Search Results (128)

Minimizing the impacts of coupling, randomness, time variation and uncertain nonlinearity to enhance real-time performance is critical for controlling complex industrial systems. This paper proposes an optimized adaptive filtering method (LAF-MTNF) for time-varying uncertain nonlinear systems with multiple-input multiple-output (MIMO) measurement noise, which integrates the multi-dimensional Taylor network (MTN) with Lyapunov stability theory (LST). Leveraging MTN’s inherent advantages—simple structure, linear parameterization, and low computational complexity—LAF-MTNF achieves efficient real-time filtering while avoiding the exponential computation burden of neural networks. The contributions of this work are threefold: (1) A novel integration of LST and MTN is proposed for MIMO filtering, in which an energy space is constructed with a unique global minimum to eliminate local optimization traps, addressing the stability deficit of traditional MTN filters using LMS/RLS algorithms. (2) Convergence performance is systematically quantified by deriving explicit expressions for the error convergence rate (regulated by a positive constant) and convergence region (a sphere centered at the origin) while modifying adaptive gain to avoid singularity, filling the gap of incomplete performance analysis in existing Lyapunov-based filters. (3) The design is disturbance-independent, relying only on input/output measurements and requiring no prior knowledge of noise statistics, thus enhancing robustness to unknown industrial disturbances. We systematically analyze the Lyapunov stability of LAF-MTNF, and simulations on a complex MIMO system verify that it outperforms existing methods in filtering precision (mean error 0.0227 vs. 0.0674 of RBFNN) and dynamic response speed, while ensuring asymptotic stability and real-time applicability. The proposed LAF-MTNF method achieves significant advantages over traditional adaptive filtering methods in filtering accuracy, convergence speed and anti-cross-coupling capability. This method has broad application prospects in high-precision industrial servo motion control, power system state monitoring and other multi-variable nonlinear industrial scenarios with complex noise environments. Full article

In this paper, we propose a novel method which utilizes samples of measured product quality characteristics to efficiently estimate the probabilities of those quality characteristics being within the desired specifications and, consequently, the process yield. Specifically, when dealing with 1D Gaussian distributions, we formally prove that the proposed yield estimator asymptotically gives a lower Mean Squared Error compared to the best unbiased estimator. In order to enable maximization of yield, this novel estimator is incorporated into the framework of Bayesian Optimization which iteratively seeks controllable tool parameters under which the outgoing product yield is maximized. The newly proposed yield maximization method is demonstrated in an application involving high-fidelity simulations of a reactive ion etch chamber, a tool component commonly used in semiconductor manufacturing. The aim of these simulations was to rapidly and reliably determine tool parameters that maximize the probability of delivering desired plasma density characteristics under stochastic variations in chamber conditions. The novel yield estimation and optimization methods show superiority when the number of experimental observations is limited and the distributions of outgoing product characteristics can be approximated well by a Gaussian distribution. Full article

High-precision trajectory tracking of robotic manipulators is fundamentally challenged by strong nonlinear dynamics, unmodeled uncertainties, and external disturbances. This paper proposes a Reciprocal Neural State–Disturbance Observer (RNSDO) featuring a neural activation mechanism for adaptive gain modulation and a reciprocally coupled state–disturbance estimation architecture. By reshaping the observer error dynamics through mutual feedback between state and disturbance estimation, the proposed structure alleviates the conflict between fast transient disturbance reconstruction and steady-state noise suppression, while requiring only position measurements. A decentralized position controller is designed based on RNSDO. The global asymptotic stability of the resulting closed-loop system is rigorously established via Lyapunov analysis. Extensive simulations on a PUMA 560 and experiments on a 7-DOF Franka FR3 robotic manipulator demonstrate highly consistent performance trends. The proposed method achieves improved state and disturbance estimation accuracy and enhanced robustness against unmodeled dynamics and payload variations compared with a linear Improved Extended State Observer (IESO), a classical Nonlinear Extended State Observer (NLESO), and a model-based Nonlinear Disturbance Observer-based Adaptive Robust Controller (NDO-ARC). Furthermore, the algorithm exhibits excellent real-time feasibility with a minimal computational footprint. Full article

