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We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinitedimensional) Koopman operator in the lifted space of observables,…

Optimization and Control · Mathematics 2019-04-25 Alexandre Mauroy , Jorge Goncalves

The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we…

Dynamical Systems · Mathematics 2026-04-07 Natsuki Katayama , Alexandre Mauroy , Yoshihiko Susuki

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under…

Machine Learning · Statistics 2025-02-06 Boya Hou , Sina Sanjari , Nathan Dahlin , Alec Koppel , Subhonmesh Bose

We use Koopman theory for data-driven model reduction of nonlinear dynamical systems with controls. We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman…

Systems and Control · Electrical Eng. & Systems 2024-01-10 Jan C. Schulze , Alexander Mitsos

Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of nonlinear dynamic behavior (e.g. through normal forms). In…

Dynamical Systems · Mathematics 2018-03-08 Erik M. Bollt , Qianxiao Li , Felix Dietrich , Ioannis Kevrekidis

We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…

Dynamical Systems · Mathematics 2019-08-14 Sebastian Peitz , Stefan Klus

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…

Systems and Control · Electrical Eng. & Systems 2025-10-06 Wenjian Hao , Lili Wang , Ayush Rai , Shaoshuai Mou

Data-driven model predictive control based on Willems' fundamental lemma has proven effective for linear systems, but extending stability guarantees to nonlinear systems remains an open challenge. In this paper, we establish conditions…

Systems and Control · Electrical Eng. & Systems 2026-03-19 Amin Taghieh , SangWoo Park

Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman…

Robotics · Computer Science 2025-09-16 Eron Ristich , Lei Zhang , Yi Ren , Jiefeng Sun

In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random…

We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…

Machine Learning · Computer Science 2020-06-23 Iva Manojlović , Maria Fonoberova , Ryan Mohr , Aleksandr Andrejčuk , Zlatko Drmač , Yannis Kevrekidis , Igor Mezić

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…

Dynamical Systems · Mathematics 2023-11-01 Jason J. Bramburger , Giovanni Fantuzzi

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Dynamical Systems · Mathematics 2024-03-25 Anna Fitzpatrick , Molly Folino , Andrea Arnold

This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Ali Azarbahram , Shenyu Liu , Gian Paolo Incremona

This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized…

Machine Learning · Computer Science 2025-11-20 Wenjian Hao , Paulo C. Heredia , Shaoshuai Mou

We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…

Robotics · Computer Science 2026-03-24 Koki Hirano , Hiroyasu Tsukamoto

In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is…

Optimization and Control · Mathematics 2020-01-08 Subhrajit Sinha , Huang Bowen , Umesh Vaidya

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…

Systems and Control · Electrical Eng. & Systems 2025-11-07 Patrik Valábek , Marek Wadinger , Michal Kvasnica , Martin Klaučo

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a…

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a…

Optimization and Control · Mathematics 2018-02-27 Prabhat Kumar Mishra , Debasish Chatterjee , Daniel E. Quevedo