Search Results (42)

In classical reliability engineering, failure is a probabilistic structural failure based on lifetime distributions of Weibull models. However, in the control-critical mechanical systems, it is possible that functional failure of the system happens before material failure occurs as a result of control power loss. This paper proposes a Controllability–Reliability Coupling (CRC) model, which redefines the concept of reliability as the stabilizability in the face of progressive degradation. The actuators’ deterioration is modeled using the time-varying input effectiveness factor $\alpha \left(t\right)$, and the actuator is said to be in failure when the minimum singular value of the finite-horizon controllability Gramian becomes less than a stabilizability threshold $\epsilon$. The performance of the simulation indicates that the functional failure is a precursor of structural failure in several degradation conditions. A baseline comparison shows that the CRC metric forecasts loss of controllability at $T_{CRC}=17.0$ s, but the classical Weibull reliability never attains the structural failure threshold even in the time horizon of 20 s. The system retains margins of Lyapunov stability and H infinity robustness are not lost, and it is still stable and attenuates disturbances even when control authority is lost. In practical degradation scenarios, the forecasted CRC failure times are 21.5 s (linear wear), 13.1 s (accelerated fatigue), 23.7 s (intermittent faults), and 24.4 s (shock damage), whereas maintenance recovery abated functional failure completely. In a case study of an industrial robotic joint, at 27.0 s, functional collapse occurred, and at the same time, structural reliability was still above the failure threshold. The findings support the hypothesis that structural survival and functional controllability are distinct concepts. The proposed CRC framework is an approach to control-conscious reliability measure, which can detect early failures and offer proactive maintenance advice in the context of a cyber–physical system. Full article

This work develops an energy-based reachability framework for linear fractional-order dynamical systems governed by Caputo derivatives of order $\alpha \in (0,1)$ in the presence of time-dependent delays acting on both the state and control channels. By combining a controllability Gramian formulation with a delay-independent algebraic characterization, explicit quantitative descriptions of reachability under finite energy constraints are obtained. It is shown that the set of terminal states attainable with bounded control energy admits a geometric characterization in terms of a Gramian-induced ellipsoidal region centered at the uncontrolled terminal state. In addition, the minimum eigenvalue of the controllability Gramian is identified as an energy-based controllability margin that provides certified reachability guarantees. Stability and sensitivity properties of the associated minimum-energy control law with respect to perturbations in the terminal target are also established. The theoretical developments are supported by implementable numerical procedures and illustrative examples that demonstrate the computation of the controllability Gramian, its spectral characteristics, and the resulting minimum-energy control inputs. Full article

This paper presents a unified framework for controllability and minimum-energy control of linear fractional differential systems with Caputo derivative order $\gamma \in (0,1)$ and fully time-varying state and control delays. An explicit mild solution representation is derived using the fractional fundamental matrix, and a new controllability Gramian is introduced. Using analytic properties of the matrix-valued Mittag-Leffler function, we prove a fractional Kalman-type theorem showing that bounded time-varying delays do not change the algebraic controllability structure determined by $(F,G,K)$. The minimum-energy control problem is solved in closed form through Hilbert space methods. Efficient numerical strategies and several examples—including delayed viscoelastic, neural, and robotic models—demonstrate practical applicability and computational feasibility. Full article

Controllability metrics based on system Gramians have been widely adopted to provide quantitative measures of the degree of controllability (DoC) and the disturbance rejection capability (DoDR) of dynamical systems. While steady-state Gramian formulations offer closed-form tractability, they are not applicable when rigid-body modes are present, as the associated poles at the origin cause the conventional Gramians to diverge. This paper presents a novel steady-state DoDR metric for linear time-invariant systems with a rigid-body mode. By block-diagonalizing the dynamics through a similarity transformation and analyzing the asymptotic behavior of the Gramian matrices, we derive an exact closed-form expression for the steady-state DoDR. The resulting formulation is numerically stable and enables systematic evaluation of disturbance-rejection capability even in the presence of a rigid-body mode. The proposed metric is validated using a mass–spring–damper chain model, where its effectiveness is demonstrated in actuator placement problems. The results show that the metric not only remains computationally well-posed but also provides physically meaningful interpretations consistent with modal characteristics. This study establishes a foundation for extending disturbance-rejection metrics to systems with multiple rigid-body modes, thereby broadening the applicability of Gramian-based controllability analysis. Full article

