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This paper presents a data-learned linear Koopman embedding of nonlinear networked dynamics and uses it to enable real-time model predictive emergency voltage control in a power network. The approach involves a novel data-driven…

Systems and Control · Electrical Eng. & Systems 2023-10-06 Ramij R. Hossain , Rahmat Adesunkanmi , Ratnesh Kumar

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

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

This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…

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

This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…

Optimization and Control · Mathematics 2021-10-25 Henk J. van Waarde , Rodolphe Sepulchre

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…

Dynamical Systems · Mathematics 2023-10-26 Samuel E. Otto , Sebastian Peitz , Clarence W. Rowley

Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schr\"odinger…

Dynamical Systems · Mathematics 2021-04-06 Stefan Klus , Feliks Nüske , Boumediene Hamzi

We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference…

Robotics · Computer Science 2021-12-07 Zi Cong Guo , Vassili Korotkine , James R. Forbes , Timothy D. Barfoot

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Dynamical Systems · Mathematics 2025-06-06 Claire Valva , Dimitrios Giannakis

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

Optimization and Control · Mathematics 2024-11-12 Yue Guo , Milan Korda , Ioannis G. Kevrekidis , Qianxiao Li

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Machine Learning · Computer Science 2020-02-23 Patrick Heas , Cedric Herzet , Benoit Combes

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

Optimization and Control · Mathematics 2011-06-15 Jake Bouvrie , Boumediene Hamzi

This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system…

Optimization and Control · Mathematics 2021-03-09 Vít Cibulka , Milan Korda , Tomáš Haniš , Martin Hromčík

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…

Systems and Control · Electrical Eng. & Systems 2023-09-11 Madhur Tiwari , George Nehma , Bethany Lusch

The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…

Fluid Dynamics · Physics 2018-06-08 Hassan Arbabi , Milan Korda , Igor Mezic

Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…

Quantum Physics · Physics 2025-07-30 Baoyang Zhang , Zhen Lu , Yaomin Zhao , Yue Yang

Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in…

Systems and Control · Electrical Eng. & Systems 2025-08-18 Yicheng Lin , Bingxian Wu , Nan Bai , Zhiyong Sun , Yunxiao Ren , Chuanze Chen , Zhisheng Duan

A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This approach approximates the Koopman operator using a set of…

Dynamical Systems · Mathematics 2015-07-29 Matthew O. Williams , Clarence W. Rowley , Ioannis G. Kevrekidis

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

Optimization and Control · Mathematics 2024-12-25 Mircea Lazar

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…