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Related papers: Model-Based Control Using Koopman Operators

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Learning dexterous manipulation skills presents significant challenges due to complex nonlinear dynamics that underlie the interactions between objects and multi-fingered hands. Koopman operators have emerged as a robust method for modeling…

The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman…

Dynamical Systems · Mathematics 2026-02-05 Roland Schurig , Pieter van Goor , Karl Worthmann , Rolf Findeisen

A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal…

Optimization and Control · Mathematics 2022-07-15 Simone Servadio , Roberto Armellin , Richard Linares

In this paper, we systematically derive a finite set of Koopman based observables to construct a lifted linear state space model that describes the rigid body dynamics based on the dual quaternion representation. In general, the Koopman…

Systems and Control · Electrical Eng. & Systems 2022-09-20 Vrushabh Zinage , Efstathios Bakolas

In this paper, an extension to rules-based fault detection is demonstrated utilizing properties of the Koopman operator. The Koopman operator is an infinite-dimensional, linear operator that captures nonlinear, finite dimensional dynamics.…

Systems and Control · Computer Science 2017-03-22 Michael Georgescu , Sophie Loire , Don Kasper , Igor Mezic

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

Machine Learning · Computer Science 2026-05-05 Tatsuya Naoi , Jun Ohkubo

Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…

Dynamical Systems · Mathematics 2025-01-08 William T. Redman , Dean Huang , Maria Fonoberova , Igor Mezić

This report presents the results of a simulation study of the linear model and bilinear model approximations of the Koopman system model of the nonlinear utility functions in optimal control of a 3-robot system. In such a control problem,…

Systems and Control · Electrical Eng. & Systems 2023-05-09 Qianhong Zhao , Gang Tao

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…

Optimization and Control · Mathematics 2021-10-27 Nibodh Boddupalli

In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…

Dynamical Systems · Mathematics 2019-10-09 Sai Pushpak Nandanoori , Subhrajit Sinha , Enoch Yeung

Koopman operator, as a fully linear representation of nonlinear dynamical systems, if well-defined on a reproducing kernel Hilbert space (RKHS), can be efficiently learned from data. For stability analysis and control-related problems, it…

Systems and Control · Electrical Eng. & Systems 2025-11-11 Wentao Tang , Xiuzhen Ye

In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on the Koopman operator…

Systems and Control · Electrical Eng. & Systems 2025-08-11 Robin Strässer , Julian Berberich , Manuel Schaller , Karl Worthmann , Frank Allgöwer

This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the…

Robotics · Computer Science 2026-04-23 Wenjian Hao , Yuxuan Fang , Zehui Lu , Shaoshuai Mou

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

Machine Learning · Computer Science 2023-05-17 King Fai Yeh , Paris Flood , William Redman , Pietro Liò

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

Systems and Control · Electrical Eng. & Systems 2021-02-09 Mario Sznaier

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

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of…

Systems and Control · Electrical Eng. & Systems 2022-05-24 Vrushabh Zinage , Efstathios Bakolas

Data-driven control methods need to be sample-efficient and lightweight, especially when data acquisition and computational resources are limited -- such as during learning on hardware. Most modern data-driven methods require large datasets…

Robotics · Computer Science 2025-09-11 Zixin Zhang , James Avtges , Todd D. Murphey

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…

Dynamical Systems · Mathematics 2025-03-03 Rishikesh Yadav , Alexandre Mauroy

Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we can figure out the synchronization process. A promising…

Adaptation and Self-Organizing Systems · Physics 2025-02-05 Yuka Hashimoto , Masahiro Ikeda , Hiroya Nakao , Yoshinobu Kawahara