相关论文: Data-driven parallel Koopman subsystem modeling an…

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…

In this paper, we propose a nonlinear probabilistic generative model of Koopman mode decomposition based on an unsupervised Gaussian process. Existing data-driven methods for Koopman mode decomposition have focused on estimating the…

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…

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…

The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…

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…

This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…

Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…

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…

In this article, we present data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media using Koopman operators. Different from the case of autonomous dynamical systems, the Koopman operator family of…

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…

Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise…

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…

In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…

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…

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…

We present a data-driven shared control algorithm that can be used to improve a human operator's control of complex dynamic machines and achieve tasks that would otherwise be challenging, or impossible, for the user on their own. Our method…

The Koopman framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding. Originally, the Koopman formalism has been derived for autonomous systems. In…

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…

Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…