Algorithms for exact and approximate linear abstractions of polynomial continuous systems

Michele Boreale ()
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Michele Boreale: Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", Università di Firenze, https://www.disia.unifi.it

No 2018_03, Econometrics Working Papers Archive from Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti"

Abstract: A polynomial continuous system S=(F, X 0 ) is specified by a polynomial vector field F and a set of initial conditions X 0 . We study polynomial changes of bases that transform S into a linear system, called linear abstractions . We first give a complete algorithm to find all such abstractions that fit a user-specified template. This requires taking into account the algebraic structure of the set X 0 , which we do by working modulo an appropriate invariant ideal. Next, we give necessary and sufficient syntactic conditions under which a full linear abstraction exists, that is one capable of representing the behaviour of the individual variables in the original system. We then propose an approximate linearization and dimension-reduction technique, that is amenable to be implemented "on the fly". We finally illustrate the encouraging results of a preliminary experimentation with the linear abstraction algorithm, conducted on challenging systems drawn from the literature.

Keywords: ordinary differential equations; abstraction; invariants; linearization (search for similar items in EconPapers)
Pages: 21 pages
Date: 2018-02
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