Abstract

This paper proposes a novel dynamic event-triggered control scheme to address the fixed-time synchronization problem for chaotic neural networks (NNs) with mixed delays. Firstly, an adaptive threshold mechanism is embedded into the dynamic event-triggered control, which occupies less communication resource in comparison with the periodic-triggered control and enables the exclusion of Zeno phenomena. Secondly, by combining Lyapunov stability theory with fixed-time convergence criteria, a sufficient condition for the fixed-time synchronization of such chaotic NNs is established. Particularly, an explicit upper-bound estimation of the settling time is derived, which solely depends on controller parameters and is independent of the initial condition. Theoretical analysis indicates that the error system can converge to a predefined neighborhood of the origin within a fixed time. Finally, numerical simulations further substantiate the feasibility and superiority of the proposed methods.OPEN ACCESS Received: 02/09/2025 Accepted: 22/12/2025 Published: 16/04/2026

Abstract

This work explores a numerical approach to solving the sine-Gordon equation using the method of lines combined with cubic B-spline interpolation. The sine-Gordon equation, a nonlinear partial differential equation, arises in various fields of physics and engineering, describing phenomena such as solitons in non-linear optics and magnetic flux lines in superconductors. In our approach the method of lines is used to discretize the spatial derivatives, thereby converting the partial differential equation into a system of ordinary differential equations. These ordinary differential equations are then solved numerically using standard techniques, specifically the Runge-Kutta method of order 4. Cubic B-spline interpolation is employed to approximate the spatial derivative, ensuring efficient and precise computation of the solution. A comprehensive stability analysis reveals that our scheme requires the time step conditiont1.53 h for numerical stability. Theoretical convergence analysis demonstrates that the method achieves O(h2)spatial convergence and O( t4)temporal convergence, resulting in an overall error bound of O(h2+ t4 ). These theoretical predictions are strongly supported by numerical experiments, where empirical convergence rates closely match the theoretical values. To validate the numerical scheme, the results are compared with existing solutions. Our findings demonstrate the accuracy and computational efficiency of the proposed method, highlighting its potential as a valuable tool for studying the dynamics and behavior of systems governed by the sine-Gordon equation.OPEN ACCESS Received: 29/08/2025 Accepted: 05/11/2025 Published: 23/01/2026

Abstract

In reliability and lifetime studies, it is often impractical to observe the failure times of all units in a sample, particularly when the process is timeconsuming or expensive. Type II censoring addresses this by terminating the experiment after a predetermined number of failures from a total sample of size. The Discrete Alpha Power Extended Inverted Weibull distribution is particularly suitable for modeling such censored discrete lifetime data. Its flexible shape parameters allow it to capture a wide range of failure behaviors, including over-dispersion, which is common in censored datasets. In this context, the likelihood function and estimation procedures (maximum likelihood and Bayesian) explicitly account for the censoring, ensuring unbiased parameter estimates and reliable predictive inferences. Consequently, the Discrete Alpha Power Extended Inverted Weibull distribution provides a practical and statistically robust framework for analyzing discrete lifetimes under type II censoring.OPEN ACCESS Received: 28/07/2025 Accepted: 19/09/2025 Published: 23/01/2026

Abstract

This paper proposes a new framework for the design of functional H∞ filters tailored for nonlinear descriptor systems affected by disturbances. Earliermethods have some significant drawbacks: they rely on the restrictive assumption of system regularity, employ implicit descriptor-form filters that complicate implementation, and emphasize full-order filtering, which is often unnecessary and computationally expensive. To overcome these drawbacks, the proposed filter is developed in an explicit state-space form that allows simple implementation with arbitrary initial conditions. Moreover, its order is minimized by matching it to the dimension of the functional vector, which reduces computational complexity compared to conventional filters. A new set of sufficient conditions is presented for the existence of a functionalH∞ filter, expressed through a rank condition and a linear matrix inequality (LMI) formulation. These conditions guarantee the stability of the estimation error dynamics while ensuring that the L2 gain from disturbances to errors remains below a specified bound. A numerical example based on a simple constrained mechanical system is presented to illustrate the effectiveness of the proposed method.

