Optimal Construction of Koopman Eigenfunctions for Prediction and Control

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimal Construction of Koopman Eigenfunctions for Prediction and Control

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Optimal Construction of Koopman Eigenfunctions for Prediction and Control

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

20205 - Automation and control systems

Projekt

<a href="/cs/project/GJ20-11626Y" target="_blank" >GJ20-11626Y: Koncept Koopmanova operátoru pro řízení komplexních nelineárních dynamických systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE Transactions on Automatic Control

ISSN

0018-9286

e-ISSN

1558-2523

Svazek periodika

65

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

5114-5129

Kód UT WoS článku

000595526300008

EID výsledku v databázi Scopus

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