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

Research output: Contribution to conference › Paper › peer-review

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.

Original language	English
Pages	163-172
Number of pages	10
DOIs	https://doi.org/10.1145/2562059.2562113
Publication status	Published - 1 Jan 2014
Externally published	Yes
Event	17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, Part of the 7th Cyber Physical Systems, CPS Week 2014 - Berlin, Germany Duration: 15 Apr 2014 → 17 Apr 2014

Conference

Conference	17th International Conference on Hybrid Systems: Computation and Control, HSCC 2014, Part of the 7th Cyber Physical Systems, CPS Week 2014
Country/Territory	Germany
City	Berlin
Period	15/04/14 → 17/04/14

Keywords

Afine arithmetic
Inner approximation
Modal intervals

Access to Document

10.1145/2562059.2562113

Cite this

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T1 - Inner approximated reachability analysis

AU - Goubault, Eric

AU - Mullier, Olivier

AU - Putot, Sylvie

AU - Kieffer, Michel

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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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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

Abstract

Conference

Keywords

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Cite this