research-article

Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier Certificates

Authors:

Zhengfeng Yang,

Xuandong LiAuthors Info & Claims

ACM Transactions on Embedded Computing Systems (TECS), Volume 16, Issue 5s

Article No.: 186, Pages 1 - 19

https://doi.org/10.1145/3126508

Published: 27 September 2017 Publication History

Abstract

The problem of probabilistic safety verification of stochastic hybrid systems is to check whether the probability that a given system will reach an unsafe region from certain initial states can be bounded by some given probability threshold. The paper considers stochastic hybrid systems where the behavior is governed by polynomial equalities and inequalities, as for usual hybrid systems, but the initial states follow some stochastic distributions. It proposes a new barrier certificate based method for probabilistic safety verification which guarantees the absolute safety in a infinite time horizon that is beyond the reach of existing techniques using either statistical model checking or probabilistic reachable set computation. It also gives a novel computational approach, by building and solving a constrained optimization problem coming from verification conditions of barrier certificates, to compute the lower bound on safety probabilities which can be compared with the given threshold. Experimental evidence is provided demonstrating the applicability of our approach on several benchmarks.

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Cited By

Nejati APrakash Nayak SSchmuck A(2024)Context-triggered Games for Reactive Synthesis over Stochastic Systems via Control Barrier CertificatesProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3650136(1-12)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3650136
Wang YZhou WFan JWang ZLi JChen XHuang CLi WZhu Q(2024)POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled SystemsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2023.333121543:3(994-1007)Online publication date: Mar-2024
https://doi.org/10.1109/TCAD.2023.3331215
Anand MLavaei AZamani M(2024) Compositional synthesis of control barrier certificates for networks of stochastic systems against -regular specifications Nonlinear Analysis: Hybrid Systems10.1016/j.nahs.2023.10142751(101427)Online publication date: Feb-2024
https://doi.org/10.1016/j.nahs.2023.101427
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Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier Certificates

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Published In

cover image ACM Transactions on Embedded Computing Systems

ACM Transactions on Embedded Computing Systems Volume 16, Issue 5s

Special Issue ESWEEK 2017, CASES 2017, CODES + ISSS 2017 and EMSOFT 2017

October 2017

1448 pages

ISSN:1539-9087

EISSN:1558-3465

DOI:10.1145/3145508

Editor:
Sandeep K. Shukla
Indian Institute of Technology, India

Issue’s Table of Contents

Copyright © 2017 ACM.

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ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 27 September 2017

Accepted: 01 June 2017

Revised: 01 May 2017

Received: 01 April 2017

Published in TECS Volume 16, Issue 5s

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Shanghai Natural Science Foundation
National Natural Science Foundation of China
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Cited By

Nejati APrakash Nayak SSchmuck A(2024)Context-triggered Games for Reactive Synthesis over Stochastic Systems via Control Barrier CertificatesProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3650136(1-12)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3650136
Wang YZhou WFan JWang ZLi JChen XHuang CLi WZhu Q(2024)POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled SystemsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2023.333121543:3(994-1007)Online publication date: Mar-2024
https://doi.org/10.1109/TCAD.2023.3331215
Anand MLavaei AZamani M(2024) Compositional synthesis of control barrier certificates for networks of stochastic systems against -regular specifications Nonlinear Analysis: Hybrid Systems10.1016/j.nahs.2023.10142751(101427)Online publication date: Feb-2024
https://doi.org/10.1016/j.nahs.2023.101427
Gray AForets MSchilling CFerson SBenet L(2024)Verified propagation of imprecise probabilities in non-linear ODEsInternational Journal of Approximate Reasoning10.1016/j.ijar.2023.109044164:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.ijar.2023.109044
Nadali ATrivedi AZamani M(2024)Transfer of Safety Controllers Through Learning Deep Inverse Dynamics ModelIFAC-PapersOnLine10.1016/j.ifacol.2024.07.43658:11(129-134)Online publication date: 2024
https://doi.org/10.1016/j.ifacol.2024.07.436
Wu HFeng SGan TWang JXia BZhan N(2024)On Completeness of SDP-Based Barrier Certificate Synthesis over Unbounded DomainsFormal Methods10.1007/978-3-031-71177-0_16(248-266)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71177-0_16
Wetzlinger MKochdumper NBak SAlthoff M(2023)Fully-Automated Verification of Linear Systems Using Reachability Analysis with Support FunctionsProceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3575870.3587121(1-12)Online publication date: 9-May-2023
https://dl.acm.org/doi/10.1145/3575870.3587121
Jahanshahi NLavaei AZamani M(2023)Compositional Construction of Safety Controllers for Networks of Continuous-Space POMDPsIEEE Transactions on Control of Network Systems10.1109/TCNS.2022.318664910:1(87-99)Online publication date: Mar-2023
https://doi.org/10.1109/TCNS.2022.3186649
Nejati ALavaei AJagtap PSoudjani SZamani M(2023)Formal Verification of Unknown Discrete- and Continuous-Time Systems: A Data-Driven ApproachIEEE Transactions on Automatic Control10.1109/TAC.2023.325514168:5(3011-3024)Online publication date: May-2023
https://doi.org/10.1109/TAC.2023.3255141
Zhu QLi WHuang CChen XZhou WWang YLi JFu F(2023)Verification and Design of Robust and Safe Neural Network-enabled Autonomous Systems2023 59th Annual Allerton Conference on Communication, Control, and Computing (Allerton)10.1109/Allerton58177.2023.10313451(1-8)Online publication date: 26-Sep-2023
https://doi.org/10.1109/Allerton58177.2023.10313451
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