Search Results (39)

Tax evasion is a dynamic process reflecting continuous interaction between taxpayers and regulatory institutions rather than a static deviation from fiscal equilibrium. This study introduces a predator-prey model of tax evasion that translates the Lotka-Volterra framework from biology into budgetary dynamics. The model captures the feedback between the volume of tax evasion and the intensity of regulation, incorporating nonlinearity, implicit reactive lag, and adaptive response. Theoretical derivation and numerical simulation identify three dynamic regimes—stable equilibrium, limit-cycle oscillation, and instability—that arise through a Hopf bifurcation. Bifurcation maps in the (r, a), (r, b), and (r, c) parameter spaces reveal how control efficiency, institutional inertia, and behavioral feedback jointly determine fiscal stability. Results show that excessive enforcement may destabilize the system by inducing regulatory fatigue, while weak control enables exponential growth in evasion. The model provides a dynamic analytical tool for evaluating fiscal policy efficiency and identifying stability thresholds. Its findings suggest that adaptive, feedback-based regulation is essential for maintaining long-term tax discipline. The study contributes to closing the research gap by providing a unified dynamic framework linking micro-behavioral decision-making with macro-fiscal stability, offering a foundation for future empirical calibration and behavioral extensions of fiscal systems. Full article

Establishing precise and reliable quadrotor dynamics model is crucial for safe and stable tracking control in obstacle environments. However, obtaining such models is challenging, as it requires precise inertia identification and accounting for complex aerodynamic effects, which handcrafted models struggle to do. To address this, this paper proposes a safety-critical control framework built on a Hamiltonian neural differential model (HDM). The HDM formulates the quadrotor dynamics under a Hamiltonian structure over the $\mathit{SE}\left(3\right)$ manifold, with explicitly optimizable inertia parameters and a neural network-approximated control input matrix. This yields a neural ordinary differential equation (ODE) that is solved numerically for state prediction, while all parameters are trained jointly from data via gradient descent. Unlike black-box models, the HDM incorporates physical priors—such as $\mathit{SE}\left(3\right)$ constraints and energy conservation—ensuring a physically plausible and interpretable dynamics representation. Furthermore, the HDM is reformulated into a control-affine form, enabling controller synthesis via control Lyapunov functions (CLFs) for stability and exponential control barrier functions (ECBFs) for rigorous safety guarantees. Simulations validate the framework’s effectiveness in achieving safe and stable tracking control. Full article

The increasing penetration of wind energy has led to reduced system inertia and heightened sensitivity to dynamic disturbances in modern power systems. This paper proposes a Newton–Raphson-Based Optimizer (NRBO) for tuning proportional, integral, and feedforward gains of a grid-forming converter applied to a wind energy conversion system operating in a low-inertia environment. The study considers an aggregated wind farm modeled as a single equivalent DFIG-based wind turbine connected to an infinite bus, with detailed dynamic representations of the converter control loops, synchronous generator dynamics, and network interactions formulated in the dq reference frame. The grid-forming converter operates in a grid-connected mode, regulating voltage and active–reactive power exchange. The NRBO algorithm is employed to optimize a composite objective function defined in terms of voltage deviation and active–reactive power mismatches. Performance is evaluated under two representative scenarios: small-signal disturbances induced by wind torque variations and short-duration symmetrical voltage disturbances of 20 ms. Comparative results demonstrate that NRBO achieves lower objective values, faster transient recovery, and reduced oscillatory behavior compared with Differential Evolution, Particle Swarm Optimization, Philosophical Proposition Optimizer, and Exponential Distribution Optimization. Statistical analyses over multiple independent runs confirm the robustness and consistency of NRBO through significantly reduced performance dispersion. The findings indicate that the proposed optimization framework provides an effective simulation-based approach for enhancing the transient performance of grid-forming wind energy converters in low-inertia systems, with potential relevance for supporting stable operation under increased renewable penetration. Improving the reliability and controllability of wind-dominated power grids enhances the delivery of cost-effective, cleaner, and more resilient energy systems, aiding in expanding sustainable electricity access in alignment with SDG7. Full article

In modern power systems, the implementation of load-frequency control (LFC) must reconcile continuous-time plant dynamics with discrete-time digital controllers operating under coarsely sampled communications. This paper develops a sampled-data $H_{\infty }$ framework for PI-type secondary LFC that explicitly accounts for aperiodic sampling and reduced inertia due to high wind penetration. Using a two-sided looped Lyapunov functional and free-matrix inequalities, sampling-interval-dependent linear matrix inequalities (LMIs) are derived for stability, $H_{\infty }$ performance and an exponential decay rate (EDR). The synthesis returns PI gains and the admissible maximum sampling period (MASP) via simple bisection. Numerical examples based on one-area, two-area, and three-area power systems demonstrate that the proposed stability conditions allow larger admissible sampling periods compared with existing approaches, while preserving satisfactory dynamic behaviour under different operating scenarios. Full article

