Applied Mathematics and Computation最新文献

英文中文

Adaptive fuzzy neural network-based smooth-switching gain dynamic surface control for constrained manipulator with error-based nonlinear disturbance observer 误差非线性扰动观测器约束机械臂的自适应模糊神经网络平滑切换增益动态面控制

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-04 DOI: 10.1016/j.amc.2025.129743

Qing Yang , Haisheng Yu , Xiangxiang Meng , Wenqian Yu

This paper studies an adaptive fuzzy neural network-based smooth-switching gain dynamic surface control with an error-based nonlinear disturbance observer for the manipulator subject to the full-state constraints and input saturation. First, the smooth-switching gain strategy is proposed to replace the conventional static control gain. This novel strategy can dynamically update the control gains according to the tracking error and its derivative, thereby optimizing tracking performance across different response phases. Second, considering that the conventional nonlinear disturbance observer generates harmful observation peaks when there is a large tracking error, an error-based nonlinear disturbance observer is designed. This observer adaptively adjust the observer gain based on the tracking error, effectively mitigating harmful observation peaks. Furthermore, the adaptive fuzzy neural network strategy is introduced to approximate the modeling uncertainties. Finally, an auxiliary system and an asymmetric time-varying barrier Lyapunov function are established to handle the input saturation and the asymmetric time-varying full-state constraints, respectively. The comparative experiment of a two-degree-of-freedom manipulator validate that the proposed strategy can effectively constrain the state and input of the system within predefined limits. The experimental results further validate that the proposed strategy can effectively optimise the tracking performance and increase the disturbance rejection performance of the system.

针对全状态约束和输入饱和条件下的机械臂，研究了一种基于误差的非线性扰动观测器的自适应模糊神经网络平滑切换增益动态面控制方法。首先，提出了一种平滑切换增益策略来取代传统的静态控制增益。该策略可以根据跟踪误差及其导数动态更新控制增益，从而优化不同响应阶段的跟踪性能。其次，针对传统非线性扰动观测器在跟踪误差较大时产生有害观测峰的问题，设计了基于误差的非线性扰动观测器。该观测器根据跟踪误差自适应调整观测器增益，有效地减轻了有害的观测峰。在此基础上，引入自适应模糊神经网络策略来逼近模型的不确定性。最后，分别建立了辅助系统和非对称时变势垒Lyapunov函数来处理输入饱和和非对称时变全态约束。通过一个二自由度机械手的对比实验，验证了所提策略能有效地将系统的状态和输入约束在预定义的范围内。实验结果进一步验证了所提策略能有效优化跟踪性能，提高系统抗扰性能。

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引用次数: 0

Density results using the method of fundamental solutions for a fluid-structure interaction problem 流固耦合问题基本解方法的密度结果

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-17 DOI: 10.1016/j.amc.2025.129769

Tielei Zhu , Zhihao Ge

We propose two numerical methods i.e., the method of fundamental solutions (MFS) and the coupling of the MFS and the plane waves method, for solving a fluid-structure interaction scattering problem numerically in two and three dimensions, which are both free of irregular frequencies. It is shown that the acoustic fields can be approximated in the

H^{1}

-norm by the fundamental solutions of the Helmholtz equation placed at distinct source points, whereas elastic fields are approximated in the same norm either by the fundamental solutions of the Navier equations at different locations or by the plane waves of the Navier equations with distinct directions. Some numerical examples are performed to show the behaviors of our methods for the two-dimensional case.

本文提出了两种数值方法，即基本解法（MFS）和基本解法与平面波法的耦合法，用于二维和三维无不规则频率流固耦合散射问题的数值求解。结果表明，声场可以用赫姆霍兹方程的基本解在不同的源点上近似于h1范数，而弹性场可以用不同位置的纳维耶方程的基本解或不同方向的纳维耶方程的平面波在同一范数中近似。通过数值算例说明了本文方法在二维情况下的性能。

引用次数: 0

Generalized Störmer-Cowell methods for the nonlinear second-order delay integro-differential equations with initial conditions 具有初始条件的二阶非线性时滞积分微分方程的广义Störmer-Cowell方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-14 DOI: 10.1016/j.amc.2025.129771

Huiru Wang , Yongtao Zhou , Wenzhuo Xiong , Xiaoqiang Yan

In this paper, a kind of adapted numerical methods are constructed to discretize nonlinear second-order integro-differential equations with delay and initial conditions. The approximation methods are developed through a combination of the fundamental generalized Störmer-Cowell methods (GSCMs) and compound quadrature (CQ) formulas. Under several appropriate conditions, we give the criteria on unique solvability, stability and convergence. Moreover, we prove that the resulting numerical methods have the accuracy of

\min {p, q}

, in which

p, q

, respectively, denotes the GSCMs’ consistence order and the CQ formulas’ convergence order. Numerical experiments are performed to show methods’ computational effectiveness and accuracy. Besides, a comparison is provided among the adapted GSCMs, the adapted implicit Runge-Kutta-Nyström methods and the extended block boundary value methods, which indicates that the constructed methods are comparable.

