Search Results (22)

Maximizing the power output of wind farms is critical for improving the economic viability and grid integration of renewable energy. Active wake control (AWC) strategies, such as yaw-based wake steering, offer significant potential for power generation increase but require predictive models that are both accurate and computationally efficient for real-time implementation. This paper proposes a data-driven observer to rapidly estimate the potential power gain achievable through AWC as a function of the ambient wind direction. The approach is rooted in Koopman operator theory, which allows a linear representation of nonlinear dynamics. Specifically, a model is developed using an Input–Output Extended Dynamic Mode Decomposition framework combined with Sparse Identification (IOEDMDSINDy). This method lifts the low-dimensional wind direction input into a high-dimensional space of observable functions and then employs iterative sparse regression to identify a minimal, interpretable linear model in this lifted space. By training on offline simulation data, the resulting observer serves as an ultra-fast surrogate model, capable of providing instantaneous predictions to inform online control decisions. The methodology is demonstrated and its performance is validated using two case studies: a 9-turbine and a 20-turbine wind farm. The results show that the observer accurately captures the complex, nonlinear relationship between wind direction and power gain, significantly outperforming simpler models. This work provides a key enabling technology for advanced, real-time wind farm control systems. Full article

Classification of neurocognitive states from Electroencephalography (EEG) data is complex due to inherent challenges such as noise, non-stationarity, non-linearity, and the high-dimensional and sparse nature of connectivity patterns. Graph-theoretical approaches provide a powerful framework for analysing the latent state dynamics using connectivity measures across spatio-temporal-spectral dimensions. This study applies the graph Koopman embedding kernels (GKKE) method to extract latent neuro-markers of seizures from epileptiform EEG activity. EEG-derived graphs were constructed using correlation and mean phase locking value (mPLV), with adjacency matrices generated via threshold-binarised connectivity. Graph kernels, including Random Walk, Weisfeiler–Lehman (WL), and spectral-decomposition (SD) kernels, were evaluated for latent space feature extraction by approximating Koopman spectral decomposition. The potential of graph Koopman embeddings in identifying latent metastable connectivity structures has been demonstrated with empirical analyses. The robustness of these features was evaluated using classifiers such as Decision Trees, Support Vector Machine (SVM), and Random Forest, on Epilepsy-EEG from the Children’s Hospital Boston’s (CHB)-MIT dataset and cognitive-load-EEG datasets from online repositories. The classification workflow combining mPLV connectivity measure, WL graph Koopman kernel, and Decision Tree (DT) outperformed the alternative combinations, particularly considering the accuracy (91.7%) and F1-score (88.9%), The comparative investigation presented in results section convinces that employing cost-sensitive learning improved the F1-score for the mPLV-WL-DT workflow to 91% compared to 88.9% without cost-sensitive learning. This work advances EEG-based neuro-marker estimation, facilitating reliable assistive tools for prognosis and cognitive training protocols. Full article

The advent of large-scale distributed generation (DG) has introduced several challenges to the voltage control of active distribution networks (ADNs). These challenges include the heterogeneity of control devices, the complexity of models, and their inherent fluctuations. To maintain ADN voltage stability more economically and quickly, a data-driven ADN voltage control scheme is proposed in this paper. Firstly, based on the multi-run state sensitivity matrix, buses with similar voltage responses are clustered, and critical buses are selected to downsize the scale of the model. Secondly, a linear voltage-to-power dynamics model in high-dimensional state space is trained based on the offline data of critical bus voltages, DGs, and energy storage system (ESS) outputs, utilizing the Koopman theory and the Extended Dynamic Mode Decomposition (EDMD) method. A linear model predictive voltage controller, which takes ADN stability and control cost into account, is also proposed. Finally, the effectiveness and applicability of the method are verified by applying it to an improved 33-bus ADN system. The proposed control method can respond more quickly and accurately to the voltage fluctuation problems caused by source-load disturbances and short-circuit faults. Full article

