Search Results (857)

Fractional calculus in discrete-time is a recent field that has drawn much interest for dealing with multidisciplinary systems. A result of this tremendous potential, researchers have been using constant and variable-order fractional discrete calculus in the modelling of financial and economic systems. This paper explores the emergence of chaotic and regular patterns of the fractional four-dimensional (4D) discrete economic system with constant and variable orders. The primary aim is to compare and investigate the impact of two types of fractional order through numerical solutions and simulation, demonstrating how modifications to the order affect the behavior of a system. Phase space orbits, the 0-1 test, time series, bifurcation charts, and Lyapunov exponent analysis for different orders all illustrate the constant and variable-order systems’ behavior. Moreover, the spectral entropy (SE) and $C_0$ complexity exhibit fractional-order effects with variations in the degree of complexity. The results provide new insights into the influence of fractional-order types on dynamical systems and highlight their role in promoting chaotic behavior. Additionally, two types of control strategies are devised to guide the states of a 4D fractional discrete economic system with constant and variable orders to the origin within a specified amount of time. MATLAB simulations are presented to demonstrate the efficacy of the findings. Full article

This paper addresses the simultaneous feeder routing and conductor sizing problem in unbalanced three-phase distribution systems, formulated as a nonconvex mixed-integer nonlinear program (MINLP) that minimizes the equivalent annualized expansion cost—combining investment and loss costs—under voltage, ampacity, and radiality constraints. The model captures nonconvex voltage–current–power couplings, $\Delta /Y$ load asymmetries, and discrete conductor selections, creating a large combinatorial design space that challenges heuristic methods. An exact MINLP formulation in complex variables is implemented in Julia/JuMP and solved with the Basic Open-source Nonlinear Mixed Integer programming (BONMIN) solver, which integrates branch-and-bound for discrete variables and interior-point methods for nonlinear subproblems. The main contributions are: (i) a rigorous, reproducible formulation that jointly optimizes routing and conductor sizing; (ii) a transparent, replicable implementation; and (iii) a benchmark against minimum spanning tree (MST)-based and metaheuristic approaches, clarifying the trade-off between computational time and global optimality. Tests on 10- and 30-node rural feeders show that, although metaheuristics converge faster, they often yield suboptimal solutions. The proposed MINLP achieves globally optimal, technically feasible results, reducing annualized cost by 14.6% versus MST and 2.1% versus metaheuristics in the 10-node system, and by 17.2% and 2.5%, respectively, in the 30-node system. These results highlight the advantages of exact optimization for rural network planning, providing reproducible and verifiable decisions in investment-intensive scenarios. Full article

In the present work, we aim to study the inverse problem of recovering an unknown spatial source term in a multi-term time-fractional diffusion equation involving the fractional Laplacian. The forward problem is first analyzed in appropriate fractional Sobolev spaces, establishing the existence, uniqueness, and regularity of solutions. Exploiting the spectral representation of the solution and properties of multinomial Mittag–Leffler functions, we prove uniqueness and derive a stability estimate for the spatial source term from finaltime observations. The inverse problem is then formulated as a Tikhonov regularized optimization problem, for which existence, uniqueness, and strong convergence of the regularized minimizer are rigorously established. On the computational side, we propose an efficient reconstruction algorithm based on the conjugate gradient method, with temporal discretization via an L¹-type scheme for Caputo derivatives and spatial discretization using a Galerkin approach adapted to the nonlocal fractional Laplacian. Numerical experiments confirm the accuracy and robustness of the proposed method in reconstructing the unknown source term. Full article

