Search Results (519)

Humanoid robots have attracted considerable attention for their anthropomorphic structure, extended workspace, and versatile capabilities. This paper presents a novel humanoid upper-body robotic system comprising a pair of 8-degree-of-freedom (DOF) arms, a 3-DOF head, and a 3-DOF torso—yielding a 22-DOF architecture inspired by human biomechanics and implemented via standardized hollow joint modules. To overcome the critical reliance of zeroing neural network (ZNN)-based trajectory tracking on the Jacobian matrix derivative, we propose an integration-enhanced matrix derivative observer (IEMDO) that incorporates nonlinear feedback and integral correction. The observer is theoretically proven to ensure asymptotic convergence and enables accurate, real-time estimation of matrix derivatives, addressing a fundamental limitation in conventional ZNN solvers. Workspace analysis reveals that the proposed design achieves an 87.7% larger total workspace and a remarkable 3.683-fold expansion in common workspace compared to conventional dual-arm baselines. Furthermore, the observer demonstrates high estimation accuracy for high-dimensional matrices and strong robustness to noise. When integrated into the ZNN controller, the IEMDO achieves high-precision trajectory tracking in both simulation and real-world experiments. The proposed framework provides a practical and theoretically grounded approach for redundant humanoid arm control. Full article

We study the shape of the Bachelier-implied volatility of a spread option on two assets following correlated local volatility models. This includes the limiting case of spread options on two correlated Black–Scholes (BS) assets. We give an analytical result for the at-the-money (ATM) skew of the spread-implied volatility, which depends only on the components’ ATM volatilities and skews. We also compute the ATM convexity of the implied spread option for the case when the assets follow correlated BS models. The results are extracted from the short-maturity asymptotics for basket options obtained previously by Avellaneda, Boyer-Olson, Busca and Friz and, thus, become exact in the short-maturity limit. Numerical testing of the short-maturity analytical results under the Black–Scholes model and in a local volatility model show good agreement for strikes sufficiently close to the ATM point. Numerical experiments suggest that a linear approximation for the spread Bachelier volatility constructed from the ATM spread volatility and skew gives a good approximation for the spread volatility for highly correlated assets. Full article

This paper studies the convergence of distances between sequences of points and that of sequences of points in metric spaces. This investigation is focused on the iterative processes built with composed self-mappings of a cyclic contraction, which can involve more than two nonempty closed subsets in a metric space, which are combined with compositions of a strict contraction with itself, which operates in each of the individual subsets, in any order and any number of mutual compositions. It is admitted, in the most general case, the involvement of any number of repeated compositions of both self-maps with themselves. It is basically seen that, if one of the best-proximity points in the cyclic disposal is unique in a boundedly compact subset of the metric space is sufficient to achieve unique asymptotic cycles formed by a best-proximity point per each adjacent subset. The same property is achievable if such a subset is strictly convex and the metric space is a uniformly convex Banach space. Furthermore, all the sequences with arbitrary initial points in the union of all the subsets of the cyclic disposal converge to such a limit cycle. Full article

This paper addresses the design of nonfragile state estimators for memristor-based fractional-order neural networks that are subject to stochastic cyber-attacks and hybrid time delays. To mitigate the issue of limited bandwidth during signal transmission, quantitative processing is introduced to reduce network burden and prevent signal blocking. In real network environments, the outputs may be compromised by cyber-attacks, which can disrupt data transmission systems. To better reflect the actual conditions of fractional-order neural networks, a Bernoulli variable is utilized to describe the statistical properties. Additionally, novel conditions are presented to ensure the stochastic asymptotic stability of the augmented error system through a new fractional-order free-matrix-based integral inequality. Finally, the effectiveness of the proposed estimation methods is demonstrated through two numerical simulations. Full article

