Computation of parametric barrier functions for dynamical systems using interval analysis

Olivier Bouissou; Alexandre Chapoutot; Adel Djaballah; Michel Kieffer

doi:10.1109/CDC.2014.7039472

Computation of parametric barrier functions for dynamical systems using interval analysis

Olivier Bouissou, Alexandre Chapoutot, Adel Djaballah, Michel Kieffer

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The formal verification of safety properties for hybrid systems is an important but challenging problem. Recently, barrier functions have been introduced to prove safety without requiring the computation of the reachable set of continuous or hybrid dynamical systems. This paper presents a new approach for the construction of barrier functions for safety verification of nonlinear dynamical systems. The proposed method is based on the search for the parameters of a parametric barrier function using interval analysis. This technique allows considering complex dynamics without needing any relaxation of constraints in the barrier function.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	753-758
Number of pages	6
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7039472
Publication status	Published - 1 Jan 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	15/12/14 → 17/12/14

Access to Document

10.1109/CDC.2014.7039472

Cite this

Bouissou, O., Chapoutot, A., Djaballah, A., & Kieffer, M. (2014). Computation of parametric barrier functions for dynamical systems using interval analysis. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 753-758). Article 7039472 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039472

Bouissou, Olivier ; Chapoutot, Alexandre ; Djaballah, Adel et al. / Computation of parametric barrier functions for dynamical systems using interval analysis. 53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 753-758 (Proceedings of the IEEE Conference on Decision and Control; February).

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title = "Computation of parametric barrier functions for dynamical systems using interval analysis",

abstract = "The formal verification of safety properties for hybrid systems is an important but challenging problem. Recently, barrier functions have been introduced to prove safety without requiring the computation of the reachable set of continuous or hybrid dynamical systems. This paper presents a new approach for the construction of barrier functions for safety verification of nonlinear dynamical systems. The proposed method is based on the search for the parameters of a parametric barrier function using interval analysis. This technique allows considering complex dynamics without needing any relaxation of constraints in the barrier function.",

author = "Olivier Bouissou and Alexandre Chapoutot and Adel Djaballah and Michel Kieffer",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

year = "2014",

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doi = "10.1109/CDC.2014.7039472",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Bouissou, O, Chapoutot, A, Djaballah, A & Kieffer, M 2014, Computation of parametric barrier functions for dynamical systems using interval analysis. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7039472, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 753-758, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15/12/14. https://doi.org/10.1109/CDC.2014.7039472

Computation of parametric barrier functions for dynamical systems using interval analysis. / Bouissou, Olivier; Chapoutot, Alexandre; Djaballah, Adel et al.
53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 753-758 7039472 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The formal verification of safety properties for hybrid systems is an important but challenging problem. Recently, barrier functions have been introduced to prove safety without requiring the computation of the reachable set of continuous or hybrid dynamical systems. This paper presents a new approach for the construction of barrier functions for safety verification of nonlinear dynamical systems. The proposed method is based on the search for the parameters of a parametric barrier function using interval analysis. This technique allows considering complex dynamics without needing any relaxation of constraints in the barrier function.

AB - The formal verification of safety properties for hybrid systems is an important but challenging problem. Recently, barrier functions have been introduced to prove safety without requiring the computation of the reachable set of continuous or hybrid dynamical systems. This paper presents a new approach for the construction of barrier functions for safety verification of nonlinear dynamical systems. The proposed method is based on the search for the parameters of a parametric barrier function using interval analysis. This technique allows considering complex dynamics without needing any relaxation of constraints in the barrier function.

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Bouissou O, Chapoutot A, Djaballah A, Kieffer M. Computation of parametric barrier functions for dynamical systems using interval analysis. In 53rd IEEE Conference on Decision and Control,CDC 2014. February ed. Institute of Electrical and Electronics Engineers Inc. 2014. p. 753-758. 7039472. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7039472

Computation of parametric barrier functions for dynamical systems using interval analysis

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