To address the challenge of monitoring the postharvest jasmine bloom stages during industrial tea scenting processes, this study proposes an efficient U-shaped Network (U-Net) model with frequency–spatial cross-attention (FSCA-EUNet) to resolve critical bottlenecks, including repetitive backgrounds and small interclass differences, caused by stacked jasmine flowers during factory production. High-resolution images of stacked jasmine flowers were first preprocessed and input into FSCA-EUNet, where the encoder extracted multi-scale spatial features and the FSCA module incorporated frequency-domain textures. The decoder then fused and refined these features, and the final classification layer output the predicted bloom stage for each image. The proposed model was designed as a “U-Net”-like structure to preserve multiscale details and employed a frequency–spatial cross-attention module to extract high-frequency texture features via a discrete cosine transform. Long-range dependencies were established by NonLocalBlook, located after the encoders in the model. Finally, a momentum-updated center loss function was introduced to constrain the feature space distribution and enhance intraclass compactness. According to the experimental results, the proposed model achieved the best metrics, including 95.52% precision, 95.42% recall, 95.40% F1-score, and 97.24% mean average precision, on our constructed dataset with only 878.851 K parameters and 15.445 G Floating Point Operations (FLOPs), and enabled real-time deployment at 22.33 FPS on Jetson Orin NX edge devices. The ablation experiments validated the improvements contributed by each module, which significantly improved the fine-grained classification capability of the proposed network. In conclusion, FSCA-EUNet effectively addresses the challenges of stacked flower backgrounds and subtle interclass differences, offering a lightweight yet accurate framework that enables real-time deployment for industrial jasmine tea scenting automation. Full article

This paper investigates the problem of data-driven optimal preview repetitive control of linear discrete-time systems. Firstly, by integrating prior information into the preview time domain, an augmented state-space system is established. Secondly, the original output tracking problem is mathematically reconstructed and transformed into the optimization problem form of a linear quadratic tracking (LQR). Furthermore, a Q-function-based iterative algorithm is designed to dynamically calculate the optimal tracking control gain based solely on online measurable data. This method has a dual-breakthrough feature: it neither requires prior knowledge of system dynamics nor provides an initial stable controller. Finally, the superiority of the proposed scheme is verified through numerical simulation experiments. Full article

This study proposes a discrete multi-agent Q-learning framework for the online tuning of PID controllers in continuous dynamic systems with limited observability. The approach treats the adjustment of each PID gain ($k_p$, $k_i$, $k_d$) as an independent learning process, in which each agent operates within a discrete state space corresponding to its own gain and selects actions from a tripartite space (decrease, maintain, or increase its gain). The agents act simultaneously under fixed decision intervals, favoring their convergence by preserving quasi-stationary conditions of the perceived environment, while a shared cumulative global reward, composed of system parameters, time and control action penalties, and stability incentives, guides coordinated exploration toward control objectives. Implemented in Python, the framework was validated in two nonlinear control problems: a water-tank and inverted pendulum (cart-pole) systems. The agents achieved their initial convergence after approximately 300 and 500 episodes, respectively, with overall success rates of $49.6\%$ and $46.2\%$ in 5000 training episodes. The learning process exhibited sustained convergence toward effective PID configurations capable of stabilizing both systems without explicit dynamic models. These findings confirm the feasibility of the proposed low-complexity discrete reinforcement learning approach for online adaptive PID tuning, achieving interpretable and reproducible control policies and providing a new basis for future hybrid schemes that unite classical control theory and reinforcement learning agents. Full article

In this paper, we study a class of time–space fractional partial differential equations involving Caputo time-fractional derivatives and Riesz space-fractional derivatives. A computational scheme is developed by combining a discrete approximation for the Caputo derivative in time with a modified trapezoidal method (MTM) for the Riesz derivative in space. We establish the stability and convergence of the scheme and provide detailed error analysis. The novelty of this work lies in the construction of an MTM-based spatial discretization that achieves ${\displaystyle \beta }$-order convergence in space and a ${\displaystyle (3-\alpha )}$-order convergence in time, while improving accuracy and efficiency compared to existing methods. Numerical experiments are carried out to validate the theoretical findings, confirm the stability of the proposed algorithm under perturbations, and demonstrate its superiority over a recent scheme from the literature. Full article

Real-time hybrid simulation (RTHS) evaluates the dynamic performance of a structure by physically testing the selected components while modeling the remaining structure numerically, making it efficient in both cost and testing space requirements. In RTHS, accurately imposing target boundary conditions on specimens is critical, as it directly influences test accuracy and overall simulation stability. However, boundary condition application often experiences tracking errors due to the dynamics of the servo–hydraulic loading system and control-structural interaction. This challenge intensifies with multiple actuators operating in a multi-axial setup, introducing dynamic coupling effects. Thus, an outer-loop controller enabling precise actuator tracking of reference boundary conditions is essential for reliable RTHS. While advancements in outer-loop controllers for uniaxial RTHS exist, multi-axial RTHS (maRTHS) employing multiple degrees of freedom control remains underexplored. This study applies the adaptive discrete feedforward controller (ADFC), consisting of a discrete feedforward compensator and an online identifier, to a multi-input, multi-output (MIMO) system for maRTHS. To validate ADFC’s performance and robustness, 1000 virtual maRTHS tests incorporating plant uncertainties were conducted under seismic excitations. Ten evaluation criteria were applied. Results confirm that ADFC achieves robust and stable control by reducing phase and amplitude errors, while also improving estimation accuracy at the physical–numerical interface. Full article