Altitude test facilities for aero-engines employ multi-chamber, multi-valve intake systems that require effective decoupling and strong disturbance rejection during transient tests. This paper proposes a coordinated active disturbance rejection control (ADRC) scheme based on external penalty functions. The chamber pressure safety limit is formulated as an inequality-constrained optimization problem, and an exponential penalty together with a gradient based algorithm is designed for dynamic constraint relaxation, with guaranteed global convergence. A coordination term is then integrated into a distributed ADRC framework to yield a multi-valve coordinated ADRC controller, whose asymptotic stability is established via Lyapunov theory. Hardware-in-the-loop simulations using MATLAB/Simulink and a PLC demonstrate that, under ±3 kPa pressure constraints, the maximum engine inlet pressure error is 1.782 kPa (77.1% lower than PID control), and under an 80 kg/s² flow-rate disturbance, valve oscillations decrease from ±27% to ±5%. These results confirm the superior disturbance rejection and decoupling performance of the proposed method. Full article

A two-dimensional time-dependent model is presented for upward-propagating internal gravity waves generated by an imposed thermal forcing in a layer of fluid with uniform background velocity and stable stratification under the anelastic approximation. The configuration studied is representative of a situation with deep or shallow latent heating in the lower atmosphere where the amplitude of the waves is small enough to allow linearization of the model equations. Approximate asymptotic time-dependent solutions, valid for late time, are obtained for the linearized equations in the form of an infinite series of terms involving Bessel functions. The asymptotic solution approaches a steady-amplitude state in the limit of infinite time. A weakly nonlinear analysis gives a description of the temporal evolution of the zonal mean flow velocity and temperature resulting from nonlinear interaction with the waves. The linear solutions show that there is a vertical variation of the wave amplitude which depends on the relative depth of the heating to the scale height of the atmosphere. This means that, from a weakly nonlinear perspective, there is a non-zero divergence of vertical momentum flux, and hence, a non-zero drag force, even in the absence of vertical shear in the background flow. Full article

The stability of a class of quaternion-valued switching neural networks (QVSNNs) with time-varying delays is investigated in this paper. Limited prior research exists on the stability analysis of quaternion-valued neural networks (QVNNs). This paper addresses the stability analysis of quaternion-valued neural networks (QVNNs). With the help of some symmetric matrices with excellent properties, the stability analysis method in this paper is undecomposed. The QVSNN discussed herein evolves with average dwell time. Based on the Lyapunov theoretical framework and Wirtinger-based inequality, QVSNNs under any switching law have global asymptotic stability (GAS) and global exponential stability (GES). The state decay estimation of the system is also given and proved. Finally, the effective and practical applicability of the proposed method is demonstrated by two comprehensive numerical calculations. Full article

In this paper, we study the beamforming design for multiple-input multiple-output (MIMO) ISAC systems, with the weighted mutual information (MI) comprising sensing and communication perspectives adopted as the performance metric. In particular, the weighted sum of the communication mutual information and the sensing mutual information is shown to asymptotically converge to a deterministic limit when the number of transmitting and receiving antennas grow to infinity. This deterministic limit is derived by utilizing the operator-valued free probability theory. Subsequently, an efficient projected gradient ascent (PGA) algorithm is proposed to optimize the transmit beamforming matrix with the aim of maximizing the weighted asymptotic MI. Numerical results validate that the derived closed-form expression matches well with the Monte Carlo simulation results and the proposed optimization algorithm is able to improve the weighted asymptotic MI significantly. We also illustrate the trade-off between asymptotic sensing and asymptotic communication MI. Full article