Subspace algorithms like canonical variate analysis (CVA) are regression-based methods for the estimation of linear dynamic state space models. They have been shown to deliver accurate (consistent and asymptotically equivalent to quasi-maximum likelihood estimation using the Gaussian likelihood) estimators for stably invertible stationary autoregressive moving average (ARMA) processes. These results use the assumption that there are no zeros of the spectral density on the unit circle corresponding to the state space system. In this technical study, we consider vector processes made stationary by applying differencing to all variables, ignoring potential co-integrating relations. This leads to spectral zeros violating the above mentioned assumptions. We show consistency for the CVA estimators, closing a gap in the literature. However, a simulation exercise shows that over-differencing (while leading to consistent estimation of the transfer function) also complicates inference for CVA estimators, not just maximum likelihood-based estimators. This is also demonstrated in a real-world data example. The result also applies to seasonal differencing. The present paper hence suggests working with original data, not working in differences. Full article

In the special case of a heavy-tailed sequence environment, change point monitoring in wireless sensor networks faces many serious challenges, such as high communication overhead, particularly sensitivity to sparse changes, and dependence on strict parameter assumptions. In order to solve these limitations, a distributed robust M-estimator-based change point monitoring (DRM-CPM) method is proposed. This method combines ratio statistics with sliding window technology so that in online detection, there is no need to know the distribution before and after changes in advance. A threshold-triggered communication strategy is introduced, where sensors exchange local statistics only when exceeding predefined thresholds, significantly reducing energy consumption. By means of theoretical analysis, the asymptotic characteristics of the statistics are confirmed, and the robustness of the algorithm to heavy-tail noise and unknown parameters is also proved. Simulation results show that the algorithm is better than the existing methods in terms of empirical size control, empirical power, and communication efficiency, particularly in the face of sparse variation or heavy-tailed data. This framework provides a scalable solution for real-time anomaly monitoring with non-Gaussian data characteristics in industrial and environmental applications. Full article

Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, or semiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affine fractals, and feature scaling with universal exponents (depending on the substrate’s dimensionality d and global topology, as well as on the driving randomness’ spatial and temporal correlations but not on the underlying mechanisms). Adding lateral growth as an essential (non-equilibrium) ingredient to the known equilibrium ones (randomness and interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding (via the dynamic renormalization group) the correct exponents for flat $d=1$ substrates and (spatially and temporally) uncorrelated randomness. It is this interplay which gives rise to the unique, non-Gaussian scaling properties characteristic of the specific, universal type of non-equilibrium roughening. Later on, the asymptotic statistics of process $h\left(x\right)$ fluctuations in the scaling regime was also analytically found for $d=1$ substrates. For $d>1$ substrates, however, one has to rely on numerical simulations. Here we review a variational approach that allows for analytical progress regardless of substrate dimensionality. After reviewing our previous numerical results in $d=1$, 2, and 3 on the time evolution of one of the functionals—which we call the non-equilibrium potential (NEP)—as well as its scaling behavior with the nonlinearity parameter $\lambda$, we discuss the stochastic thermodynamics of the roughening process and the memory of process $h\left(x\right)$ in KPZ and in the related Golubović–Bruinsma (GB) model, providing numerical evidence for the significant dependence on initial conditions of the NEP’s asymptotic behavior in both models. Finally, we highlight some open questions. Full article

Based on existing models, this paper incorporates some key ecological factors, thereby obtaining a class of eco-epidemiological models that can more objectively reflect natural phenomena. This model simultaneously integrates disease dynamics within the prey population and the Beddington–DeAngelis functional response, thus achieving an organic combination of ecological dynamics, epidemic transmission, and spatial movement under time-varying environmental conditions. The proposed framework significantly enhances ecological realism by simultaneously accounting for spatial dispersal, predator–prey interactions, disease transmission within prey species, and seasonal or temporal variations, providing a comprehensive mathematical tool for analyzing complex eco-epidemiological systems. The theoretical results obtained from this study can be summarized as follows: Firstly, the existence and uniqueness of globally positive solutions for any positive initial data are rigorously established, ensuring the well-posedness and biological feasibility of the model over extended temporal scales. Secondly, analytically tractable sufficient conditions for uniform population persistence are derived, which elucidate the mechanisms of species coexistence and biodiversity preservation even under sustained epidemiological pressure. Thirdly, by employing innovative applications of differential inequalities and fixed point theory, the existence and uniqueness of a positive spatially homogeneous periodic solution in the presence of time-periodic coefficients are conclusively demonstrated, capturing essential rhythmicities inherent in natural systems. Fourthly, through a sophisticated combination of the upper and lower solution method for parabolic partial differential equations and Lyapunov stability theory, the global asymptotic stability of this periodic solution is rigorously established, offering a powerful analytical guarantee for long-term predictive modeling. Beyond theoretical contributions, these research findings provide actionable insights and quantitative analytical tools to tackle pressing ecological and public health challenges. They facilitate the prediction of thresholds for maintaining ecosystem stability using real-world data, enable the analysis and assessment of disease persistence in spatially structured environments, and offer robust theoretical support for the planning and design of wildlife management and conservation strategies. The derived criteria support evidence-based decision-making in areas such as controlling zoonotic disease outbreaks, maintaining ecosystem stability, and mitigating anthropogenic impacts on ecological communities. A representative numerical case study has been integrated into the analysis to verify all of the theoretical findings. In doing so, it effectively highlights the model’s substantial theoretical value in informing policy-making and advancing sustainable ecosystem management practices. Full article

