Partial shading fragments the power-voltage characteristic of series-connected photovoltaic (PV) arrays into multiple local peaks, rendering conventional trackers ineffective and exposing the reliance of metaheuristic global maximum power point tracking (GMPPT) methods on random initialization and empirical tuning coefficients. This paper proposes TSB-GMPPT, a deterministic tanh-surrogate branch-and-bound GMPPT algorithm that eliminates both dependencies. A control-oriented hyperbolic-tangent surrogate of the PV I-V characteristic admits a non-iterative Lambert W asymptotic approximation for the maximum power point voltage. During discovery, a single saturation-region measurement per candidate is sufficient to construct a calibrated optimistic bound, safely pruning the search space before final peak localization. An offline polynomial calibration recovers the remaining parameters from short-circuit current. During discovery, an optimistic branch-and-bound rule maintains an upper power bound for each unconfirmed layer and permanently discards candidates that cannot exceed the incumbent confirmed power, contracting the admissible search space without exhaustive probing. A five-state finite-state machine governs initialization, shading-topology detection, discovery, winner refitting, convergence, and adaptive reinitialization. Experimental validation using a Chroma 62150H solar array simulator and a dSPACE DS1104 platform on five-module benchmark cases and additional eight-module complex multi-peak shading cases demonstrates average tracking efficiencies of 99.94% under partial shading and 99.98% under uniform irradiance, with corresponding average convergence times of 0.25 s and 0.21 s, respectively, for the five-module test set. Further validation under eight-module complex multi-peak shading cases and dynamic irradiance transitions confirms rapid re-tracking, accurate GMPP identification, and robust operation under realistic operating conditions.
This study investigates quasi-consensus in fractional-order multi-agent systems (FOMASs) with three time-varying delays, unknown nonlinear dynamics, bounded disturbances, and intermittent Denial-of-Service (DoS) attacks. A dual-channel adaptive Radial Basis Function Neural Network (RBFNN) is developed to estimate unknown nonlinearities online. An adaptive impulsive pinning strategy dynamically selects agents according to their consensus errors, concentrating control effort on agents with larger deviations. A Lyapunov-Razumikhin-based framework is established to derive sufficient conditions for quasi-consensus under delayed and attacked communication. A DoS-aware impulsive contraction factor is introduced to capture the effects of adaptive pinning and attack frequency-duration characteristics. An explicit quasi-consensus error bound is derived to quantify the effects of disturbances, neural approximation errors, fractional-order dynamics, and impulsive intervals. Numerical results demonstrate accurate leader-following tracking, rapid convergence, and strong resilience against intermittent DoS attacks, confirming the effectiveness of the proposed approach for secure coordination of uncertain FOMASs.
This study presents a novel Machine Learning (ML) approach for predicting the central and minimum film thickness in isothermal elastohydrodynamically lubricated (EHL) smooth line contacts under non-Newtonian conditions. A modular, generalized ML approach based on the similarity analysis is proposed and compared with a direct one. The Moes dimensionless parameters and pressure-viscosity adaptation are employed to account for different operating conditions, solid body, and lubricant properties, incorporating non-Newtonian effects and correction for compressibility. Both ML approaches are trained using a database generated by solving the coupled generalized Reynolds, linear elasticity, load balance, and shear stress equations for EHL line contacts using a Finite Element Method (FEM)-based numerical model. The database comprises 1055 data points for Newtonian conditions and 1004 data points for non-Newtonian conditions. The widely used ML regression algorithms are implemented comprehensively for both approaches. Prediction accuracy and robustness are then analyzed in detail for the best-performing ML model configurations. The modular approach achieves a slightly lower predictive accuracy, but enhanced robustness, compared to the direct approach. Moreover, it offers greater flexibility in terms of decoupling physical effects and reducing dataset requirements and provides good generalization capability. This could potentially extend the proposed modular approach to thermal EHL, and incorporate other non-conventional configurations (e.g., surface coatings and mixed lubrication).
The KdV is one of the most widespread nonlinear models, commonly used by coastal engineers, to describe wave propagation in weakly nonlinear and weakly dispersive shallow water problems. In this paper, we investigate the solutions of the extended KdV equation, previously formally derived for both the velocity and the free-surface elevation, by analyzing its consistency with the extended Boussinesq equations. Combined with a stability result, this leads to a convergence result. This analysis enables us to derive new linear asymptotic models based on this equation. We then explicitly solve these new linear models and illustrate the residual behavior of the resulting approximate solutions through numerical computations for representative initial data. Finally, we analyze solitary-wave solutions of the extended KdV model and quantify its improved accuracy.
Parallel to the main results of C. Nour, R. J. Stern and J. Takche in " Proximal smoothness and the exterior sphere condition" [J. Convex Analysis 16/2 (2009) 501–514] and of C. Nour and J. Takche in "A new class of sets regularity" [J. Convex Analysis 25/4 (2018) 1059–1074], which explore the equivalence between prox-regularity, the exterior sphere condition, and S-convexity, we present novel characterizations of the r-strong convexity property, namely, of the sets that can be expressed as the intersection of closed balls with the same radius r > 0
