Search Results (639)

Distributed maximum correntropy Kalman filters improve robustness to non-Gaussian noise, but existing variants generally introduce consensus through average or weighted fusion without explicitly separating the innovation residual from the state-disagreement residual in a dimensionally consistent objective. This paper proposes a Distributed Maximum Correntropy Kalman Filter with Innovation and Consensus Weighting Terms (DMCKF-IW-CWT). The innovation and consensus residuals are normalized separately and mapped by Gaussian kernels, after which the resulting information matrices are incorporated into a fixed-point local update. Posterior covariance intersection (CI) is then used to fuse neighboring estimates without requiring the unavailable cross-covariances. A sufficient contraction condition is given for the fixed-point iteration. In a five-node benchmark with 500 independent Monte Carlo runs and 1000 sampling steps, the proposed method obtains overall, transient, and steady-state MAEs of 0.172210, 0.188271, and 0.168195, respectively, corresponding to reductions of 0.254%, 0.526%, and 0.178% relative to DMCKF-W; the paired 95% confidence intervals of all three differences remain below zero. The consensus RMS is further reduced by 5.371%. Additional tests involving five noise families, packet loss and communication noise, a four-state nonlinear model, and systems with up to eight states and twenty nodes confirm the numerical convergence and extensibility of the framework. Full article

This paper proposes and analyzes a modified version of the Hănțilă Method (HM) for solving electrical circuits with nonlinear inductive elements. The method replaces the nonlinear inductor with a generator comprising a nonlinear source and a linear impedance. The value of the nonlinear source is determined by defining a Picard–Banach fixed-point sequence that converges to the solution. This approach transfers the nonlinearity from the inductance to the generator’s source. The resulting circuit consists of linear and nonlinear sources and only linear components. It is solved in the harmonic domain using classical theorems and algorithms. A comparative analysis is performed on an RL circuit (a transformer primary winding at no-load). Both accuracy and computational effort are evaluated. The proposed iterative method is compared against steady-state time-domain transient analysis and frequency-domain approaches (Harmonic Balance Method) implemented in commercial software. This method is particularly suitable for analyzing circuits with nonlinear inductive components, such as iron-core coils and equivalent circuits for electrical machines. Full article

This article introduces the concept of proximal enriched contractions for nonself mappings by integrating the enrichment technique of Berinde and Păcurar with the relation-theoretic approach of Alam and Imdad. The existence of best proximity points for this notion is ensured by two distinct results. The proofs are aligned with the proximal enriched contraction condition and are based on a constructive iteration scheme that generates a sequence converging to the best proximity point of T. Furthermore, the sequence generated by the constructive iteration satisfies the Cauchy property via a nonstandard inequality between consecutive elements. These theoretical results are utilized to derive an algorithm for computing an approximate best proximity point of T. Numerical examples in ${\mathbb{R}}^3$ are presented to demonstrate the effectiveness of both the main results and the proposed algorithm. Additionally, an application section is included wherein the fixed point result derived from our best proximity point theorems is employed to establish the existence of solutions for a nonlinear fractional integral equation. Full article

Compressor surge poses a critical safety risk for aero-engines. However, conventional physics-driven detection methods—relying on single-domain features and fixed empirical thresholds—struggle to adapt across varying compressor configurations, wide operating ranges, and complex interference environments. This paper proposes a multi-feature fusion adaptive surge detection method that integrates time-domain amplitude, frequency-weighted power and slope features within a joint threshold criteria, enabling reliable and adaptive surge detection according to the statistical characteristics of the signal itself. A wavelet-based preprocessing strategy is established with the db4 wavelet and four-level decomposition identified as the optimal setting through systematic evaluation. A novel feature FWP is introduced herein, which applies frequency-dependent weighting to the power spectral density to suppress noise components while amplifying energy changes within surge-relevant bands, achieving 1.7 to 6.1 times greater magnitude variation near the surge point compared with total spectral power. The slope feature is further discovered to distinguish surge from transient interferences such as rapid valve throttling, fuel stepping and rapid acceleration. Among 100 samples, the three-feature joint detection strategy integrated with adaptive threshold criteria improves accuracy from 61% to 98%. A Bayesian optimization framework using Gaussian process surrogate models is developed for efficient cross-engine hyperparameter tuning, converging to optimal solutions within merely 11 to 13 iterations across two distinct compressors. Lastly, the method is implemented on an NI cRIO-based real-time platform and validated on two distinct ten-stage high-pressure compressors, covering surge tests across a wide speed range of 45% to 98%. Comparative tests against an industry-standard reference device demonstrate earlier warning lead times of 41 to 99 ms. The results confirm that the proposed method herein achieves high accuracy, strong robustness against operational interferences, and good cross-platform adaptability for practical application. Full article

