相关论文: Online Estimation of the Koopman Operator Using Fo…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
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…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
The Koopman representation is an infinite dimensional linear representation of linear or nonlinear dynamical systems. It represents the dynamics of output maps (aka observables), which are functions on the state space whose evaluation is…
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…
The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present…
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…
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…
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…
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…
The Koopman operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system.…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…