Decoupling Abstractions of Non-linear Ordinary Differential Equations

TitleDecoupling Abstractions of Non-linear Ordinary Differential Equations
Publication TypeConference Paper
Year of Publication2016
AuthorsSogokon, A., K. Ghorbal, and T. T. Johnson
Refereed DesignationRefereed
Conference NameFM 2016, 21st International Symposium on Formal Methods
Date Published11/2016
Conference LocationLimassol, Cyprus

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.

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