Time-Varying Koopman Operator Theory for Nonlinear Systems Prediction

Damien Gueho, Puneet Singla, Manoranjan Majji

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

This paper introduces the concept of time-varying Koopman operator to predict the flow of a nonlinear dynamical system. The Koopman operator provides a linear prediction model for nonlinear systems in a lifted space of infinite dimension. An extension of time-invariant subspace realization methods known as the time-varying Eigensystem Realization Algorithm (TVERA) in conjunction with the time-varying Observer Kalman Identification Algorithm (TVOKID) are used to derive a finite dimensional approximation of the infinite dimensional Koopman operator at each time step. An isomorphic coordinate transformations is defined to convert different system realizations from different sets of experiments into a common frame for state propagation and to extract dynamical features in the lifted space defined by the eigenvalues of the Koopman operator. Two benchmark numerical examples are considered to demonstrate the capability of the proposed approach.

Original languageEnglish (US)
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2294-2299
Number of pages6
ISBN (Electronic)9781665436595
DOIs
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: Dec 13 2021Dec 17 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2021-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States
CityAustin
Period12/13/2112/17/21

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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