Search Results (50)

Biologically related time-series data characterize the dynamic evolution of biological systems, including genetic inheritance, disease diagnosis, and the biological microenvironment. However, accurate prediction of these data remains challenging due to their pronounced time-varying, non-stationary, and noisy characteristics. Existing approaches often fail to capture latent shifts of biologically related time series, limiting both predictive performance and time-varying pattern recognition capability. Thus, in this study, we first propose a time-varying neural network (TVNN) model that combines frequency-domain information with Koopman theory. TVNN-model Koopman transition matrices are used to model global dynamics and local time-varying behaviors for pattern extraction. Secondly, a time-varying pattern recognition large language model (TVPRLLM) is introduced to recognize and classify the extracted time-varying patterns, enabling the identification of potential pattern categories. Thirdly, we have developed a biology-related time-series predictive platform that can offer visualization, data analysis, and predictive services. Experimental results demonstrate that the TVNN model outperforms existing mainstream methods in predicting biology-related time-varying time series, and that it achieves competitive forecasting performance, though its behavior depends strongly on the design of the frequency-domain decomposition. Additional robustness analyses reveal that the choice of Fourier masking strategy can materially affect both RMSE and long-horizon stability. We further show that Koopman-derived time-varying representations are highly discriminative for dynamic state recognition. Full article

Structural health monitoring (SHM) is essential for the safety and long-term performance of civil and mechanical infrastructure, yet traditional vibration-based approaches often struggle with nonlinear behavior and environmental variability. Koopman operator theory provides a promising alternative by enabling linear analysis of nonlinear structural dynamics through observable functions. This review examines 67 peer-reviewed studies published between 2010 and 2025 and selected using Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. We outline the development of Koopman-based methods from Dynamic Mode Decomposition (DMD) and Extended-DMD (EDMD) to recent applications in civil, mechanical, and aerospace systems. This review clarifies the mathematical foundations of Koopman analysis and its relationship to structural dynamics. It also identifies major research gaps, including limited damage-sensitive observable design, insufficient use of structural mechanics constraints, the absence of quantitative links between Koopman spectra and physical damage, inadequate benchmarking, and the need for real-time deployment strategies. We conclude by outlining a hybrid Koopman framework that integrates physics-based information with data-driven learning to support interpretable and scalable SHM. Full article

Omni-directional mobile manipulators (OMMs) are inherently nonlinear, strongly coupled, and multiple-input multiple-output systems, posing significant challenges in developing accurate mechanistic models due to their complexity. Koopman operator theory offers a data-driven modeling framework that leverages input–output data to characterize system dynamics, but there often exist modeling errors. In this paper, an event-triggered data-driven linear model predictive control (MPC) framework is proposed for an OMM, without using any prior knowledge of the robot system. A finite-dimensional approximate linear Koopman model is established for an OMM using input–output data. The Gaussian process regression (GPR) is employed to estimate the model’s errors, while an extended state observer (ESO) is designed to estimate external disturbances. Since the introduction of GPR increases the computational burden, an event-triggered (ET) mechanism is introduced to reduce unnecessary controller recomputations and controller update frequency. Finally, comparative experiments are carried out to verify the effectiveness and performance superiority of the proposed control scheme. Full article

A piezoelectric actuator (PEA) is a fundamental part of a high-precision motion system, yet its performance is critically constrained by inherent nonlinearities such as the velocity dead zone and hysteresis. To overcome these limitations and the associated time-varying dynamics, this study introduces a novel control framework for a dual-mode standing wave PEA. The framework integrates a Global Linearized Sparse Prediction (GLSP) model with an Adaptive Kalman Observer-based Model Predictive Control (AKOBMPC) strategy, specifically designed for velocity dead-zone compensation. The GLSP model employs Koopman operator theory to lift the complex, nonlinear electromechanical and contact dynamics into a linear invariant subspace. Incorporated with a deep learning-based structured pruning mechanism, the model achieves an effective balance between prediction accuracy and computational efficiency, facilitating real-time implementation. Leveraging this high-fidelity model, the AKOBMPC algorithm is developed to estimate unmeasurable disturbances and optimize the control sequence for precise velocity tracking. Experimental results demonstrate the GLSP model’s accurate prediction of system behavior under varying loads and excitation frequencies. The proposed controller effectively suppresses the velocity dead zone, achieving tracking errors within ±0.35 mm/s for a 40.00 mm/s trapezoidal reference and within ±0.50 mm/s for sinusoidal tracking. These results confirm the superior performance of the AKOBMPC scheme over conventional methods, offering a robust solution for high-precision velocity regulation in PEA system and contributing to the advancement of next-generation precision actuator. Full article

