Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control

Autor:	Folkestad, Carl, Pastor, Daniel, Mezic, Igor, Mohr, Ryan, Fonoberova, Maria, Burdick, Joel
Rok vydání:	2019
Předmět:	Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear state-space model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control. Comment: 2020 American Control Conference
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1911.08751 Zobrazit plný text záznamu View this record from Arxiv