Efficient Sampling Methods of, by, and for Stochastic Dynamical Systems by Zhang, Benjamin Jiahong

“…Our approach exploits the relationship between the stochastic Koopman operator and the Kolmogorov backward equation to derive optimal importance sampling and multilevel splitting estimators. …”
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Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator by Stefan Klus, Feliks Nüske, Boumediene Hamzi

“…Important examples include the Koopman operator and its generator, but also the Schrödinger operator. …”
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Control-Oriented, Data-Driven Models of Thermal Dynamics by Ljuboslav Boskic, Igor Mezic

“…Despite the nonlinearity of the underlying dynamics, using Koopman operator theory framework in this study we show that a linear second order model embedding, that captures the physics that occur inside a single or multi zone space does well when compared with data simulated using EnergyPlus. …”
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Robot Manipulator Control Using a Robust Data-Driven Method by Mehran Rahmani, Sangram Redkar

“…The data mode decomposition (DMD) method is applied to generate the Koopman operator. A fractional sliding mode control (FOSMC) is employed to govern the data-driven linearized dynamic model. …”
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Approximate Reachability for Koopman Systems Using Mixed Monotonicity by Omanshu Thapliyal, Inseok Hwang

“…We present a data-driven method for computing reachable sets for unknown nonlinear dynamical systems using a Koopman operator based approach. We find mixed-monotone decompositions for a class of Koopman lifted dynamics. …”
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Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems by Alexander Schaum

“…The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. …”
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Online real-time learning of dynamical systems from noisy streaming data by S. Sinha, S. P. Nandanoori, D. A. Barajas-Solano

“…In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. …”
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A Koopman-Based Reduced-Order State Observer for Visual Localization of Robots by Williams, Jadal

“…A reduced-order observer using Koopman lifting linearization is developed for localization of a robot guided by a vision system. The Koopman operator is a powerful method for representing nonlinear robot dynamics as a linear model in a lifted space. …”
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Experimental Study of Dynamical Airfoil and Aerodynamic Prediction by Zheyu Shi, Kaiwen Zhou, Chen Qin, Xin Wen

“…In summary, using the Koopman operator obtained by DMD with time-delay embedding, the future dynamic pressure on an oscillating airfoil can be accurately predicted. …”
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Data‐driven stochastic model predictive control for regulating wind farm power generation with controlled battery storage by Zishuo Huang, Wenchuan Wu, Zizhen Guo

“…Firstly, to address the non‐linear dynamic model of wind turbines, the dynamic mode decomposition method accompanying Koopman operator is used to learn a lifted linear dynamic model from measurements. …”
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Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows by Shnitzer, Tal, Talmon, Ronen, Slotine, Jean-Jacques

“…We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. …”
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Cooperative braking of urban rail vehicles with Koopman model predictive control by Dianzhu Gao, Jun Peng, Hui Peng, Bin Chen, Zhiwu Huang

“…First, a cyber‐physical model is established, where the physical layer characterizes the dynamic model of multiple carriages using the Koopman operator. The cyber layer represents the communication topology of carriages with graph theory. …”
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Non-Stationary Dynamic Mode Decomposition by John Ferre, Ariel Rokem, Elizabeth A. Buffalo, J. Nathan Kutz, Adrienne Fairhall

“…Dynamic Mode Decomposition is a means to achieve this goal, allowing the identification of key spatiotemporal modes through the diagonalization of a finite dimensional approximation of the Koopman operator. However, these methods apply best to time-translationally invariant or stationary data, while in many typical cases, dynamics vary across time and conditions. …”
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Data-Driven Model Predictive Control for Uncalibrated Visual Servoing by Tianjiao Han, Hongyu Zhu, Dan Yu

“…Then, a data-driven MPC strategy is proposed, wherein the unknown nonlinear dynamic model is learned using the Koopman operator theory, resulting in a linear Koopman prediction model. …”
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Dynamics Analysis Using Koopman Mode Decomposition of a Microgrid Including Virtual Synchronous Generator-Based Inverters by Yuko Hirase, Yuki Ohara, Naoya Matsuura, Takeaki Yamazaki

“…Therefore, Koopman mode decomposition (KMD) was utilized in this study for consideration as a future method of data-driven analysis of the measured frequencies and voltages, and a frequency response analysis of the power system dynamics was performed. The Koopman operator is a linear operator on an infinite dimensional space, whereas the original dynamics is a nonlinear map on a finite state space. …”
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On the Application of Machine Learning and Physical Modeling Theory to Causal Lifting Linearizations of Nonlinear Dynamical Systems with Exogenous Input and Control by Selby, Nicholas Stearns

“…Methods for constructing causal linear models from nonlinear dynamical systems through lifting linearization underpinned by Koopman operator and physical system modeling theory are presented. …”
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Automatic Tracking of Surgical Instruments with a Continuum Laparoscope Using Data‐Driven Control in Robotic Surgery by Xiaowen Kong, Hangjie Mo, Erbao Dong, Yunhui Liu, Dong Sun

“…Shifted Chebyshev polynomials are used to construct observation functions that transfer low‐dimension observations to high‐dimension ones. The Koopman operator is approximated using a finite‐dimensional estimation method. …”
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A data-driven method for quantifying the impact of a genetic circuit on its host by Dorfan, Yuval, Espah Borujeni, Amin, Park, YongJin, Saxena, Uma, Gondon, Ben, Voigt, Christopher A., Yeung, Enoch

“…In this work we utilize Koopman operator theory to construct data-driven models of transcriptomic-level dynamics from noisy and temporally sparse RNAseq measurements. …”
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Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators by Sotiropoulos, Filippos Edward, Asada, H. Harry

“…A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. …”
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Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators by Paul M. Riechers, James P. Crutchfield

“…Finally, we draw connections to the Ruelle–Frobenius–Perron and Koopman operators for chaotic dynamical systems and propose how to extract eigenvalues from a time-series.…”
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