Conventional integer-order models fail to adequately capture non-local memory effects and constrained nonlinear interactions in emotional dynamics. To address these limitations, we propose a coupled framework that integrates Caputo fractional derivatives with hyperbolic tangent–based interaction functions. The fractional-order term quantifies power-law memory decay in affective states, while the nonlinear component regulates connection strength through emotional difference thresholds. Mathematical analysis establishes the existence and uniqueness of solutions with continuous dependence on initial conditions and proves the local asymptotic stability of network equilibria ($W_{ij}^{*}={\displaystyle \frac{1}{\delta }}{\sec \mathrm{h}}^2(\parallel {\mathrm{E}}_i-{\mathrm{E}}_j\parallel )$, e.g., $W^{*}\approx 1.40$ under typical parameters $\eta =0.5$, $\delta =0.3$). We further derive closed-form expressions for the steady-state variance under stochastic perturbations ($\mathrm{Var}\left(W_{ij}\right)={\displaystyle \frac{{\sigma }_{\zeta }^2}{2\eta \delta }}$) and demonstrate a less than 6% deviation between simulated and theoretical values when ${\sigma }_{\zeta }=0.1$. Numerical experiments using the Euler–Maruyama method validate the convergence of connection weights toward the predicted equilibrium, reveal Gaussian features in the stationary distributions, and confirm power-law scaling between noise intensity and variance. The numerical accuracy of the fractional system is further verified through L1 discretization, with observed error convergence consistent with theoretical expectations for $\mu =0.5$. This framework advances the mechanistic understanding of co-evolutionary dynamics in emotion-modulated social networks, supporting applications in clinical intervention design, collective sentiment modeling, and psychophysiological coupling research. Full article

In this paper, we focus on mean-field stochastic differential equations driven by G-Brownian motion (G-MFSDEs for short) with a drift coefficient satisfying the local one-sided Lipschitz condition with respect to the state variable and the global Lipschitz condition with respect to the law. We are concerned with the well-posedness and the numerical approximation of the G-MFSDE. Probability uncertainty leads the resulting expectation usually to be the G-expectation, which means that we cannot apply the numerical approximation for McKean–Vlasov equations to G-MFSDEs directly. To numerically approximate the G-MFSDE, with the help of G-expectation theory, we use the sample average value to represent the law and establish the interacting particle system whose mean square limit is the G-MFSDE. After this, we introduce the modified stochastic theta method to approximate the interacting particle system and study its strong convergence and asymptotic mean square stability. Finally, we present an example to verify our theoretical results. Full article

Metaconcrete (MC) is a class of engineered cementitious composites that integrates locally resonant inclusions to filter stress waves. While the dynamic benefits are well established, the effect of resonator content and geometry on static compressive resistance remains unclear. This study develops the first two-dimensional mesoscale finite-element model that explicitly represents steel cores, rubber coatings, and interfacial transition zones to predict the quasi-static behavior of MC. The model is validated against benchmark experiments, reproducing the 56% loss of compressive strength recorded for a 10.6% resonator volume fraction with an error of less than 1%. A parametric analysis covering resonator ratios from 1.5% to 31.8%, diameters from 16.8 mm to 37.4 mm, and coating thicknesses from 1.0 mm to 4.2 mm shows that (i) strength decays exponentially with volumetric content, approaching an asymptote at ≈20% of plain concrete strength; (ii) larger cores with thinner coatings minimize stiffness loss (<10%) while limiting strength reduction to 15–20%; and (iii) material properties of the resonator have a secondary influence (<6%). Two closed-form expressions for estimating MC strength and Young’s modulus (R² = 0.83 and 0.94, respectively) are proposed to assist with the preliminary design. The model and correlations lay the groundwork for optimizing MC that balances vibration mitigation with structural capacity. Full article

Hydraulically driven flexible robotic arms (HDFRAs) play an indispensable role in industrial precision operations such as aerospace assembly and nuclear waste handling, owing to their high power density and adaptability to complex environments. However, inherent mechanical flexibility-induced vibrations, hydraulic nonlinear dynamics, and electromechanical coupling effects lead to multi-timescale control challenges, severely limiting high-precision trajectory tracking performance. The present study introduces a novel hierarchical control framework employing dual-timescale perturbation analysis, which effectively addresses the constraints inherent in conventional single-timescale control approaches. First, the system is decoupled into three subsystems via dual perturbation parameters: a second-order rigid-body motion subsystem (SRS), a second-order flexible vibration subsystem (SFS), and a first-order hydraulic dynamic subsystem (FHS). For SRS/SFS, an adaptive fast terminal sliding mode active disturbance rejection controller (AFTSM-ADRC) is designed, featuring a dual-bandwidth extended state observer (BESO) to estimate parameter perturbations and unmodeled dynamics in real time. A novel reaching law with power-rate hybrid characteristics is developed to suppress sliding mode chattering while ensuring rapid convergence. For FHS, a sliding mode observer-integrated sliding mode coordinated controller (SMO-ISMCC) is proposed, achieving high-precision suppression of hydraulic pressure fluctuations through feedforward compensation of disturbance estimation and feedback integration of tracking errors. The globally asymptotically stable property of the composite system has been formally verified through systematic Lyapunov-based analysis. Through comprehensive simulations, the developed methodology demonstrates significant improvements over conventional ADRC and PID controllers, including (1) joint tracking precision reaching ${10}^{-4}$ rad level under nominal conditions and (2) over 40% attenuation of current oscillations when subjected to stochastic disturbances. These results validate its superiority in dynamic decoupling and strong disturbance rejection. Full article

