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The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Authors:

Pieter Collins,

Alexandre GoldsztejnAuthors Info & Claims

Electronic Notes in Theoretical Computer Science (ENTCS), Volume 223

Pages 87 - 102

https://doi.org/10.1016/j.entcs.2008.12.033

Published: 01 December 2008 Publication History

Abstract

This paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems. The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs. In continuous time, this algorithm is called the Reach and Evolve algorithm. The Reach and Evolve algorithm is based on interval analysis and a rigorous discretization of space and time. Promising numerical experiments are presented.

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Cited By

Bogomolov SForets MFrehse GPodelski ASchilling C(2022)Decomposing reach set computations with low-dimensional sets and high-dimensional matrices (extended version)Information and Computation10.1016/j.ic.2022.104937289:PAOnline publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.ic.2022.104937
Beneš NBrim LDražanová JPastva SŠafránek DOzay NPrabhakar P(2019)Facetal abstraction for non-linear dynamical systems based on δ-decidable SMTProceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control10.1145/3302504.3311793(99-108)Online publication date: 16-Apr-2019
https://dl.acm.org/doi/10.1145/3302504.3311793
Le Mzo TJaulin LZerr B(2018)Bracketing the solutions of an ordinary differential equation with uncertain initial conditionsApplied Mathematics and Computation10.1016/j.amc.2017.07.036318:C(70-79)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1016/j.amc.2017.07.036
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The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

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cover image Electronic Notes in Theoretical Computer Science (ENTCS)

Electronic Notes in Theoretical Computer Science (ENTCS) Volume 223, Issue

December, 2008

256 pages

ISSN:1571-0661

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Copyright © Elsevier B.V. © 2008.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 December 2008

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Cited By

Bogomolov SForets MFrehse GPodelski ASchilling C(2022)Decomposing reach set computations with low-dimensional sets and high-dimensional matrices (extended version)Information and Computation10.1016/j.ic.2022.104937289:PAOnline publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.ic.2022.104937
Beneš NBrim LDražanová JPastva SŠafránek DOzay NPrabhakar P(2019)Facetal abstraction for non-linear dynamical systems based on δ-decidable SMTProceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control10.1145/3302504.3311793(99-108)Online publication date: 16-Apr-2019
https://dl.acm.org/doi/10.1145/3302504.3311793
Le Mzo TJaulin LZerr B(2018)Bracketing the solutions of an ordinary differential equation with uncertain initial conditionsApplied Mathematics and Computation10.1016/j.amc.2017.07.036318:C(70-79)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1016/j.amc.2017.07.036
Rohou SJaulin LMihaylova LLe Bars FVeres S(2017)Guaranteed computation of robot trajectoriesRobotics and Autonomous Systems10.1016/j.robot.2017.03.02093:C(76-84)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1016/j.robot.2017.03.020
Ishii DYonezaki NGoldsztejn A(2015)Monitoring Bounded LTL Properties Using Interval AnalysisElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2015.10.009317:C(85-100)Online publication date: 18-Nov-2015
https://dl.acm.org/doi/10.1016/j.entcs.2015.10.009
Ishii DUeda KHosobe H(2011)An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systemsInternational Journal on Software Tools for Technology Transfer (STTT)10.5555/3220907.322115813:5(449-461)Online publication date: 1-Oct-2011
https://dl.acm.org/doi/10.5555/3220907.3221158

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