Global climate change demands modeling approaches that are both computationally efficient and physically faithful to the system’s long-term dynamics. Classical Energy Balance Models (EBMs), while valuable, are fundamentally limited by their memoryless exponential response, which fails to represent the prolonged thermal inertia of the climate system—particularly that associated with deep-ocean heat uptake. In this study, we introduce a fractional Energy Balance Model (fEBM) by replacing the classical integer-order time derivative with a Caputo fractional derivative of order $\alpha (0<\alpha \le 1)$, thereby embedding long-range memory directly into the model structure. We establish a rigorous mathematical foundation for the fEBM, including proofs of existence, uniqueness, and asymptotic stability, ensuring theoretical well-posedness and numerical reliability. The model is calibrated and validated against historical global mean surface temperature data from NASA GISTEMP and radiative forcing estimates from IPCC AR6. Relative to the classical EBM, the fEBM achieves a substantially improved representation of observed temperatures, reducing the root mean square error by approximately 29% during calibration (1880–2010) and by 47% in out-of-sample forecasting (2011–2023). The optimized fractional order $\alpha =0.75\pm 0.03$ emerges as a physically interpretable measure of aggregate climate memory, consistent with multi-decadal ocean heat uptake and observed persistence in temperature anomalies. Residual diagnostics and robustness analyses further demonstrate that the fractional formulation captures dominant temporal dependencies without overfitting. By integrating mathematical rigor, uncertainty quantification, and physical interpretability, this work positions fractional calculus as a powerful and responsible framework for reduced-order climate modeling and long-term projection analysis. Full article

The stability of energy demand–supply systems is often affected by delayed feedback caused by regulatory inertia, communication lags, and heterogeneous agent responses. Conventional models typically assume discrete delays, which may oversimplify real dynamics and reduce controller effectiveness. This work addresses this limitation by introducing a novel class of nonlinear energy models with distributed delay feedback governed by gamma-distributed memory kernels. Specifically, we consider both weak (exponential) and strong (Erlang-type) kernels to capture a spectrum of memory effects. Using the linear chain trick, we reformulate the resulting integro-differential model into a higher-dimensional system of ordinary differential equations. Analytical conditions for local asymptotic stability and Hopf bifurcation are derived, complemented by Lyapunov-based global stability criteria. The related numerical analysis confirms the theoretical findings and reveals a distinct stabilization regime. Compared to fixed-delay approaches, the proposed framework offers improved flexibility and robustness, with implications for delay-aware energy control and infrastructure design. Full article

In the last decades, small satellites such as CubeSats and PocketQubes have become popular platforms for scientific and applied missions in low Earth orbit (LEO). However, prolonged exposure to atomic oxygen, ultraviolet radiation, and thermal cycling in LEO leads to gradual degradation of onboard solar panels, reducing mission lifetime and performance. This study addresses the need to quantify and compare the degradation behavior of different solar cell technologies and protective coatings used in nanosatellites and pico-satellites. The aim is to evaluate the in-orbit performance of monocrystalline silicon (Si), gallium arsenide (GaAs), triple-junction (TJ) structures, and copper indium gallium selenide (CIGS) cells under varying orbital and satellite parameters. Telemetry data from recent small satellite missions launched after 2020, combined with numerical modeling in GNU Octave, were used to assess degradation trends. The models were validated using empirical mission data, and statistical goodness-of-fit metrics (RMSE, R²) were applied to evaluate linear and exponential degradation patterns. Results show that TJ cells exhibit the highest resistance to LEO-induced degradation, while Si-based panels experience more pronounced power loss, especially in orbits below 500 km. Furthermore, smaller satellites (<10 kg) display higher degradation rates due to lower thermal inertia and limited shielding. These findings provide practical guidance for the selection of solar cell technologies, anti-degradation coatings, and protective strategies for long-duration CubeSat missions in diverse LEO environments. Full article

