scholarly journals Data-driven identification of vehicle dynamics using Koopman operator

2019 ◽  
Author(s):  
Vit Cibulka ◽  
Tomas Hanis ◽  
Martin Hromcik
Keyword(s):  
Vehicle Dynamics ◽  
Data Driven ◽  
Koopman Operator

scholarly journals Gain-Preserving Data-Driven Approximation of the Koopman Operator and Its Application in Robust Controller Design

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 949
Author(s):  
Keita Hara ◽  
Masaki Inoue
Keyword(s):  
Controller Design ◽  
Internal Model Control ◽  
Feedback Controller ◽  
Data Driven ◽  
Koopman Operator ◽  
Plant System ◽  
Dimensional Approximation ◽  
Model Control ◽  
Data Driven Modeling ◽  
L2 Gain

In this paper, we address the data-driven modeling of a nonlinear dynamical system while incorporating a priori information. The nonlinear system is described using the Koopman operator, which is a linear operator defined on a lifted infinite-dimensional state-space. Assuming that the L2 gain of the system is known, the data-driven finite-dimensional approximation of the operator while preserving information about the gain, namely L2 gain-preserving data-driven modeling, is formulated. Then, its computationally efficient solution method is presented. An application of the modeling method to feedback controller design is also presented. Aiming for robust stabilization using data-driven control under a poor training dataset, we address the following two modeling problems: (1) Forward modeling: the data-driven modeling is applied to the operating data of a plant system to derive the plant model; (2) Backward modeling: L2 gain-preserving data-driven modeling is applied to the same data to derive an inverse model of the plant system. Then, a feedback controller composed of the plant and inverse models is created based on internal model control, and it robustly stabilizes the plant system. A design demonstration of the data-driven controller is provided using a numerical experiment.

scholarly journals Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
J. Nathan Kutz ◽  
J. L. Proctor ◽  
S. L. Brunton
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Data Driven ◽  
Nonlinear Pdes ◽  
Dynamic Mode ◽  
Partial Differential ◽  
Koopman Operator ◽  
Dimensional Approximation ◽  
Spatio Temporal ◽  
The Impact

We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition (DMD) algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues, and Koopman modes. We demonstrate simple rules of thumb for selecting a parsimonious set of observables that can greatly improve the approximation of the Koopman operator. Further, we show that the clear goal in selecting observables is to place the DMD eigenvalues on the imaginary axis, thus giving an objective function for observable selection. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. Our method provides a valuable intermediate, yet interpretable, approximation to the Koopman operator that lies between the DMD method and the computationally intensive extended DMD (EDMD). We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on several canonical nonlinear PDEs: Burgers’ equation, the nonlinear Schrödinger equation, the cubic-quintic Ginzburg-Landau equation, and a reaction-diffusion system. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.

scholarly journals A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

2015 ◽  
Vol 25 (6) ◽  
pp. 1307-1346 ◽  
Author(s):  
Matthew O. Williams ◽  
Ioannis G. Kevrekidis ◽  
Clarence W. Rowley
Keyword(s):  
Dynamic Mode Decomposition ◽  
Data Driven ◽  
Dynamic Mode ◽  
Koopman Operator ◽  
Mode Decomposition

scholarly journals Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator

2021 ◽  
Vol 31 (5) ◽  
pp. 053116
Author(s):  
Manuel Santos Gutiérrez ◽  
Valerio Lucarini ◽  
Mickaël D. Chekroun ◽  
Michael Ghil
Keyword(s):  
Dynamical Systems ◽  
Data Driven ◽  
Reduced Order Models ◽  
Koopman Operator ◽  
Reduced Order

scholarly journals Data-driven Koopman operator approach for computational neuroscience

2019 ◽  
Vol 88 (11-12) ◽  
pp. 1155-1173 ◽  
Author(s):  
Natasza Marrouch ◽  
Joanna Slawinska ◽  
Dimitrios Giannakis ◽  
Heather L. Read
Keyword(s):  
Computational Neuroscience ◽  
Low Frequency ◽  
Spatiotemporal Dynamics ◽  
Data Driven ◽  
Operator Approach ◽  
Koopman Operator ◽  
Electrophysiological Signals ◽  
High Gamma ◽  
Frequency Components ◽  
Selection Of

Abstract This article presents a novel, nonlinear, data-driven signal processing method, which can help neuroscience researchers visualize and understand complex dynamical patterns in both time and space. Specifically, we present applications of a Koopman operator approach for eigendecomposition of electrophysiological signals into orthogonal, coherent components and examine their associated spatiotemporal dynamics. This approach thus provides enhanced capabilities over conventional computational neuroscience tools restricted to analyzing signals in either the time or space domains. This is achieved via machine learning and kernel methods for data-driven approximation of skew-product dynamical systems. The approximations successfully converge to theoretical values in the limit of long embedding windows. First, we describe the method, then using electrocorticographic (ECoG) data from a mismatch negativity experiment, we extract time-separable frequencies without bandpass filtering or prior selection of wavelet features. Finally, we discuss in detail two of the extracted components, Beta ($ \sim $ ∼ 13 Hz) and high Gamma ($ \sim $ ∼ 50 Hz) frequencies, and explore the spatiotemporal dynamics of high- and low- frequency components.

scholarly journals Data-Driven quasi-LPV Model Predictive Control Using Koopman Operator Techniques

2020 ◽  
Vol 53 (2) ◽  
pp. 6062-6068
Author(s):  
Pablo. S.G. Cisneros ◽  
Adwait Datar ◽  
Patrick Göttsch ◽  
Herbert Werner
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Data Driven ◽  
Koopman Operator
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