Abstract

Modern high-reliability products fail rarely, so researchers rely on accelerated life testing to obtain failure information within practical time limits. This study presents a useful framework integrating constant-stress accelerated life tests with an improved adaptive progressive Type-II censoring plan to estimate the reliability function under normal operating conditions of the Hjorth model. The Hjorth model is chosen because its hazard rate can be constant, increasing, decreasing, or bathtub-shaped, which reduces errors due to incorrect hazard assumptions. Stress affects lifetime through a log-linear relationship applied to the scale and the shape parameter. We derive the full likelihood for the proposed censoring plan across several stress levels, obtain maximum likelihood estimates with confidence intervals based on the observed information matrix, and develop a Bayesian analysis with informative prior distributions and sampling by Markov chain Monte Carlo technique. We then estimate reliability at normal operating conditions together with its interval estimates by both approaches. Extensive Monte Carlo simulations demonstrate the superior accuracy of the Bayesian estimators, especially when the number of observed failures is small or censoring is heavy, while maintaining interval coverage close to the nominal level. The practical utility of the proposed methodology is demonstrated through its application to real-world accelerated lifetime data sets. Applications to real-world data sets show that the proposed model fits the data well and yields reliable estimates of reliability at normal operating conditions.OPEN ACCESS Received: 26/07/2025 Accepted: 28/10/2025 Published: 23/01/2026

Abstract

Load modelling is a crucial element of power system study that significantly affects the field’s planning, operation, and control methods. With the increasing penetration of renewable energy sources, electric vehicles, demand-side management, and distributed generation (DG), the traditional static and dynamic load model approaches are being replaced. This paper reviews extensively the existing load modelling techniques, namely, component-based load modelling, measurement-based load modelling, and hybrid methods. In addition, advancements tuned by artificial intelligence (AI) and machine learning (ML) are critically reviewed, emphasizing improving the accuracy, flexibility, and real-time adaptability of load models. For instance, Long Short-Term Memory (LSTM) networks have demonstrated significant improvements in forecasting accuracy, while Reinforcement Learning (RL) techniques enable adaptive and real-time control of load dynamics. Special focus is laid on load modelling in conditions of imbalance, dynamic parameter identification, and integration with smart grids and active distribution networks (ADNs). The review also discusses the importance of uncertainty embedded in probabilistic and data-driven models, customer behaviour, and the stochastic nature of distributed energy resources (DERs). The areas of future study emphasized AI-assisted adaptive architectures, hybrid frameworks, and digital twin applications for resilient and intelligent load modelling.OPEN ACCESS Received: 01/08/2025 Accepted: 26/09/2025 Published: 27/11/2025

Abstract

Reliability analysis is critical in various scientific fields, necessitating robust lifetime models that effectively capture real-world failure mechanisms. This work explores a novel extension of the classical ToppLeone (TL) lifespan model, called the generalized-TL (GTL) distribution, when datasets are gathered from adaptive progressive Type-II censoring. This model is highly superior for analyzing complex lifetime data with diverse hazard rate structures, including decreasing, increasing, and bathtub-shaped patterns. Employing both likelihood and Bayes estimation approaches, this work attempts to infer the unknown parameters and the reliability and failure rate functions of the GTL model. The Bayesian inference is created using the squared-error loss and independent gamma assumptions. Asymptotic and credible intervals are also established for each unknown quantity. Since the posterior density is complicated, the Markov chain using the Monte Carlo approach is utilized to get information from the whole marginal posterior densities and thus assess the acquired Bayesian point and interval estimations. Using four optimality criteria, the optimum censoring is given among competing progressive techniques. The effectiveness of the offered estimations is tested against numerous parameters using comprehensive Monte Carlo comparisons. Lastly, the practical utility of the GTL model is demonstrated through two applications using different real-world datasets collected from veterinary medicine and engineering reliability studies. Our findings state that the Bayes’ setup outperforms classical approaches, particularly in smallsample settings, making the proposed methodology flexible and beneficial in concluding the study when the researcher’s foremost concern is the total number of failed items.OPEN ACCESS Received: 29/03/2025 Accepted: 21/05/2025 Accepted: 22/09/2025