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Decoupling Abstractions of Non-linear Ordinary Differential Equations

  • Andrew Sogokon
  • Khalil Ghorbal
  • Taylor T. Johnson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9995)

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) sub-systems, 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.

Keywords

Ordinary differential equations Darboux polynomials Simulation Abstraction Decoupling 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their careful reading and judicious critique and extend their thanks to Dr. André Platzer at Carnegie Mellon University for his technical questions and helpful insights into differential ghosts.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.InriaRennesFrance
  3. 3.Vanderbilt UniversityNashvilleUSA

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