Skip to main content
Home
ENHU

Main navigation

  • Discover
    • News
    • Events
  • Research & development
    • Areas of application
    • Research topics
  • Resources
    • Publications
    • Lead researchers
  • Partners
    • Consortium members
    • International partners
    • Industry contacts
    • University contacts
  1. Home
  2. Publications
IFAC-PapersOnLine

Optimal synthesis of LTI Koopman models for nonlinear systems with inputs

Széchenyi Plusz RRF

A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called observables. In the lifted space, the dynamics are linear and represented by a so-called Koopman operator. While the Koopman theory was originally introduced for autonomous systems, it has been widely used to derive linear time-invariant (LTI) models for nonlinear systems with inputs through various approximation schemes such as the extended dynamics mode decomposition (EDMD). However, recent extensions of the Koopman theory show that the lifting process for such systems results in a linear parameter-varying (LPV) model instead of an LTI form. As LTI Koopman model based control has been successfully used in practice and it is generally temping to use such LTI descriptions of nonlinear systems, due to the simplicity of the associated control tool chain, a systematic approach is needed to synthesise optimal LTI approximations of LPV Koopman models compared to the ad-hoc schemes such as EDMD, which is based on least-squares regression. In this work, we introduce optimal LTI Koopman approximations of exact Koopman models of nonlinear systems with inputs by using ℓ2-gain and generalized H2 norm performance measures. We demonstrate the advantages of the proposed Koopman modelling procedure compared to EDMD.

Url
https://www.sciencedirect.com/science/article/pii/S2405896322029329?via%3Dihub=
Authors
Iacob, L. C.
Roland Tóth, PhD
Schoukens, M.
Institutes

Kapcsolat

Prof. Dr. Péter Gáspár

Hungary, H-1111 Budapest,
Kende u. 13-17.
+36 1 279 6000
autonom@nemzetilabor.hu

© 2020-2023 National Laboratory for Autonomous Systems, Budapest