Traffic accidents on highway are often characterized by high destructiveness and severe casualties. Predicting accident severity and understanding its causes are crucial for enhancing highway safety. To address the issues of limited prediction accuracy and poor interpretability of traditional machine learning and deep learning methods at the current stage, this study proposes an accident severity prediction model based on a hybrid architecture of MobileNetV3 and a Transformer. The model first encodes numerical accident-related variables into two-dimensional images using the Gramian Angular Field (GAF) method. Local spatial features are then extracted via the depthwise separable convolution modules of MobileNetV3, and long-range temporal dependencies are captured through the Transformer encoder, which outputs the final prediction. The proposed model is compared with Convolutional Neural Networks (CNNs), Long Short-Term Memory networks (LSTMs), MobileNetV3, a Transformer, and LSTM–Transformer architectures in terms of prediction performance. Results show that the MobileNetV3–Transformer model achieves the highest accuracy of 0.9549. Finally, the DeepSHAP interpretability algorithm is introduced to reveal the systemic influence and contribution of significant factors to accident severity. The results indicate that vehicle age, special road conditions, speed limits, and lighting conditions are closely related to the severity of highway accidents. This study provides a reliable theoretical basis for early warning of highway accidents and refines control measures to further enhance highway safety. Full article

This paper addresses the solvability and controllability of fractional delay differential Sylvester matrix equations with non-permutable coefficient matrices. By applying a vectorization approach and Kronecker product algebra, we transform the matrix-valued problem into an equivalent vector system, enabling the derivation of explicit solution representations using a delayed perturbation of two-parameter Mittag-Leffler-type matrix functions. We establish necessary and sufficient conditions for controllability via a fractional delay Gramian matrix, providing a computationally verifiable criterion that requires no commutativity assumptions. The theoretical results are validated through numerical examples, demonstrating effectiveness in noncommutative scenarios where classical methods fail. Full article

This work introduces a unified framework for analyzing linear delay differential Sylvester matrix equations with noncommuting coefficients. The methodology employs a Kronecker product-based vectorization to transform the system, yielding explicit closed-form solutions via a novel delayed perturbation matrix function. Additionally, a delay-adapted Gramian matrix is formulated to derive necessary and sufficient controllability criteria. The approach’s efficacy is confirmed through a numerical example, demonstrating its capability in complex, noncommutative scenarios where classical methods are inapplicable. Full article

The online rapid classification of multi-cultivar watermelon, including seedless and seeded types, has far-reaching significance for enhancing quality control in the watermelon industry. However, interference in one-dimensional spectra affects the high-accuracy classification of multi-cultivar watermelons with similar appearances. This study proposed an innovative method integrating Gramian Angular Field (GAF), feature fusion, and Squeeze-and-Excitation (SE)-guided convolutional neural networks (CNN) based on VIS-NIR transmittance spectroscopy. First, one-dimensional spectra of 163 seedless and 160 seeded watermelons were converted into two-dimensional Gramian Angular Summation Field (GASF) and Gramian Angular Difference Field (GADF) images. Subsequently, a dual-input CNN architecture was designed to fuse discriminative features from both GASF and GADF images. Feature visualization of high-weight channels of the input images in convolutional layer revealed distinct spectral features between seedless and seeded watermelons. With the fusion of distinguishing feature information, the developed CNN model achieved a classification accuracy of 95.1% on the prediction set, outperforming traditional models based on one-dimensional spectra. Remarkably, wavelength optimization through competitive adaptive reweighted sampling (CARS) reduced GAF image generation time to 55.19% of full-wavelength processing, while improving classification accuracy to 96.3%. A better generalization of the model was demonstrated using 17 seedless and 20 seeded watermelons from other origins, with a classification accuracy of 91.9%. These findings substantiated that GAF-enhanced feature fusion CNN can significantly improve the classification accuracy of multi-cultivar watermelons, casting innovative light on fruit quality based on VIS-NIR transmittance spectroscopy. Full article