Global value chains (GVCs) have evolved into highly interconnected and geographically fragmented production networks, increasing exposure to systemic disruptions and revealing the limitations of static input–output and conventional network approaches. This study develops a unified analytical framework for modeling the structure, dynamics, and resilience of GVCs by integrating input–output economics with network theory, control theory, optimal transport, information theory, and cooperative game theory. The framework represents GVCs as time-varying, multi-level networks and formalizes shock propagation through stochastic normalization and state-space dynamics. Entropy-regularized optimal transport is employed to model friction-dependent substitution and supply chain reconfiguration, while Koopman operator methods approximate nonlinear adjustment dynamics. Cooperative flow-based indices are introduced to assess systemic importance and bargaining power. The analysis produces a coherent set of structural and dynamic indicators capturing vulnerability, adaptability, and controllability across country–sector nodes. Overall, the framework provides an empirically applicable toolkit for diagnosing structural fragilities, comparing resilience across economies, and supporting scenario-based evaluation of industrial and trade policies in complex global production networks. Full article

This paper addresses the transient voltage stability problem in power systems with high penetration of renewable energy by proposing a hierarchical risk-warning method that integrates Koopman-theory-based transient voltage trajectory prediction and stability margin quantification. First, an online Koopman-theory-based transient voltage trajectory prediction model is constructed through the adaptive optimization of basis functions, a dynamic operator update mechanism, and multistage error correction, significantly enhancing prediction accuracy and generalization capability. Second, a piecewise-weighted quantitative index for transient voltage stability margins is proposed, achieving refined stability assessments ranging from individual nodes to the entire system. Finally, a risk-mapping function based on utility theory is established to convert continuous margin indices to discrete risk levels, forming a complete hierarchical warning system for the transient voltage risk. Simulation results demonstrate that the proposed method achieves precise voltage trajectory prediction and stable-state judgment across various scenarios, effectively identifies critical system weaknesses, and provides reliable technical support for the safety prevention and control of the power system’s transient voltage. Full article

Modeling forced nonlinear multivariable dynamical systems remains challenging, particularly when first-principles models are unavailable or strong nonlinear couplings are present. In recent years, data-driven approaches grounded in the Koopman operator theory have gained attention for their ability to represent nonlinear dynamics via linear evolution in appropriately lifted spaces. This work presents a data-driven modeling framework for forced nonlinear multiple-input multiple-output (MIMO) systems based on Hankel Dynamic Mode Decomposition with control and lifting functions (HDMDc+Lift). The proposed methodology exploits Hankel matrices to encode temporal correlations and employs lifting functions to approximate the Koopman operator’s action on observable functions. As a result, an augmented-order linear state-space model is identified exclusively from input–output data, without relying on explicit knowledge of the system’s governing equations. The effectiveness of the proposed approach is demonstrated using operational data from a real multivariable tank system that was not used during the identification stage. The identified model achieves a coefficient of determination exceeding 0.87 in multi-step prediction tasks. Furthermore, spectral analysis of the resulting linear operator reveals that the dominant dynamical modes of the physical system are accurately captured. At the same time, additional modes associated with nonlinear interactions are also identified. These results highlight the HDMDc+Lift framework’s ability to provide accurate and interpretable linear representations of forced nonlinear MIMO dynamics. Full article

Aiming at the dynamic characteristics and stability of smart distribution network stations under the combined effect of the uncertainty of new energy output and the control logic of power electronics, an adaptive dimensionally increasing linear dynamic modeling method based on Koopman theory is proposed. Firstly, a regional nonlinear model of an intelligent transformer integrating photovoltaic, wind power, battery, hydrogen fuel cell, and synchronous generator is constructed. The control logic of the virtual synchronous generator is then integrated to characterize the dynamic response of the power electronic interface. Secondly, by constructing a set of nonlinear observation functions, including high-order polynomials, exponents, and periodic functions, the dimensional upgrade mapping of the system state is carried out. The dynamic mode decomposition algorithm is adopted to adaptively extract the dominant dynamic modes in the dimensional upgrade space, achieving global linear approximation of complex nonlinear dynamical systems. Finally, the simulation example results show that the average RMAE error of the Koopman method proposed in this paper in voltage spatiotemporal reconstruction is 0.1419, and the maximum RMSE error is 0.1915, significantly improving the accuracy and stability of dynamic modeling. Full article

