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Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is linear and encompasses full information on the (expected…

The expansion in technology and attainability of a large number of sensors has led to a huge amount of real-time streaming data. The real-time data in the electrical distribution system is collected through distribution-level phasor…

Extended Dynamic Mode Decomposition (EDMD) is a widely used data-driven algorithm for estimating the Koopman Operator. EDMD extends Dynamic Mode Decomposition (DMD) by lifting the snapshot data using nonlinear dictionary functions before…

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…

This paper explores a novel data-driven approach based on recent developments in Koopman operator theory and dynamic mode decomposition (DMD) for modeling signalized intersections. Vehicular flow and queue formation on signalized…

Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M.…

Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the…

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…

This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear…

The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional…

This paper presents an optic flow-guided approach for achieving soft landings by resource-constrained unmanned aerial vehicles (UAVs) on dynamic platforms. An offline data-driven linear model based on Koopman operator theory is developed to…

Multi-event detection and recognition in real time is of challenge for a modern grid as its feature is usually non-identifiable. Based on factor model, this paper porposes a data-driven method as an alternative solution under the framework…

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the…

We show the skills of a data-driven low-dimensional linear model in predicting the spatio-temporal evolution of turbulent Rayleigh-B\'enard convection. The model is based on dynamic mode decomposition with delay-embedding, which provides a…

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…

Modeling wave energy converters (WECs) to accurately predict their hydrodynamic behavior has been a challenge for the wave energy field. Often, this results in either low-fidelity, linear models that break down in energetic seas, or…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of…

Recently, subsynchronous oscillations (SSOs) have emerged frequently worldwide, with the high penetration of renewable power generation in modern power systems. The SSO introduced by renewables has become a prominent new stability problem,…