Detector-assisted promptable segmentation can reuse box annotations, but prompt design creates an accuracy–efficiency trade-off in dense scenes. We study a training-free interface in which a detector trained with bounding-box annotations localizes stacked cartons and a frozen segmenter generates masks. Four interfaces are evaluated: Point-Single, Box, ambiguity-aware Point-Max, and Grid-Iter with sparse positive points and one mask-logit feedback pass. On a leakage-audited split, COCO mask AP, fixed-threshold Hungarian-matched metrics, paired bootstrap uncertainty, and synchronized latency were measured. On 773 test images, Box and Grid-Iter achieved mask AP values of 0.8984 and 0.8988. Their paired AP difference was 0.0007 (95% CI, $-0.0035$ to 0.0047), while matched-mIoU and F1 intervals also included zero. Box required 604.67 ms/image versus 677.33 ms/image for Grid-Iter. A YOLO26s–SAM 3 Box reference achieved a mask AP value of 0.9115 at 320.74 ms/image, whereas mask-supervised YOLOv9c-seg achieved a value of 0.9235 AP on the same cleaned split. The results indicate a metric-dependent Pareto trade-off rather than overall Grid-Iter superiority and position detector-to-segmenter prompting as a reproducible annotation–accuracy option for densely stacked cartons. Full article

In this paper, we introduce a hybrid inertial algorithm for solving variational inequality problems and split common fixed point problems in real Hilbert spaces. The proposed method combines inertial and viscosity techniques within a unified framework and extends several existing iterative schemes. Under appropriate conditions, we establish strong convergence of the generated sequence. As applications, we consider the generalized split feasibility problem and convex minimization. A numerical example arising from traffic flow modeling is presented to demonstrate the effectiveness of the proposed method. Full article

We develop a Laurent-series framework for the analytical characterization of singularities in any three-step frozen-Jacobian iterative operator parametrized by $(\lambda ,\alpha ,\beta )$ (where $\lambda$ controls the predictor step and $(\alpha ,\beta )$ are the weight-function coefficients) and apply it to the fifth-order Newton–Jarratt–Newton (NJN) method. Three principal results are established. First, any operator with a quadratic weight function ($\beta \ne 0$) possesses a pole of order $m=d(d+1)+1$ at every simple critical point of f, where d is the asymptotic polynomial degree, independently of $\lambda$ and $\alpha$; when $\beta =0$ the order reduces to $m=d+1$, recovering the classical Jarratt-class result. Second, for each fixed $\lambda$ there exists a unique parameter pair $({\alpha }^{*}\left(\lambda \right),{\beta }^{*}\left(\lambda \right))$ that minimises the Laurent residue $|a_{-1}|$ subject to fifth-order convergence; for the NJN ($\lambda =2/3$) the explicit solution ${\alpha }^{*}=\frac{1}{4}$, ${\beta }^{*}=\frac{3}{8}$ provides the first analytical justification for these design values. Third, the Laurent Validity Radius ${\rho }_L={\inf }_{z_s\in S\setminus \left\{z_c\right\}}|z_c-z_s|$ is the exact boundary of the domain in which the single-pole representation is valid; starting points satisfying $|z_0-z_c|\ll \left|\kappa \right|$ experience pole-dominated first-iterate growth $|G\left(z_0\right){|\sim |\kappa |}^m{\delta }^{-m}\to +\infty$. All results are validated on five test functions (including polynomial, transcendental, meromorphic, and non-symmetric cases) and all three, quantities can be computed from $f\left(z_c\right)$, $f^{\prime }\left(z_c\right)$, $f^{″}\left(z_c\right)$ alone. Full article

