: A Comparative Study of Analysis MethodsIEEE Transactions on Power Electronics10.1109/TPEL.2024.348149540:1(749-763)Online publication date: Jan-2025
https://doi.org/10.1109/TPEL.2024.3481495
Miller JDai TSznaier M(2025)Robust Data-Driven Control of Discrete-Time Linear Systems With Errors in VariablesIEEE Transactions on Automatic Control10.1109/TAC.2024.344780970:2(947-962)Online publication date: Feb-2025
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Index Terms

FOSSIL: a software tool for the formal synthesis of lyapunov functions and barrier certificates using neural networks

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cover image ACM Conferences

HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control

May 2021

300 pages

ISBN:9781450383394

DOI:10.1145/3447928

Program Chairs:
Sergiy Bogomolov
Newcastle University, UK
,
Raphaël Jungers
UCLouvain, Belgium

Copyright © 2021 ACM.

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Published: 19 May 2021

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May 19 - 21, 2021

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HSCC '21 Paper Acceptance Rate 27 of 77 submissions, 35%;

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
Liu CTse CHuang MWu ZHan HYang J(2025)Design-Oriented Transient Stability Analysis of Grid-Connected Converters: A Comparative Study of Analysis MethodsIEEE Transactions on Power Electronics10.1109/TPEL.2024.348149540:1(749-763)Online publication date: Jan-2025
https://doi.org/10.1109/TPEL.2024.3481495
Miller JDai TSznaier M(2025)Robust Data-Driven Control of Discrete-Time Linear Systems With Errors in VariablesIEEE Transactions on Automatic Control10.1109/TAC.2024.344780970:2(947-962)Online publication date: Feb-2025
https://doi.org/10.1109/TAC.2024.3447809
Liu JMeng YFitzsimmons MZhou R(2025)Physics-informed neural network Lyapunov functions: PDE characterization, learning, and verificationAutomatica10.1016/j.automatica.2025.112193175(112193)Online publication date: May-2025
https://doi.org/10.1016/j.automatica.2025.112193
Arena PLi Noce APatanè L(2024)Stability and Safety Learning Methods for Legged RobotsRobotics10.3390/robotics1301001713:1(17)Online publication date: 17-Jan-2024
https://doi.org/10.3390/robotics13010017
Chen SMolu LFazlyab M(2024)Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees2024 American Control Conference (ACC)10.23919/ACC60939.2024.10645043(3610-3617)Online publication date: 10-Jul-2024
https://doi.org/10.23919/ACC60939.2024.10645043
Zhao HQi NRen MZeng XZeng ZYang ZDe V(2024)Neural Barrier Certificates Synthesis of NN-Controlled Continuous Systems via Counterexample-Guided LearningProceedings of the 61st ACM/IEEE Design Automation Conference10.1145/3649329.3658256(1-6)Online publication date: 23-Jun-2024
https://dl.acm.org/doi/10.1145/3649329.3658256
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
Liu JMeng YFitzsimmons MZhou R(2024)TOOL LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of AttractionProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3650134(1-8)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3650134
Sun XShoukry Y(2024)Neurosymbolic Motion and Task Planning for Linear Temporal Logic TasksIEEE Transactions on Robotics10.1109/TRO.2024.339207940(2749-2768)Online publication date: 2024
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