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Related papers: An Introductory Guide to Koopman Learning

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Mean field control provides a robust framework for coordinating large-scale populations with complex interactions and has wide applications across diverse fields. However, the inherent nonlinearity and the presence of unknown system…

Optimization and Control · Mathematics 2024-11-12 Yuhan Zhao , Juntao Chen , Yingdong Lu , Quanyan Zhu

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…

Machine Learning · Computer Science 2017-12-11 Enoch Yeung , Soumya Kundu , Nathan Hodas

We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a…

Analysis of PDEs · Mathematics 2021-10-07 Alexandre Mauroy

Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear…

Robotics · Computer Science 2021-05-18 Carl Folkestad , Joel W. Burdick

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…

Machine Learning · Computer Science 2026-01-21 Minchan Jeong , J. Jon Ryu , Se-Young Yun , Gregory W. Wornell

Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…

Systems and Control · Electrical Eng. & Systems 2023-03-22 Waqas Manzoor , Samir Rawashdeh , Alireza Mohammadi

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…

Dynamical Systems · Mathematics 2016-04-27 Steven L. Brunton , Bingni W. Brunton , Joshua L. Proctor , J. Nathan Kutz

Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…

Machine Learning · Computer Science 2025-03-26 Yuhong Jin , Andong Cong , Lei Hou , Qiang Gao , Xiangdong Ge , Chonglong Zhu , Yongzhi Feng , Jun Li

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional…

Machine Learning · Computer Science 2026-02-05 Xiaoyuan Cheng , Wenxuan Yuan , Yiming Yang , Yuanzhao Zhang , Sibo Cheng , Yi He , Zhuo Sun

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We…

Robotics · Computer Science 2019-06-13 Ian Abraham , Todd D. Murphey

The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…

Robotics · Computer Science 2026-03-02 Rajpal Singh , Chandan Kumar Sah , Jishnu Keshavan

This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…

Optimization and Control · Mathematics 2024-12-05 Daisuke Uchida , Karthik Duraisamy

The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…

Robotics · Computer Science 2025-06-04 Feihan Li , Abulikemu Abuduweili , Yifan Sun , Rui Chen , Weiye Zhao , Changliu Liu

Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models…

Robotics · Computer Science 2026-05-12 Chandan Kumar Sah , Rajpal Singh , Jishnu Keshavan

This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…

Optimization and Control · Mathematics 2024-12-05 Daisuke Uchida , Karthik Duraisamy

The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear…

Dynamical Systems · Mathematics 2024-12-17 Stefan Klus , Nataša Djurdjevac Conrad

The Koopman operator approach to the state estimation problem for nonlinear systems is a promising research area. The main goal of this paper is an attempt to provide a rigorous theoretical framework for this approach. In particular, the…

Optimization and Control · Mathematics 2025-03-12 Judicaël Mohet , Alexandre Mauroy , Joseph J. Winkin

We present task-oriented Koopman-based control that utilizes end-to-end reinforcement learning and contrastive encoder to simultaneously learn the Koopman latent embedding, operator, and associated linear controller within an iterative…

Robotics · Computer Science 2023-11-02 Xubo Lyu , Hanyang Hu , Seth Siriya , Ye Pu , Mo Chen

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…

Systems and Control · Electrical Eng. & Systems 2024-08-06 Zhaoyang Li , Minghao Han , Dat-Nguyen Vo , Xunyuan Yin

Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its…

Machine Learning · Computer Science 2025-05-28 Yuanchao Xu , Kaidi Shao , Nikos Logothetis , Zhongwei Shen