High photovoltaic (PV) penetration can reduce grid-energy imports but may worsen voltage performance in radial distribution feeders. This paper develops a unified mixed-discrete PV–BESS planning framework that jointly optimizes siting, sizing, hourly storage operation, and a common inverter voltage-support gain subject to inverter capability limits. Five metaheuristic algorithms are compared over 30 independent runs on the 33-bus system using an explicitly converged under-relaxed fixed-point iteration. Adaptive Differential Evolution achieves the lowest best and median fitness values. Its best solution reduces active-loss energy by 38.0%, grid-energy import by 14.9%, peak grid power by 12.5%, voltage deviation by 53.7%, voltage-violation duration by 100%, and annual cost by 8.4% relative to the no-PV/no-BESS case. A separately optimized comparison shows substantial additional voltage and loss improvements from inverter reactive-power support. Objective-weight, voltage-penalty, BESS energy-CAPEX, and representative-day analyses clarify key planning trade-offs. On the 69-bus feeder, the 30-run ADE validation reduces active-loss energy by 51.2%, grid-energy import by 19.5%, peak grid power by 10.5%, voltage deviation by 39.5%, voltage-violation duration by 98.8%, and annual cost by 12.2%. A supplementary analysis with a higher PV upper bound further clarifies the influence of the adopted planning limit. Full article

We introduce finite-observation conditional guarded language operators on the complete length-based ultrametric space of formal languages over a finite alphabet. A finite observation map selects a guarded branch according to the membership of prescribed test words. Although each branch is Banach-contractive, branch switching may destroy global Banach contractivity. We derive depth–residual conditions yielding a max-type Kannan inequality with an explicit constant $\alpha <1/2$. Consequently, the operator has a unique fixed language, and the Picard iteration converges from every initial language. We also construct multi-branch operators that are Kannan-contractive but not Banach contractive and obtain residual error estimates, explicit convergence bounds, finite-depth certification, and eventual stabilization of the selected branch. Full article

This paper investigates an infinite-horizon discounted stochastic maintenance optimization problem within the framework of dynamic programming. The system degradation is modeled by a discrete-time stochastic process affected by maintenance actions and random disturbances, while the objective is to minimize the expected discounted maintenance and degradation costs. The analysis is carried out on the Banach space of continuous functions equipped with the supremum norm. It is proved that the associated Bellman operator is well defined, maps the function space into itself, and is a contraction with contraction modulus equal to the discount factor. Consequently, the existence and uniqueness of the optimal value function follow from the Banach Fixed Point Theorem, and the convergence of value iteration is established. In addition, rigorous a priori and a posteriori error estimates are derived, providing theoretical stopping criteria for numerical computation. The theoretical results are complemented by numerical experiments illustrating the optimal stationary maintenance policy, the stability of the computed solution under grid refinement, and the influence of the discount factor on both the optimal policy and the convergence rate of value iteration. Full article

This paper establishes existence and uniqueness results for a generalized Ćirić–Reich–Rus interpolative contraction involving distinct forward horizons $p,q>1$ and a delay parameter $r>1$. By employing a Matkowski comparison function $\phi$ and introducing a composite condition $\Psi \left(t\right)=\phi \left(p^{\beta }{q}^{\gamma }{t}^{\alpha +\beta +\gamma }\right)<t$, we overcome the geometric expansion induced by multi-step triangle inequalities. The framework guarantees asymptotic regularity and the Cauchy property of Picard sequences, yielding a unique fixed point under mild continuity and right-continuity assumptions. We further demonstrate generalized Ulam–Hyers stability with explicit error bounds under a summability condition on the iterates of $\Psi$; apply the abstract result to fractional integral, Volterra, Hammerstein, and perturbed integral equations; and provide a sharp counterexample illustrating the necessity of the composite hypothesis. The analysis reveals how asymmetric iteration parameters optimize expansion absorption, offering a tunable framework for nonlinear discrete and integral dynamics. Full article