This paper presents a structured and experimentally validated approach to the parameter identification, modeling, and real-time speed control of a brushless DC (BLDC) motor. Electrical parameters, including resistance and inductance, were measured through DC and AC testing under controlled conditions, respectively, while mechanical and electromagnetic parameters such as the back electromotive force (EMF) constant and rotor inertia were determined experimentally using an AVL dynamometer. The back EMF was obtained by operating the motor as a generator under varying speeds, and inertia was identified using a deceleration method based on the relationship between angular acceleration and torque. The identified parameters were used to construct a transfer function model of the motor, which was implemented in MATLAB/Simulink R2024b and validated against real-time experimental data using sinusoidal and exponential input signals. The comparison between simulated and measured speed responses showed strong agreement, confirming the accuracy of the model. A proportional–integral (PI) controller was developed and implemented for speed regulation, using a low-cost National Instruments (NI) USB-6009 data acquisition (DAQ) and a Kelly controller. A first-order low-pass filter was integrated into the control loop to suppress high-frequency disturbances and improve transient performance. Experimental tests using a stepwise reference speed profile demonstrated accurate tracking, minimal overshoot, and robust operation. Although the modeling and control techniques applied are well known, the novelty of this work lies in its integration of experimental parameter identification, real-time validation, and practical hardware implementation within a unified and replicable framework. This approach provides a solid foundation for further studies involving more advanced or adaptive control strategies for BLDC motors. Full article

This study investigates the thermal response and surface modification of low-carbon manganese-alloyed 20GL steel during electrolytic plasma hardening. The objective was to evaluate the feasibility of surface hardening 20GL steel—traditionally considered difficult to quench—by combining high-rate surface heating with rapid cooling in an electrolyte medium. To achieve this, a transient two-dimensional heat conduction model was developed to simulate temperature evolution in the steel sample under three voltage regimes. The model accounted for dynamic thermal properties and non-linear boundary conditions, focusing on temperature gradients across the thickness. Experimental temperature measurements were obtained using a K-type thermocouple embedded at a depth of 2 mm, with corrections for sensor inertia based on exponential response behavior. A comparison between simulation and experiment was conducted, focusing on peak temperatures, heating and cooling rates, and the effective thermal penetration depth. Microhardness profiling and metallographic examination confirmed surface strengthening and structural refinement, which intensified with increasing voltage. Importantly, the study identified a critical cooling rate threshold of approximately 50 °C/s required to initiate martensitic transformation in 20GL steel. These findings provide a foundation for future optimization of quenching strategies for low-carbon steels by offering insight into the interplay between thermal fluxes, surface kinetics, and process parameters. Full article

The increasing incorporation of renewable energy into power grids has significantly reduced system inertia and damping, posing challenges to frequency stability and power quality. To address this issue, an adaptive virtual synchronous generator (VSG) control strategy is proposed, which dynamically adjusts virtual inertia and damping in response to real-time frequency variations. Virtual inertia is modulated by an exponential function according to the frequency variation rate, while damping is regulated via a hyperbolic tangent function, enabling minor support during small disturbances and robust compensation during severe events. Control parameters are optimized using an enhanced particle swarm optimization (PSO) algorithm based on a composite performance index that accounts for frequency deviation, overshoot, settling time, and power tracking error. Simulation results in MATLAB/Simulink under step changes, load fluctuations, and single-phase faults demonstrate that the proposed method reduces the frequency deviation by over 26.15% compared to fixed-parameter and threshold-based adaptive VSG methods, effectively suppresses power overshoot, and eliminates secondary oscillations. The proposed approach significantly enhances grid transient stability and demonstrates strong potential for application in power systems with high levels of renewable energy integration. Full article

Hydraulic excavators operate in harsh environments where direct measurement of actuator chamber pressures and boom displacement is often unreliable or infeasible. This study presents a novel control strategy that estimates actuator chamber pressures from work port pressures using differential equations, eliminating the need for direct pressure or position sensors. A fuzzy logic-based proportional–derivative (PD) controller is developed to mitigate boom oscillations, particularly under high-inertia load conditions and variable operator inputs. The controller dynamically adjusts gains through fuzzy logic-based gain scheduling, enhancing adaptability across a wide range of operating conditions. The proposed method addresses the limitations of classical PID controllers, which struggle with the nonlinearities, parameter uncertainties, and instability introduced by counterbalance valves and pressure-compensated proportional valves. Experimental data is used to design fuzzy rules and membership functions, ensuring robust performance. Simulation and full-scale experimental validation demonstrate that the fuzzy PD controller significantly reduces pressure overshoot (by 23% during extension and 32% during retraction) and decreases settling time (by 31.23% and 28%, respectively) compared to conventional systems. Frequency-domain stability analysis confirms exponential stability and improved damping characteristics. The proposed control scheme enhances system reliability and safety, making it ideal for excavators operating in remote or rugged terrains where conventional sensor-based systems may fail. This approach is generalizable and does not require modifications to the existing hydraulic circuit, offering a practical and scalable solution for modern hydraulic machinery. Full article

