相关论文: Koopman operator based identification of nonlinear…

Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode…

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…

Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…

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…

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…

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…

Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…

Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…

A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…

A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…

The theory of network identification, namely identifying the (weighted) interaction topology among a known number of agents, has been widely developed for linear agents. However, the theory for nonlinear agents using probing inputs is far…

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…

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…

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…

Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an…

With the development of end-to-end control based on deep learning, it is important to study new system modeling techniques to realize dynamics modeling with high-dimensional inputs. In this paper, a novel Koopman-based deep convolutional…

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…

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…

Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…