This study presents an efficient high-order radius function Hermite finite difference (RBF-HFD) scheme for the numerical solution of Caputo time-fractional sub-diffusion equations with integral boundary conditions. The spatial derivatives are approximated using a fourth-order RBF-HFD scheme, while the Caputo fractional derivative in time is discretized via the L$2-1_{\sigma }$ formula. To ensure global fourth-order spatial accuracy, the integral boundary conditions are discretized with the composite Simpson rule. As a result, we obtain an unconditionally stable numerical scheme that achieves fourth-order convergence in space and second-order convergence in time. The solvability, stability, and convergence of the scheme are rigorously established using the discrete energy method. The proposed method is validated through three numerical examples and is compared with existing approaches. The numerical results demonstrate that the proposed scheme achieves higher accuracy than the methods available in the literature. Full article

To address the challenges of strong nonlinearity, stringent terminal constraints, and the trade-off between computational efficiency and accuracy in the midcourse guidance trajectory optimization problem of aerodynamically controlled interceptors, this paper proposes a variable-discrete-scale sequential convex programming (SCP) method. Firstly, a dynamic model is established by introducing the range domain to replace the traditional time domain, thereby reducing the approximation error of the planned trajectory. Second, to overcome the critical issues of solution space restriction and trajectory divergence caused by terminal equality constraints, a terminal error-proportional relaxation approach is proposed. Subsequently, an improved second-order cone programming (SOCP) formulation is developed through systematic integration of three key techniques: terminal error-proportional relaxation, variable trust region, and path normalization. Finally, an initial trajectory generation algorithm is proposed, upon which a variable-discrete-scale optimization framework is constructed. This framework incorporates a residual-driven discrete-scale adaptation mechanism, which balances discretization errors and computational load. Numerical simulation results indicate that under large discretization scales, the computation time required by the improved SOCP is only about 5.4% of that of GPOPS-II. For small-discretization-scale optimization, the SCP method with the variable discretization framework demonstrates high efficiency, achieving comparable accuracy to GPOPS-II while reducing the computation time to approximately 7.4% of that required by GPOPS-II. Full article

We present a concise and self-contained extension of the Finite Ring Continuum (FRC) program, showing that symmetry-complete prime shells ${\mathbb{F}}_{\mathsf{p}}$ with $\mathsf{p}=4\mathsf{t}+1$ exhibit a fundamental Euclidean-Lorentzian dichotomy. A genuine Lorentzian quadratic form cannot be realized within a single space-like prime shell ${\mathbb{F}}_{\mathsf{p}}$, since to split time from space one requires a time coefficient $c^2$ in the nonsquare class of ${\mathbb{F}}_{\mathsf{p}}^{\times }$, but then $c\notin {\mathbb{F}}_{\mathsf{p}}$. An explicit finite-field Lorentz transformation is subsequently derived that preserves the Minkowski form and generates a finite orthogonal group $O(Q_{\nu },{\mathbb{F}}_{p^2})$ of split type (Witt index 1). These results demonstrate that the essential algebraic features of special relativity—the invariant interval and Lorentz symmetry—emerge naturally within finite-field arithmetic, thereby establishing an intrinsic relativistic algebra within FRC. Finally, this dichotomy implies the algebraic origin of causality: Euclidean invariants reside within a space-like shell ${\mathbb{F}}_{\mathsf{p}}$, while Lorentzian structure and causal separation arise in its quadratic spacetime extension ${\mathbb{F}}_{{\mathsf{p}}^2}$. Full article