Bio-inspired robots are devices that mimic an animal’s motions and structures in nature. Worm robots are robots that are inspired by the movements of the worm in nature. This robot has different applications such as medicine and rescue plans. However, control of the worm robot is a challenging task due to the high-nonlinearity dynamic model and external noises that are applied to that robot. This research uses an optimal data-driven controller to control the worm robot. First, data are obtained from the nonlinear model of the worm robot. Then, the Koopman theory is used to generate a linear dynamic model of the Worm robot. The dynamic mode decomposition (DMD) method is used to generate the Koopman operator. Finally, a linear quadratic regulator (LQR) control method is applied for the control of the worm robot. The simulation results verify the performance of the proposed control method. Full article

In this paper, we aimed to identify the dynamics of a crude distillation unit (CDU) using closed-loop data with NARX−NN and the Koopman operator in both linear (KL) and bilinear (KB) forms. A comparative analysis was conducted to assess the performance of each method under different experimental conditions, such as the gain, a delay and time constant mismatch, tight constraints, nonlinearities, and poor tuning. Although NARX−NN showed good training performance with the lowest Mean Squared Error (MSE), the KB demonstrated better generalization and robustness, outperforming the other methods. The KL observed a significant decline in performance in the presence of nonlinearities in inputs, yet it remained competitive with the KB under other circumstances. The use of the bilinear form proved to be crucial, as it offered a more accurate representation of CDU dynamics, resulting in enhanced performance. Full article

Accurate flight training trajectory prediction is a key task in automatic flight maneuver evaluation and flight operations quality assurance (FOQA), which is crucial for pilot training and aviation safety management. The task is extremely challenging due to the nonlinear chaos of trajectories, the unconstrained airspace maps, and the randomization of driving patterns. In this work, a deep learning model based on data-driven modern koopman operator theory and dynamical system identification is proposed. The model does not require the manual selection of dictionaries and can automatically generate augmentation functions to achieve nonlinear trajectory space mapping. The model combines stacked neural networks to create a scalable depth approximator for approximating the finite-dimensional Koopman operator. In addition, the model uses finite-dimensional operator evolution to achieve end-to-end adaptive prediction. In particular, the model can gain some physical interpretability through operator visualization and generative dictionary functions, which can be used for downstream pattern recognition and anomaly detection tasks. Experiments show that the model performs well, particularly on flight training trajectory datasets. Full article

We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras. Full article

Robotic manipulators with diverse structures find widespread use in both industrial and medical applications. Therefore, designing an appropriate controller is of utmost importance when utilizing such robots. In this research, we present a robust data-driven control method for the regulation of a 2-degree-of-freedom (2-DoF) robot manipulator. The nonlinear dynamic model of the 2-DoF robot arm is linearized using Koopman theory. 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. We compare the performance of Koopman fractional sliding mode control (KFOSMC) with conventional proportional integral derivative (PID) control and FOSMC prior to linearization by Koopman theory. The results demonstrate that KFOSMC outperforms PID and FOSMC in terms of high tracking performance, low tracking error, and minimal control signals. Full article

Deep space missions, and particularly cislunar endeavors, are becoming a major field of interest for the space industry, including for the astrodynamics research community. While near-Earth missions may be completely covered by perturbed Keplerian dynamics, deep space missions require a different modeling approach, where multi-body gravitational interactions play a major role. To this end, the Restricted Three-Body Problem stands out as an insightful first modeling strategy for early mission design purposes, retaining major dynamical transport structures while still being relatively simple. Dynamical Systems Theory and classical Hamiltonian Mechanics have proven themselves as remarkable tools to analyze deep-space missions within this context, with applications ranging from ballistic capture trajectory design to stationkeeping. In this work, based on this premise, a Hamiltonian derivation of the Restricted Three-Body Problem co-orbital dynamics between two spacecraft is introduced in detail. Thanks to the analytical and numerical models derived, connections between the relative and classical Keplerian and CR3BP problems are shown to exist, including first-order linear solutions and an inherited Hamiltonian normal form. The analytical linear and higher-order models derived allow the theoretical finding and unveiling of natural co-orbital phase space structures, including relative periodic and quasi-periodic orbital families, which are further exploited for general proximity operation applications. In particular, a novel reduced-order, optimal low-thrust stationkeeping controller is derived in the relative Floquet phase space, hybridizing the classical State Dependent Ricatti Equation (SDRE) with Koopman control techniques for efficient unstable manifold regulation. The proposed algorithm is demonstrated and validated within several end-to-end low-cost stationkeeping missions, and comparison against classical continuous stationkeeping algorithms presented in the literature is also addressed to reveal its enhanced performance. Finally, conclusions and open lines of research are discussed. Full article

