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Vector barrier certificates and comparison systems

Vector barrier certificates and comparison systems
Vector barrier certificates and comparison systems
Vector Lyapunov functions are a multi-dimensional extension of the more familiar (scalar) Lyapunov functions, commonly used to prove stability properties in systems of non-linear ordinary differential equations (ODEs). This paper explores an analogous vector extension for so-called barrier certificates used in safety verification. As with vector Lyapunov functions, the approach hinges on constructing appropriate comparison systems, i.e., related differential equation systems from which properties of the original system may be inferred. The paper presents an accessible development of the approach, demonstrates that most previous notions of barrier certificate are special cases of comparison systems, and discusses the potential applications of vector barrier certificates in safety verification and invariant synthesis.
safety verification, differential inequalities, ordinary differential equations, barrier certificates
0302-9743
418-437
Springer
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Ghorbal, Khalil
78ea6702-dcc4-41a9-b197-b850ff086df2
Tan, Yong Kiam
09ebcf1a-92e4-4b3b-9d57-b08934e67b0a
Platzer, André
aea44fc1-de31-434a-8b47-82e22b675ee9
Havelund, K.
Peleska, J.
Roscoe, B.
de Vink, E.
Sogokon, Andrew
2600b17f-45e5-4e54-9a99-44baaf8eaf18
Ghorbal, Khalil
78ea6702-dcc4-41a9-b197-b850ff086df2
Tan, Yong Kiam
09ebcf1a-92e4-4b3b-9d57-b08934e67b0a
Platzer, André
aea44fc1-de31-434a-8b47-82e22b675ee9
Havelund, K.
Peleska, J.
Roscoe, B.
de Vink, E.

Sogokon, Andrew, Ghorbal, Khalil, Tan, Yong Kiam and Platzer, André (2018) Vector barrier certificates and comparison systems. Havelund, K., Peleska, J., Roscoe, B. and de Vink, E. (eds.) In Proceedings of the 22nd International Symposium on Formal Methods, FM 2018, Held as Part of the Federated Logic Conference, FloC 2018. vol. 10951, Springer. pp. 418-437 . (doi:10.1007/978-3-319-95582-7_25).

Record type: Conference or Workshop Item (Paper)

Abstract

Vector Lyapunov functions are a multi-dimensional extension of the more familiar (scalar) Lyapunov functions, commonly used to prove stability properties in systems of non-linear ordinary differential equations (ODEs). This paper explores an analogous vector extension for so-called barrier certificates used in safety verification. As with vector Lyapunov functions, the approach hinges on constructing appropriate comparison systems, i.e., related differential equation systems from which properties of the original system may be inferred. The paper presents an accessible development of the approach, demonstrates that most previous notions of barrier certificate are special cases of comparison systems, and discusses the potential applications of vector barrier certificates in safety verification and invariant synthesis.

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fm-2018-vector-barrier-certificates
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Accepted/In Press date: 1 April 2016
e-pub ahead of print date: 12 July 2018
Published date: July 2018
Keywords: safety verification, differential inequalities, ordinary differential equations, barrier certificates

Identifiers

Local EPrints ID: 434326
URI: http://eprints.soton.ac.uk/id/eprint/434326
ISSN: 0302-9743
PURE UUID: 7666b17f-4fcc-4233-8246-815e1d925371

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Date deposited: 19 Sep 2019 16:30
Last modified: 06 Oct 2020 17:14

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Contributors

Author: Andrew Sogokon
Author: Khalil Ghorbal
Author: Yong Kiam Tan
Author: André Platzer
Editor: K. Havelund
Editor: J. Peleska
Editor: B. Roscoe
Editor: E. de Vink

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