Accurate suction control underpins thermo-hydro-mechanical (THM) characterization of unsaturated soils, yet conventional polyethylene-glycol (PEG) osmotic methods suffer from membrane degradation, polymer intrusion, and marked temperature sensitivity. This study evaluates a potassium-neutralized poly (acrylamide-co-acrylic acid) hydrogel (PP) as a high-suction osmotic medium for water-retention testing of compacted kaolin using a sealed cell with a grade-42 filter paper separator (no semi-permeable membrane). The water-activity–suction relation of PP was calibrated with a chilled-mirror hygrometer (WP4C) over the high-suction domain, and temperature effects were assessed between 20–30 °C. The PP imposed stable target suctions across the practical engineering range, with cross-validation to WP4C of R² ≈ 0.985 and RMSE ≈ 0.09 MPa, and exhibited modest thermal sensitivity (~2–3% per 10 °C). Mass–time records showed a two-regime equilibration (rapid first-day moisture loss then slowing to asymptote), with time to 95% equilibrium t₉₅ ≈ 3–7 days depending on suction, and equilibrium within ~2 weeks under a normalized mass change, ${\displaystyle \frac{1}{m}}\left|{\displaystyle \frac{∆m}{∆t}}\right|<{\displaystyle \frac{0.1\%}{24h}}$ criterion. The resulting kaolin water-retention curves are smooth soil moisture factor (SMF) reproducible, and exhibited minor wetting–drying hysteresis (~20–25% gap at matched suctions). Collectively, the results indicate that PP provides a practical, membrane-free (in the semi-permeable sense) and accurate means to control high-range suction for unsaturated soil testing, showing only modest suction variations within the tested 20–30 °C range, while mitigating long-standing PEG limitations and simplifying laboratory workflows. Full article

In this paper, we investigate the optimal control problem regarding a class of dynamic systems, aiming to address the challenge of simultaneously ensuring cost minimization and system asymptotic stability. The theoretical framework proposed in this paper integrates the value function concept from optimal control theory with Lyapunov stability theory. By setting the impulse cost at any finite time to be strictly positive, we exclude Zeno behavior, and a set of sufficient conditions is established that simultaneously guarantees system asymptotic stability and cost minimization based on Quasi-Variational Inequalities (QVIs). To address the challenge of solving the Hamilton–Jacobi–Bellman (HJB) equation in high-dimensional nonlinear systems, we employ an inverse optimal control framework to synthesize the strategy and its corresponding cost function. Finally, we validate the feasibility of our method by applying the theoretical results obtained to three numerical examples. Full article

In this work, we propose and study an inertial hybrid projection algorithm to approximate a common solution of a system of unrelated generalized mixed variational-like inequalities and the common fixed points of Bregman asymptotically quasi-nonexpansive mappings in the intermediate sense. We establish a strong convergence theorem for the generated sequence and derive several corollaries. Further, we provide applications of Bregman asymptotically quasi-nonexpansive mappings in the intermediate sense. Numerical examples are provided to demonstrate the effectiveness of the method, and we also present a comparative analysis. Full article