This paper presents a method for optimizing the inertia constants and damping coefficients of interconnected virtual synchronous generators (VSGs) using a genetic algorithm. The goal of optimization is to find a balance between minimizing the rate of change of frequency (RoCoF) and enhancing controllability. Five controllability-based metrics are tested: the minimum eigenvalue, the sum of the two smallest eigenvalues, the maximum eigenvalue, the trace, and the determinant of the controllability Gramian matrix. The approach includes the oscillatory modes’ damping ratio constraints to ensure the small-signal stability of the entire system. The results of optimization on the IEEE 9-bus system with three VSGs show that the proposed method improves controllability, reduces RoCoF, and maintains the desired oscillation damping. The proposed approach was tested through time-domain simulations. Full article

In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermore, the optimal control of nonlinear NFEEs with integral index functionals is studied, and the existence of optimal control pairs is proven. Finally, by constructing a corresponding Gramian controllability operator using the solution operator, a sufficient condition is provided for the existence of approximate controllability of the corresponding problem. Full article

This paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid the computationally expensive generalized Lyapunov equation solvers used in traditional methods. These algorithms employ recursive formulas to calculate Laguerre expansion coefficients, which are then used to derive low-rank decomposition factors for frequency-limited controllability and observability Gramians. Additionally, we enhance the Laguerre-based low-rank MOR algorithm by incorporating a modified frequency-limited BT method, further improving its computational efficiency. Numerical simulations validate the effectiveness of the proposed approach, demonstrating significant reductions in computational complexity while maintaining accuracy in system approximation. Full article

This paper introduces a novel Gramian-based quantitative metric to evaluate the disturbance rejection capabilities of linear unstable systems. The proposed metric addresses key limitations of the previously introduced degree of disturbance rejection (DoDR) metrics, including their dependency on the final time and numerical problems arising from differential equation computations. Specifically, this study defines the steady-state solution of the DoDR metric, which avoids numerical issues by relying only on solving four algebraic equations, even when the Gramian matrices diverge. This study further strengthens its contributions by providing rigorous mathematical proofs supporting the proposed method, ensuring a strong theoretical foundation. The derived results demonstrate that the proposed metric represents the sum of the steady-state input energies required to reject the disturbances in the asymptotically stable and anti-stable subsystems. Numerical examples demonstrated that the proposed metric maintained the physical meaning of the original DoDR while offering practical computational advantages. This study represents a significant step toward the efficient and reliable assessment of disturbance rejection capabilities in unstable systems. Full article

State-of-the-art smart cities have been calling for economic but efficient energy management over a large-scale network, especially for the electric power system. It is a critical issue to monitor, analyze, and control electric loads of all users in the system. In this study, a non-intrusive load monitoring method was designed for smart power management using computer vision techniques popular in artificial intelligence. First of all, one-dimensional current signals are mapped onto two-dimensional color feature images using signal transforms (including the wavelet transform and discrete Fourier transform) and Gramian Angular Field (GAF) methods. Second, a deep neural network with multi-scale feature extraction and attention mechanism is proposed to recognize all electrical loads from the color feature images. Third, a cloud-based approach was designed for the non-intrusive monitoring of all users, thereby saving energy costs during power system control. Experimental results on both public and private datasets demonstrate that the method achieves superior performances compared to its peers, and thus supports efficient energy management over a large-scale Internet of Things network. Full article

In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented. We show that the controllability of the local fractional system can be determined by the invertibility of the Gramian matrix and the full rank of the Kalman matrix. We also show that the local fractional system involving distinct orders is controllable if and only if the Gramian matrix is invertible. Illustrative examples and an application are provided to demonstrate the validity of the theoretical findings. Full article

Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fractional derivative. By utilizing the Cayley–Hamilton theorem and Laplace transformation, a concise proof is given to determine the controllability of linear fractional complex networks. Subsequently, leveraging the Schauder Fixed-Point theorem, controllability Gramian matrix, and fractional calculus theory, we derive controllability conditions for nonlinear fractional complex networks with a weighted adjacency matrix and Laplacian matrix, respectively. Finally, a numerical method for the controllability of fractional complex networks is obtained using Matlab (2021a)/Simulink (2021a). Three examples are provided to illustrate the theoretical results. Full article