Optimal Construction of Koopman Eigenfunctions for Prediction and Control
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00344904" target="_blank" >RIV/68407700:21230/20:00344904 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1109/TAC.2020.2978039" target="_blank" >https://doi.org/10.1109/TAC.2020.2978039</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TAC.2020.2978039" target="_blank" >10.1109/TAC.2020.2978039</a>
Alternative languages
Result language
angličtina
Original language name
Optimal Construction of Koopman Eigenfunctions for Prediction and Control
Original language description
This article presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct a set of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. The eigenfunction construction is optimization-based with no dictionary selection required. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multistep prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control (MPC) framework of (M. Korda and I. Mezić, 2018) to control nonlinear dynamical systems using linear MPC tools. The method is entirely data-driven and based predominantly on convex optimization. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples demonstrate the approach, both for prediction and feedback control.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
<a href="/en/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koopman operator framework for control of complex nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Automatic Control
ISSN
0018-9286
e-ISSN
1558-2523
Volume of the periodical
65
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
5114-5129
UT code for WoS article
000595526300008
EID of the result in the Scopus database
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