To address the issue that the current research on TBM disc cutter rock breaking insufficiently considers actual stratified rock masses, this study constructs numerical models of stratified rock masses with different bedding dip angles and bedding spacings based on the discrete element method (DEM). The whole process of TBM disc cutter rock breaking is numerically simulated through the displacement loading mode. The research results show that the bedding dip angle has a significant impact on the crack propagation mode. When α = 45°, the bedding intersects with the contact point of the disc cutter, and cracks penetrate directly along the bedding without an obvious “crushed zone”, resulting in the minimum number of cracks. The bedding spacing regulates the rock-breaking effect in stages. When d = 45°, the “crushed zone” interacts with two beddings to form three branch cracks, reaching the peak number of cracks and achieving the optimal rock-breaking efficiency. The cracks generated by disc cutter rock breaking exhibit the characteristic of “slow initial growth and rapid later surge” with the increase in time steps, which is highly consistent with the actual mechanical process of rock breaking. This study reveals the influence mechanism of bedding properties on TBM disc cutter rock breaking, verifies the reliability of the DEM combined with PB and SJ models in the simulation of stratified rock mass breaking, and provides theoretical support and data references for the parameter optimization of TBM disc cutters and efficient tunneling under complex stratified geological conditions. Full article

High-voltage fuses are critical safety components in electric vehicle (EV) battery systems, yet their thermal behavior under charging currents remains insufficiently characterized. This study develops and validates a physics-based thermal resistor-capacitor (RC) network model of a high-voltage melting fuse, accounting for copper elements, quartz sand filling, and polyester casing. Experimental accelerated life tests and current step load profiles were performed in a climate chamber at 70 °C, with temperature measurements at the fuse terminals. The RC model was constructed using material properties and geometry-derived parameters, including three copper element sections, one quartz sand node, and one case node. A discretized state–space formulation was implemented to simulate the transient thermal behavior. The results reveal distinct dynamic and stationary characteristics, with thermal time constants varying strongly between fuse sections. Comparisons with experimental data demonstrate that the proposed model captures both rise time and steady-state behavior, with deviations attributable to contact resistances and parasitic effects. The findings highlight that charging currents in practical profiles typically remain below 50% of fuse current ratings, leaving optimization potential for higher permissible currents, faster charging, and reduced downtime while maintaining safety. The outcome of this model is highly relevant for lifetime prediction models. Full article

Space robots are vital for in-orbit maintenance of large satellites, but dense payloads and complex surface structures pose challenges for safe crawling operations. This study proposes an improved trajectory planning framework for three-dimensional satellite surfaces. In the path search stage, the traditional A* algorithm is enhanced with traction cost, reflecting surface adhesion, and proximity cost, ensuring collision avoidance. The resulting comprehensive cost function integrates path length, safety, and feasibility, producing paths more consistent with real mobility constraints. In the smoothing stage, cubic B-spline curves refine the discrete path, with real-time collision detection embedded in the optimization of control points to prevent trajectory penetration. Simulations show that the method achieves millisecond-level planning, with path length reduced by 6.82% and trajectory smoothness significantly improved, eliminating the phenomenon of sharp turns with folded corners. The approach ensures continuous, stable, and collision-free movement of space robots, highlighting its potential for reliable in-orbit operations. Full article

To increase target acquisition probability and the signal-to-noise ratio (SNR) of hyperspectral images, this paper presents a wide-field, dual-slit, low-distortion, and high-sensitivity Offner hyperspectral imager, with a wavelength range of 0.4 μm to 0.9 μm, a numerical aperture of 0.15, and a slit length of 73 mm. To avoid signal aliasing, the space between the dual slits is 2.4 mm, increasing the SNR by 1.4 times after dual-slit image fusion. Furthermore, to achieve the required registration accuracy of dual-slit images, the spectral performance of the hyperspectral imager is critical. Thus, we compensate and correct the spectral performance and dispersion nonlinearity of the hyperspectral imager by taking advantages of the material properties and tilt eccentricity of a low-dispersion internal reflection curved prism and high-dispersion double-pass curved prisms. To meet the final operation requirements, the tilt of the internal reflection curved prism is used as a compensator. Using the modulation transfer function (MTF) as the evaluation criterion, an inverse sensitivity analysis confirmed that the compensator is a highly sensitive component. Additionally, the root mean square standard deviation (RSS) discrete calculation method was adopted to assess the influence of actual assembly tolerance on spectral performance. The test results demonstrate that the hyperspectral imager meets the registration accuracy requirements of dual-slit images, with an MTF better than 0.4. Furthermore, the spectral smile and spectral keystone of the dual-slit images are both less than or equal to 0.3 pixels. Full article