High-frequency surface wave radar (HFSWR) is unable to measure the target’s altitude information due to its limited antenna aperture in the elevation dimension. This paper focuses on the 3-D localization problem for moving targets within the line of sight (LOS) in multistatic HFSWR. For this purpose, the 1-D space angle (SA) measurement is introduced into multistatic HFSWR to perform 3-D joint localization together with bistatic range (BR) and bistatic range rate (BRR) measurements. The target’s velocity can also be estimated due to the inclusion of BRR. In multistatic HFSWR, commonly used azimuth measurements offer no information about the target’s altitude. Since SA is associated with the target’s 3-D coordinates, combining SA measurements from multiple receivers can effectively enhance localization accuracy, particularly in altitude estimation. In this paper, we develop a two-stage localization algorithm that first derives a weighted least-squares (WLS) coarse estimate and then performs an algebraic error reduction (ER) procedure to enhance accuracy. Both stages yield closed-form results, thus ensuring overall computational efficiency. Theoretical analysis shows that the proposed WLS-ER algorithm can asymptotically attain the Cramér–Rao lower bound (CRLB) as the measurement noise decreases. Simulation results demonstrate the effectiveness of the proposed WLS-ER algorithm and highlight the contribution of SA measurements to altitude estimation in multistatic HFSWR. Full article

The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding the flexible MEF margin in the FGM and AMH copulas. The resulting distributions accommodate a wide range of positive or negative dependence while retaining analytical traceability. Closed-form expressions for the joint and marginal density, survival, hazard, and reliability functions are derived, together with product moments and moment-generating functions. Unknown parameters are estimated through the maximum likelihood estimation (MLE) and inference functions for margins (IFM) methods, with asymptotic confidence intervals provided for these parameters. An extensive Monte Carlo simulation quantifies the bias, mean squared error, and interval coverage, indicating that IFM retains efficiency while reducing computational complexity for moderate sample sizes. The models are validated using two real datasets, from the medical sector regarding the infection recurrence times of 30 kidney patients undergoing peritoneal dialysis, and from the economic sector regarding the growth of the gross domestic product (GDP). Overall, the proposed copula-linked MFE distributions provide a powerful and economical framework for survival analysis, reliability, and economic studies. Full article

Recent observations suggest that General Relativity (GR) faces challenges in fully explaining phenomena in regimes of strong gravitational fields. A promising alternative is the $f\left(R\right)$ theory of gravity, where R denotes the Ricci scalar. This modified theory aims to address the limitations observed in standard GR. In this study, we derive a black hole (BH) solution without introducing nonlinear electromagnetic fields or imposing specific constraints on R or the functional form of $f\left(R\right)$ gravity. The BH solution obtained here is different from the classical Schwarzschild solution in GR and, under certain conditions, reduces to the Schwarzschild (A)dS solution. This BH is characterized by the gravitational mass of the system and an additional parameter, which distinguishes it from GR BHs, particularly in the asymptotic regime. We show that the curvature invariants of this solution remain well defined at both small and large values of r. Furthermore, we analyze their thermodynamic properties, demonstrating consistency with established principles such as Hawking radiation, entropy, and quasi-local energy. This analysis supports their viability as alternative models to classical GR BHs. Full article