IDEAS home Printed from https://ideas.repec.org/p/fir/econom/wp2018_03.html
   My bibliography  Save this paper

Algorithms for exact and approximate linear abstractions of polynomial continuous systems

Author

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
    as

    Download full text from publisher

    File URL: https://labdisia.disia.unifi.it/wp_disia/2018/wp_disia_2018_03.pdf
    File Function: First version, 2018-02
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fir:econom:wp2018_03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Fabrizio Cipollini (email available below). General contact details of provider: https://edirc.repec.org/data/dsfirit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.