Inner approximated reachability analysis

Eric Goubault; Olivier Mullier; Sylvie Putot; Michel Kieffer

doi:10.1145/2562059.2562113

Inner approximated reachability analysis

Eric Goubault
, Olivier Mullier
, Sylvie Putot
, Michel Kieffer

Institut Pierre Simon Laplace, CNRS and CEA
L2S, CNRS, Univ Paris-Sud

Résultats de recherche: Contribution à une conférence › Papier › Revue par des pairs

38 Citations (Scopus)

Résumé

Computing a tight inner approximation of the range of a function over some set is notoriously dificult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves afine forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.

langue originale	Anglais
Pages	163-172
Nombre de pages	10
Les DOIs	https://doi.org/10.1145/2562059.2562113
état	Publié - 1 janv. 2014
Modification externe	Oui
Evénement	17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, Part of the 7th Cyber Physical Systems, CPS Week 2014 - Berlin, Allemagne Durée: 15 avr. 2014 → 17 avr. 2014

Une conférence

Une conférence	17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, Part of the 7th Cyber Physical Systems, CPS Week 2014
Pays/Territoire	Allemagne
La ville	Berlin
période	15/04/14 → 17/04/14

Accès au document

10.1145/2562059.2562113

Contient cette citation

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title = "Inner approximated reachability analysis",

abstract = "Computing a tight inner approximation of the range of a function over some set is notoriously dificult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves afine forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.",

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Inner approximated reachability analysis. / Goubault, Eric; Mullier, Olivier; Putot, Sylvie et al.
2014. 163-172 Papier présenté � 17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, Part of the 7th Cyber Physical Systems, CPS Week 2014, Berlin, Allemagne.

Résultats de recherche: Contribution à une conférence › Papier › Revue par des pairs

TY - CONF

T1 - Inner approximated reachability analysis

AU - Goubault, Eric

AU - Mullier, Olivier

AU - Putot, Sylvie

AU - Kieffer, Michel

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Computing a tight inner approximation of the range of a function over some set is notoriously dificult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves afine forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.

AB - Computing a tight inner approximation of the range of a function over some set is notoriously dificult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves afine forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.

KW - Afine arithmetic

KW - Inner approximation

KW - Modal intervals

U2 - 10.1145/2562059.2562113

DO - 10.1145/2562059.2562113

M3 - Paper

AN - SCOPUS:84899764111

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EP - 172

T2 - 17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, Part of the 7th Cyber Physical Systems, CPS Week 2014

Y2 - 15 April 2014 through 17 April 2014

ER -

Inner approximated reachability analysis

Résumé

Une conférence

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