Electric trucks operating as mobile depots for delivery drones are promising for last-mile logistics, yet fleet electrification makes depot charging a critical issue governed by distribution-grid limits. Existing truck–drone routing formulations omit the electrical network, treating energy as exogenous, while grid-aware routing models overlook the combinatorial structure of mobile-depot drone synchronization. This paper introduces an energy-aware bi-level framework for the truck–drone routing problem that closes this gap. A distribution-grid leader solves slot-wise alternating current (AC) optimal power flow (OPF) under time-varying base loads and line deratings, returning a grid-feasible energy headroom and shadow prices. A logistics follower then co-optimizes truck routes, drone sorties, and ramp-constrained charging against this effective price, within a multi-objective cost structure. A damped fixed-point iteration couples the two levels, communicating grid scarcity through a single price signal without the logistics layer solving power-flow equations. On a Tokyo-inspired 100-customer instance with a stressed IEEE 33-bus feeder, the framework confines charging to slots with genuine headroom, reaching at most 81% loading and returning the fleet fully charged, whereas a grid-blind baseline reaches 109% loading. This comparison validates shadow pricing as an effective coordination mechanism. Full article

In the work by W. Takahashi and M. Toyoda (2003) it was introduced and studied an iterative process for solving a variational inequality problem which is induced by a inverse strongly-monotone mapping. They showed the weak convergence of the iteration process. Recently we established that most of exact iterates of the same iterative process are approximate solutions of the variational inequality. In the present work we use the dynamic string-averaging algorithm for finding a common solution of a finite family of variational inequality problems, generated by inverse strongly-monotone mappings, and a finite family of fixed point problems. We study this algorithm in the presence of summable computational errors. It is shown that the cardinality of the set of iterates which are not approximate solutions is finite and does not exceed a certain constant which is calculated. Full article

Multi-agent interaction in linear–quadratic (LQ) differential games gives rise to open-loop Nash equilibria that rarely admit closed-form expressions, motivating the development of reliable numerical solvers. Classical approaches such as shooting and spectral collocation are sensitive to the initial guess on the unknown boundary values and accumulate discretisation error over long horizons, while deep-learning alternatives require iterative gradient-based training with architecture- and convergence-specific overhead. To overcome these limitations, we recast the LQ nonzero-sum game as a linear two-point boundary value problem (TPBVP) via the Pontryagin maximum principle (PMP) and solve it with a single-layer feedforward neural network (SLFN) in which hidden-layer parameters are sampled once and fixed. The state and all player-specific costates are parameterised by random hidden features on a uniform time grid, the boundary conditions are appended as dedicated rows of the linear collocation system, and the output weights follow from a single Moore–Penrose pseudoinverse, entirely bypassing gradient-based iteration. For the scalar LQ optimal-control TPBVP, a residual-to-solution stability theorem converts the continuous equation and boundary residuals into uniform state, costate, control, and cost error bounds. Validation across two-player low- and high-dimensional benchmarks, a heterogeneous three-player game, and paired seed sweeps confirms high accuracy against analytical and matrix-exponential references, while revealing that no single activation function dominates across all problem types: tanh is most accurate in one-dimensional settings, and Gaussian RBF leads in multidimensional cases. Full article

We introduce a novel generalization of the classical Ćirić–Reich–Rus (CRR) contraction, termed the Asymmetric Cross-Iterate CRR (ACI-CRR). The contraction condition involves distinct iterate orders $p\ne q$ in an asymmetric cross-coupled form. We establish the existence and uniqueness of a fixed point under the assumption of continuity. We then analyze the symmetric case $p=q$, demonstrating that continuity is indispensable for $p>1$, and contrast this with the classical $p=q=1$ case where continuity is unnecessary. We conclude with a structural example and a conjecture regarding the necessity of continuity in higher-iterate asymmetric contractions. Full article