Decoupling Abstractions of Non-linear Ordinary Differential Equations - Archive ouverte HAL Access content directly
Conference Papers Year : 2016

Decoupling Abstractions of Non-linear Ordinary Differential Equations

Abstract

We investigate decoupling abstractions, by which we seek to simulate (i.e. abstract) a given system of ordinary differential equations (ODEs) by another system that features completely independent (i.e. uncoupled) subsystems , which can be considered as separate systems in their own right. Beyond a purely mathematical interest as a tool for the qualitative analysis of ODEs, decoupling can be applied to verification problems arising in the fields of control and hybrid systems. Existing verification technology often scales poorly with dimension. Thus, reducing a verification problem to a number of independent verification problems for systems of smaller dimension may enable one to prove properties that are otherwise seen as too difficult. We show an interesting correspondence between Darboux polynomials and decoupling simulating abstractions of systems of polynomial ODEs and give a constructive procedure for automatically computing the latter.
Fichier principal
Vignette du fichier
main.pdf (366.46 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01374899 , version 1 (02-10-2016)
hal-01374899 , version 2 (28-11-2016)

Licence

Copyright

Identifiers

Cite

Andrew T Sogokon, Khalil Ghorbal, Taylor T Johnson. Decoupling Abstractions of Non-linear Ordinary Differential Equations. FM 2016 - 21st International Symposium of Formal Methods, Nov 2016, Limassol, Cyprus. pp.628-644, ⟨10.1007/978-3-319-48989-6_38⟩. ⟨hal-01374899v2⟩
576 View
266 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More