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Algorithms for exact and approximate linear abstractions of polynomial continuous systems

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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.

Suggested Citation

  • Michele Boreale, 2018. "Algorithms for exact and approximate linear abstractions of polynomial continuous systems," Econometrics Working Papers Archive 2018_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  • Handle: RePEc:fir:econom:wp2018_03
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    File URL: https://labdisia.disia.unifi.it/wp_disia/2018/wp_disia_2018_03.pdf
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