This paper presents a robust and reliable voltage regulation method in DC–DC converters, for which a multiloop control strategy is developed and analyzed for a boost converter. The proposed control scheme consists of an inner current loop and an outer voltage loop, both systematically designed using the control Lyapunov function (CLF) methodology. The main contributions of this work are (1) the formulation of a control structure capable of maintaining performance under variations in load, reference voltage, and input voltage; (2) the theoretical demonstration of global asymptotic stability of the closed-loop system in the Lyapunov sense; and (3) the experimental validation of the proposed controller on a physical DC–DC boost converter, confirming its effectiveness. The results support the advancement of high-efficiency nonlinear control methods for power electronics applications. Furthermore, the experimental findings reinforce the practical relevance and real-world applicability of the proposed approach. Full article

The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov–Mitropolsky). Using this methods, differential equations were obtained in a standard form, determining the law of variation in amplitude and frequency as functions of kinematic, force, and physico-mechanical parameters in both resonant and non-resonant regimes. The fourth-order Runge–Kutta method was applied for the oscillatory system numerical analysis. The computation of complex mathematical expressions and graphical representation of the results were implemented in the mathematical software Maple 15. The results obtained can be applied for engineering calculations of structures containing moving beams subjected to compressive or tensile forces. Full article

This paper theoretically and numerically investigates temperature-dependent band structures in elastic metamaterial lattices using a plane wave expansion method incorporating thermal effects. We first analyze a one-dimensional (1D) elastic metamaterials beam, demonstrating that band frequencies decrease with rising temperature and increase with cooling. Then, the method is extended to square and rectangular 2D lattices, where temperature variations show remarkable influence on individual bands; while all bands shift to higher frequencies monotonically with cooling, their rates of change diminish asymptotically as they approach characteristic limiting values. Band structure predictions are validated against frequency response simulations of finite-structure. We further characterize temperature dependence of bands and bandgap widths, and quantify thermal sensitivity for the first four bands. These findings establish passive, robust thermal tuning strategies for ultralow frequency vibration suppression, offering new design routes for space-deployed lattice structures. Full article

This study develops a tractable, closed-form expression for the asymptotic variance of the coefficient of variation (CV) estimator under a reparameterized Birnbaum–Saunders (BirSau) distribution. Using the method of moments, we derive analytical formulas for the mean, variance, and coefficient of variation of $X\sim \mathrm{BirSau}(\mu ,\lambda )$ and construct a plug-in estimator for the CV. By applying the delta method within this new nonlinear parametrization, we obtain an explicit and compact expression for the asymptotic variance of the CV estimator, thereby extending general asymptotic theory to a distribution-specific setting where higher-order moments lack closed forms under the classical parametrization. Extensive Monte Carlo simulations are conducted to examine the estimator’s finite-sample performance under various parameter configurations and sample sizes. The results demonstrate that the estimator exhibits decreasing bias and variance as the sample size increases, with strong convergence to its theoretical asymptotic behavior. A real-data application using rainfall measurements from northeastern Thailand further illustrates the practical utility of the proposed approach in quantifying relative variability across regions. These findings provide a concise analytical foundation for the coefficient of variation under the Birnbaum–Saunders framework, enhancing its theoretical development and facilitating practical implementation in environmental and reliability analyses. Full article

This study introduces a novel control strategy aimed at achieving projective synchronization in incommensurate fractional-order chaotic systems (IFOCS). The approach integrates the mathematical framework of fractional calculus with the recursive structure of the backstepping control technique. A key feature of the proposed method is the systematic use of the Mittag–Leffler function to verify stability at every step of the control design. By carefully constructing the error dynamics and proving their asymptotic convergence, the method guarantees the overall stability of the coupled system. In particular, stabilization of the error signals around the origin ensures perfect projective synchronization between the master and slave systems, even when these systems exhibit fundamentally different fractional-order chaotic behaviors. To illustrate the applicability of the method, the proposed fractional order backstepping control (FOBC) is implemented for the synchronization of two representative systems: the fractional-order Van der Pol oscillator and the fractional-order Rayleigh oscillator. These examples were deliberately chosen due to their structural differences, highlighting the robustness and versatility of the proposed approach. Extensive simulations are carried out under diverse initial conditions, confirming that the synchronization errors converge rapidly and remain stable in the presence of parameter variations and external disturbances. The results clearly demonstrate that the proposed FOBC strategy not only ensures precise synchronization but also provides resilience against uncertainties that typically challenge nonlinear chaotic systems. Overall, the work validates the effectiveness of FOBC as a powerful tool for managing complex dynamical behaviors in chaotic systems, opening the way for broader applications in engineering and science. Full article