Related papers: Deep Koopman Learning of Nonlinear Time-Varying Sy…
We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators…
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…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
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…
The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing…
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…
In this paper, data-driven algorithms based on Koopman Operator Theory are applied to identify and predict the nonlinear dynamics of a vapor compression system and cabin temperature in a light-duty electric vehicle. By leveraging a…
We address the problem of learning a neural Koopman operator model that provides dissipativity guarantees for an unknown nonlinear dynamical system that is known to be dissipative. We propose a two-stage approach. First, we learn an…
The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show…
The strong performance of simple neural networks is often attributed to their nonlinear activations. However, a linear view of neural networks makes understanding and controlling networks much more approachable. We draw from a dynamical…
Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by…
In this paper, we provide a unified analysis of temporal difference learning algorithms with linear function approximators by exploiting their connections to Markov jump linear systems (MJLS). We tailor the MJLS theory developed in the…
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…
Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…
Koopman operator has been recognized as an ongoing data-driven modeling method for vehicle dynamics which lifts the original state space into a high-dimensional linear state space. The deep neural networks (DNNs) are verified to be useful…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
This paper presents a novel identification approach of Koopman models of nonlinear systems with inputs under rather general noise conditions. The method uses deep state-space encoders based on the concept of state reconstructability and an…