research-article

Inner approximated reachability analysis

Authors:

Olivier Mullier,

Michel KiefferAuthors Info & Claims

HSCC '14: Proceedings of the 17th international conference on Hybrid systems: computation and control

Pages 163 - 172

https://doi.org/10.1145/2562059.2562113

Published: 15 April 2014 Publication History

Abstract

Computing a tight inner approximation of the range of a function over some set is notoriously difficult, 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 affine 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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Cited By

Rohou SJaulin L(2023)Brunovsky Decomposition for Dynamic Interval LocalizationIEEE Transactions on Automatic Control10.1109/TAC.2023.324694368:11(6937-6943)Online publication date: Nov-2023
https://doi.org/10.1109/TAC.2023.3246943
Bourgois ARohou SJaulin LRauh A(2022)Proving Feasibility of a Docking Mission: A Contractor Programming ApproachMathematics10.3390/math1007113010:7(1130)Online publication date: 1-Apr-2022
https://doi.org/10.3390/math10071130
Le Mézo TJaulin LMassé DZerr B(2022)Kleene Algebra to Compute Invariant Sets of Dynamical SystemsAlgorithms10.3390/a1503009015:3(90)Online publication date: 8-Mar-2022
https://doi.org/10.3390/a15030090
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Index Terms

Inner approximated reachability analysis
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Interval arithmetic
      2. Numerical differentiation
  2. Mathematical software
2. Theory of computation
  1. Design and analysis of algorithms
  2. Semantics and reasoning
    1. Program reasoning
      1. Invariants
      2. Program verification

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cover image ACM Conferences

HSCC '14: Proceedings of the 17th international conference on Hybrid systems: computation and control

April 2014

328 pages

ISBN:9781450327329

DOI:10.1145/2562059

Program Chairs:
Martin Fráänzle
Carl von Ossietziky Universität Oldenburg, Germany
,
John Lygeros
ETH Zurich, Switzerland

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGBED: ACM Special Interest Group on Embedded Systems

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 April 2014

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Agence Nationale de la Recherche
Digiteo SANSCRIT

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HSCC'14

Sponsor:

SIGBED

HSCC'14: 17th International Conference on Hybrid Systems: Computation and Control

April 15 - 17, 2014

Berlin, Germany

Acceptance Rates

HSCC '14 Paper Acceptance Rate 29 of 69 submissions, 42%;

Overall Acceptance Rate 153 of 373 submissions, 41%

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Citations

Cited By

Rohou SJaulin L(2023)Brunovsky Decomposition for Dynamic Interval LocalizationIEEE Transactions on Automatic Control10.1109/TAC.2023.324694368:11(6937-6943)Online publication date: Nov-2023
https://doi.org/10.1109/TAC.2023.3246943
Bourgois ARohou SJaulin LRauh A(2022)Proving Feasibility of a Docking Mission: A Contractor Programming ApproachMathematics10.3390/math1007113010:7(1130)Online publication date: 1-Apr-2022
https://doi.org/10.3390/math10071130
Le Mézo TJaulin LMassé DZerr B(2022)Kleene Algebra to Compute Invariant Sets of Dynamical SystemsAlgorithms10.3390/a1503009015:3(90)Online publication date: 8-Mar-2022
https://doi.org/10.3390/a15030090
Wang JBu LXing SLi X(2022)PDF: Path-Oriented, Derivative-Free Approach for Safety Falsification of Nonlinear and Nondeterministic CPSIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2021.305636041:2(238-251)Online publication date: Feb-2022
https://doi.org/10.1109/TCAD.2021.3056360
Damers JJaulin LRohou S(2022)Lie symmetries applied to interval integrationAutomatica10.1016/j.automatica.2022.110502144(110502)Online publication date: Oct-2022
https://doi.org/10.1016/j.automatica.2022.110502
Rauh ABourgois AJaulin L(2021)Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer DesignAlgorithms10.3390/a1403008814:3(88)Online publication date: 14-Mar-2021
https://doi.org/10.3390/a14030088
Faure MCieslak JHenry DVerhaegen AAnkersen F(2021)Reachable Tube Computation of Uncertain LTI Systems using Support Functions2021 European Control Conference (ECC)10.23919/ECC54610.2021.9654890(2670-2675)Online publication date: 29-Jun-2021
https://doi.org/10.23919/ECC54610.2021.9654890
Rauh AJaulin L(2021)A Novel Thick Ellipsoid Approach for Verified Outer and Inner State Enclosures of Discrete-Time Dynamic SystemsIFAC-PapersOnLine10.1016/j.ifacol.2021.08.42654:7(601-606)Online publication date: 2021
https://doi.org/10.1016/j.ifacol.2021.08.426
Xue BFranzle MZhan N(2020)Inner-Approximating Reachable Sets for Polynomial Systems With Time-Varying UncertaintiesIEEE Transactions on Automatic Control10.1109/TAC.2019.292304965:4(1468-1483)Online publication date: Apr-2020
https://doi.org/10.1109/TAC.2019.2923049
Tillet JJaulin LBars F(2020)Non-linear control under state constraints with validated trajectories for a mobile robot towing a trailer2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS45743.2020.9341712(7729-7736)Online publication date: 24-Oct-2020
https://doi.org/10.1109/IROS45743.2020.9341712
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