This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity and no manual parameter adjustment. The method integrates a novel algorithm with Pareto front analysis to construct a compact, high-fidelity reduced-order model that balances accuracy and efficiency. An explainable NLARX deep learning framework enables real-time, adaptive calibration and prediction, while a key innovation—computing orthogonal Koopman modes via randomized orthogonal projections—ensures optimal data representation. This approach for data-driven twin modeling is fully self-consistent, avoiding heuristic choices and enhancing interpretability through integrated explainable learning techniques. The proposed method is demonstrated on shock wave phenomena using three experiments of increasing complexity accompanied by a qualitative analysis of the resulting data-driven twin models. Full article

With the development of digital power systems, the establishment of digital twin models for transformers is of great significance in enhancing power system stability. Consequently, greater demands are placed on the real-time performance and accuracy of thermal-fluid-coupled transient multi-physics field calculations for transformers. However, traditional numerical methods, such as finite element or computational fluid dynamics techniques, often require days or even weeks to simulate full-scale high-fidelity transformer models containing millions of grid nodes. The high computational cost and long runtime make them impractical for real-time simulations in digital twin applications. To address this, this paper employs the dynamic mode decomposition (DMD) method in conjunction with Koopman operator theory to perform data-driven reduced-order modeling of the transformer’s thermal–fluid-coupled multi-physics field. A fast computational approach based on extended dynamic mode decomposition (EDMD) is proposed to enhance the modal decomposition capability of nonlinear systems and improve prediction accuracy. The results show that this method greatly improves computational efficiency while preserving accuracy in high-fidelity models with millions of grids. The errors in the thermal and flow field calculations remain below 3.06% and 3.01%, respectively. Furthermore, the computation time is reduced from hours to minutes, with the thermal field achieving a 97-fold speed-up and the flow field an 83-fold speed-up, yielding an average speed-up factor of 90. This enables fast computation of the transformer’s thermal–fluid-coupled field and provides effective support for the application of digital twin technology in multi-physics field simulations of power equipment. Full article

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

The identification of dynamical systems from data is essential in control theory, enabling the creation of mathematical models that accurately represent the behavior of complex systems. However, real-world applications often present challenges such as the unknown dimensionality of the system and limited access to measurements, particularly in partially observed systems. The Hankel alternative view of Koopman (HAVOK) method offers a data-driven approach to identify linear representations of nonlinear systems, but it often overlooks the influence of external control signals (inputs) and disturbances. This paper introduces a novel input-aware modeling method for unstable linear systems using data-driven Koopman analysis. By explicitly incorporating the impact of inputs and disturbances, our method enhances the accuracy and robustness of system identification, even in the face of incomplete observations. The proposed approach leverages Koopman operator theory on augmented state-input data to capture both the intrinsic dynamics and the system’s sensitivity to external control. Through extensive numerical examples, we demonstrate the effectiveness of our method in accurately identifying and predicting the behavior of various dynamical systems, including real-world nonlinear systems and simulated unstable linear systems with and without disturbances. The results highlight the potential of our approach to advance the field of system identification and control, offering a powerful tool for modeling and analyzing complex systems in diverse applications. 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

Recent progress in autonomous vehicle technology has led to the development of accurate and efficient tools for ensuring safety, which is crucial for verifying the reliability and security of vehicles. These vehicles operate under diverse conditions, necessitating the analysis of varying initial conditions and parameter values. Ensuring the safe operation of the vehicle under all these varying conditions is essential. Reachability analysis is an important tool to certify the safety and stability of the vehicle dynamics. We propose a reachability analysis approach for evaluating the response of the vehicle dynamics, specifically addressing uncertainties in the initial states and model parameters. Reachable sets illustrate all the possible states of a dynamical system that can be obtained from a given set of uncertain initial conditions. The analysis is crucial for understanding how variations in initial conditions or system parameters can lead to outcomes such as vehicle collisions or deviations from desired paths. By mapping out these reachable states, it is possible to design systems that maintain safety and reliability despite uncertainties. These insights help to ensure the stability and reliability of the vehicles, even in unpredictable conditions, by reducing accidents and optimizing performance. The nonlinearity of the model complicates the computation of reachable sets in vehicle dynamics. This paper proposes a Koopman theory-based approach that utilizes the Koopman principal eigenfunctions and the Koopman spectrum. By leveraging the Koopman principal eigenfunction, our method simplifies the computational process and offers a formal approximation for backward and forward reachable sets. First, our method effectively computes backward and forward reachable sets for a nonlinear quarter-car model with fixed parameter values. Furthermore, we applied our approach to analyze the uncertainty response for cases with uncertain parameters of the vehicle model. When compared to time-domain simulations, our proposed Koopman approach provided accurate results and also reduced the computational time by half in most cases. This demonstrates the efficiency and reliability of our proposed approach in dynamic systems uncertainty analysis using the reachable sets. Full article