Finitely-additive measures invariant to the action of some groups on a separable infinitedimensional real Hilbert space are constructed. The invariantness of a measure is studied with respect to the group of shifts on a vector of Hilbert space, the orthogonal group and some groups of symplectomorphisms of the Hilbert space equipped with the shift-invariant symplectic form. A considered invariant measure is locally finite, σ finite, but it is not countably additive. The analog of the ergodic decomposition of invariant finitely additivemeasures with respect to some groups are obtained. The set of measures that are invariant with respect to a group is parametrized using the obtained decomposition. The paper describes the spaces of complex-valued functions which are quadratically integrable with respect to constructed invariant measures. This space is used to define the Koopman unitary representation of the group of transformations of the Hilbert space. To define the strong continuity subspaces of a Koopman group, we analyze the spectral properties of its generator. Full article

Extended Dynamic Mode Decomposition (EDMD) allows an approximation of the Koopman operator to be derived in the form of a truncated (finite dimensional) linear operator in a lifted space of (nonlinear) observable functions. EDMD can operate in a purely data-driven way using either data generated by a numerical simulator of arbitrary complexity or actual experimental data. An important question at this stage is the selection of basis functions to construct the observable functions, which in turn is determinant of the sparsity and efficiency of the approximation. In this study, attention is focused on orthogonal polynomial expansions and an order-reduction procedure called p-q quasi-norm reduction. The objective of this article is to present a Matlab library to automate the computation of the EDMD based on the above-mentioned tools and to illustrate the performance of this library with a few representative examples. Full article

We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode Decomposition-type methods in the context of Finite Section theory of infinite dimensional operators, and provide an example of a mixing map for which the finite section method fails. Under assumptions on the underlying dynamics, we provide the first result on the convergence rate under sample size increase in the finite-section approximation. We study the error in the Krylov subspace version of the finite section method and prove convergence in pseudospectral sense for operators with pure point spectrum. Since Krylov sequence-based approximations can mitigate the curse of dimensionality, this result indicates that they may also have low spectral error without an exponential-in-dimension increase in the number of functions needed. Full article

The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in describing circuit dynamics in rapidly dividing cells, assuming fixed or time-invariant kinetic rates. There is a growing interest in being able to model and extend synthetic biological function for growth conditions such as stationary phase or during nutrient starvation. As cells transition from one growth phase to another, kinetic rates become time-varying parameters. In this paper, we propose a novel class of parameter varying nonlinear models that can be used to describe the dynamics of genetic circuits, including the toggle switch, as they transition from different phases of growth. We show that there exists unique solutions for this class of systems, as well as for a class of systems that incorporates the microbial phenomena of quorum sensing. Further, we show that the domain of these systems, which is the positive orthant, is positively invariant. We also showcase a theoretical control strategy for these systems that would grant asymptotic monostability of a desired fixed point. We then take the general form of these systems and analyze their stability properties through the framework of time-varying Koopman operator theory. A necessary condition for asymptotic stability is also provided as well as a sufficient condition for instability. A Koopman control strategy for the system is also proposed, as well as an analogous discrete time-varying Koopman framework for applications with regularly sampled measurements. Full article

The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. 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. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated $L^2$ error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load. Full article

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on a projected space. In the spirit of Johnson–Lindenstrauss lemma, we will use a random projection to estimate the DMD modes in a reduced dimensional space. In practical applications, snapshots are in a high-dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is expensive, so our main computational goal is to estimate the eigenvalue and eigenvectors of the DMD operator in a projected domain. We generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage costs. While, clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, the results can generally be excellent, nonetheless, and the quality could be understood through a well-developed theory of random projections. We will demonstrate that modes could be calculated for a low cost by the projected data with sufficient dimension. Full article