This study introduces an Enhanced Error-Adaptive Extended-State Kalman Filter Model Predictive Control (EEA-ESKF-MPC) method to tackle strong coupling and inertia in supercritical power plants. By enhancing the ESKF-MPC framework with a mechanism that dynamically adjusts error weights based on real-time deviations and employs exponential smoothing, alongside a BP neural network for thermal unit simulation, the approach achieves superior performance. Simulations show reductions in the Integrated Absolute Error (IAE) for load and temperature by 3.05% and 2.46%, respectively, with a modest 0.43% pressure IAE increase compared to ESKF-MPC. Command disturbance tests and real condition tracking experiments, utilizing data from a 350 MW supercritical unit, reinforce the method’s effectiveness, highlighting its exceptional dynamic performance and precise tracking of operational parameter changes under multivariable coupling conditions, offering a scalable solution for modern power systems. Full article

In the context of the booming digital economy, the energy consumption of data centers (DC) is experiencing exponential growth, and achieving green transformation has become a crucial issue. This paper presents a coordinated spatio-temporal operation of wind–solar–storage-powered DCs considering building thermal inertia. Firstly, based on users’ differentiated needs, the spatio-temporal flexibility of data loads is deeply explored to lower DC’s operation costs through load shifting. Secondly, a DC mathematical model considering building thermal inertia is established, revealing the quantitative relationship among air-conditioning power, data load rate, and building parameters. Finally, a coordinated spatio-temporal operation of wind–solar–storage-powered DCs considering building thermal inertia is proposed to promote renewable energy consumption and realize the green transformation of DC. The case study results show that the proposed strategy reduces the DC operation cost by 37.92% and significantly increases the renewable energy-consumption ratio. Full article

We study the large-time behavior of solutions to Darcy–Boussinesq equations with a non-vanishing scalar acceleration coefficient, which model buoyancy-driven flows in porous media with spatially varying gravity. First, we show that the system admits steady-state solutions of the form $(\mathbf{u},\rho ,p)=(\mathbf{0},{\rho }_s,p_s)$, where ${\rho }_s$ is characterised by the hydrostatic balance $\nabla p_s=-{\rho }_s\nabla \mathrm{\Psi }$. Second, we prove that the steady-state solution satisfying $\nabla {\rho }_s=\delta (x,y)\nabla \mathrm{\Psi }$ is linearly stable provided that $\delta (x,y)<{\delta }_0<0$, while the system exhibits Rayleigh–Taylor instability if $\mathrm{\Psi }=gy$, ${\rho }_s={\delta }_{0}g$ and ${\delta }_0>0$. Finally, despite the inherent Rayleigh–Taylor instability that may trigger exponential growth in time, we prove that for any sufficiently regular initial data, the solutions of the system asymptotically converge towards the vicinity of a steady-state solution, where the velocity field is zero, and the new state is determined by hydrostatic balance. This work advances porous media modeling for geophysical and engineering applications, emphasizing the critical interplay of gravity, inertia, and boundary conditions. Full article

This study proposes a hybrid PSO-EDO algorithm, integrating Particle Swarm Optimization (PSO) and the Exponential Distribution Optimizer (EDO) for efficient and accurate estimation of soil property parameters. The proposed algorithm combines the strengths of Standard PSO (SPSO) and the Exponential Distribution Optimizer (EDO). Three key innovations are introduced: (1) SPM chaotic mapping enhances initial population diversity; (2) dynamic inertia weight balances global exploration and local exploitation; (3) the memoryless property of EDO improves escape capability from local optima. Benchmark tests demonstrate that PSO-EDO achieves near-theoretical optimal convergence errors (mean error ≤ 10⁻¹⁶ for unimodal functions such as F1 and F2) and reduces the computation time by 14.5% compared to EDO. For multimodal functions (e.g., F3), PSO-EDO significantly outperforms PSO-WOA (Particle Swarm Optimization-Whale Optimization Algorithm) with a 22.3% reduction in error. Simulation experiments further validate its engineering practicality: in soil parameter estimation, PSO-EDO completes 1000 iterations in just 1.95 s, with key parameters (e.g., sinkage coefficient n) controlled within a 7.32% error margin. This provides an efficient solution for real-time traversability assessment of autonomous vehicles on soft terrains. Full article