本文构造了一种具有初始条件和时滞的二阶非线性积分微分方程离散化的自适应数值方法。近似方法是通过基本广义Störmer-Cowell方法（GSCMs）和复合正交（CQ）公式的结合而发展起来的。在适当的条件下，给出了该方法的唯一可解性、稳定性和收敛性准则。此外，我们还证明了所得到的数值方法具有min{p，q}的精度，其中p，q分别表示GSCMs的一致性阶和CQ公式的收敛阶。数值实验验证了该方法的计算有效性和准确性。此外，还将改进的gscm方法与改进的隐式Runge-Kutta-Nyström方法和扩展块边界值方法进行了比较，表明所构造的方法具有可比性。

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引用次数: 0

Representations of the Moore-Penrose inverse of a 2 × 2 block matrix based on Schur complements 基于Schur补的2 × 2块矩阵的Moore-Penrose逆表示

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-17 DOI: 10.1016/j.amc.2025.129776

Daochang Zhang , Leiming Ma , Dijana Mosić

Utilizing two different Schur complements, our purpose is to derive new explicit representations of the Moore-Penrose inverse of a

2 \times 2

complex block matrix under corresponding hypotheses. By this way, we generalized several known results in the literature. A numerical example is given to illustrate our results.

利用两种不同的Schur补，我们的目的是在相应的假设下推导出2×2复块矩阵的Moore-Penrose逆的新的显式表示。通过这种方式，我们概括了文献中几个已知的结果。最后给出了一个数值例子来说明我们的结果。

引用次数: 0

Hierarchical estimation method for fractional-order systems based on the auxiliary model 基于辅助模型的分数阶系统层次估计方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-10 DOI: 10.1016/j.amc.2025.129749

Yufan Zhang, Xiao Zhang, Feng Ding

This paper investigates the identification of nonlinear fractional Hammerstein-Wiener systems. Considering the coupled terms of the system, the over-parametrization method is used for obtaining a linearly parameterized form with the cross-products between the parameters. To enhance the computational efficiency, a novel least squares algorithm is presented by applying the hierarchical identification principle. The main idea is to decompose the original system into several subsystems to simultaneously estimate the coupled parameters. For the unknown variables, the auxiliary model is constructed and the immeasurable variables are replaced with the outputs of the auxiliary model. Then an auxiliary model based hierarchical least squares algorithm is proposed to identify the parameters of the fractional-order systems. The computational analysis and simulation results validate the performance of the proposed algorithms.

研究了非线性分数阶Hammerstein-Wiener系统的辨识问题。考虑到系统的耦合项，采用过参数化方法得到参数间的叉积线性参数化形式。为了提高计算效率，应用层次辨识原理，提出了一种新的最小二乘算法。其主要思想是将原系统分解为多个子系统，同时对耦合参数进行估计。对于未知变量，构建辅助模型，将不可测变量替换为辅助模型的输出。然后提出了一种基于辅助模型的分层最小二乘算法来识别分数阶系统的参数。计算分析和仿真结果验证了所提算法的有效性。

引用次数: 0

Robust numerical analysis for 2D singularly perturbed elliptic delay differential equations exhibiting interior layers due to singularity propagation 二维奇异摄动椭圆型时滞微分方程的鲁棒数值分析

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-16 DOI: 10.1016/j.amc.2025.129770

Garima , Kapil K. Sharma , Komal Bansal

The purpose of this work is to develop a numerical method and its robust convergence analysis for 2D elliptic delay differential equations. The elliptic problems have been considered with unit shifts in undifferentiated terms of both spatial directions resulting in interior layers. The exploration of 2D singularly perturbed elliptic reaction-diffusion delay differential equations exhibiting characteristics boundary and interior layers is a novel and unexplored area in the current scientific literature. In this work, the study of interior layers has been extended to the solution of the problems. A fitted mesh robust numerical method has been developed, which is almost second-order convergent up to the logarithmic factor. The numerical results have been included to demonstrate the singularity propagation in the layer behavior of the numerical solution due to delay arguments.

本文的目的是建立二维椭圆型时滞微分方程的数值方法及其鲁棒收敛性分析。考虑了在两个空间方向上产生内层的单位位移的椭圆问题。探索具有特征边界层和内层的二维奇摄动椭圆反应-扩散时滞微分方程是当前科学文献中一个新的和未开发的领域。在这项工作中，内层的研究已经扩展到解决这些问题。提出了一种拟合网格鲁棒数值方法，该方法在对数因子上几乎是二阶收敛的。数值结果证明了由于延迟参数的影响，数值解在层内的奇异传播行为。

引用次数: 0

Adaptive fault tolerant optimal control for high-order fully actuated system and its application in spacecraft attitude tracking using reinforcement learning 高阶全驱动系统的自适应容错最优控制及其在航天器姿态跟踪中的应用

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-17 DOI: 10.1016/j.amc.2025.129774

Xueqi Wu, Wei Sun

This study addresses the adaptive optimal tracking problem for high-order fully actuated system (FAS). First, an optimal control strategy based on FAS theory and reinforcement learning (RL) is proposed, effectively solving the tracking problem within the actor-critic framework. Next, within the identifier-actor-critic framework, a sliding mode optimized control scheme for high-order FAS with actuator fault is introduced. Specifically, unlike existing fault-tolerant control results for high-order FAS, this method ensures trajectory tracking and performance optimization even in the presence of actuator faults, while avoiding the need for persistent excitation condition. Considering the strong robustness and rapid response advantages of sliding mode control (SMC), synchronous rapid tracking and optimal control of multiple variables are achieved by establishing a (n-1)-order sliding mode surface. Furthermore, rigorous theoretical analysis proves the boundedness of all signals within the closed-loop system. Finally, the effectiveness of the proposed control approaches are verified by a numerical simulation and a practical example of the spacecraft attitude system.

研究了高阶全驱动系统的自适应最优跟踪问题。首先，提出了一种基于FAS理论和强化学习（RL）的最优控制策略，有效地解决了actor-critic框架下的跟踪问题。其次，在辨识器-行为者-批评框架下，介绍了一种针对执行器故障的高阶FAS的滑模优化控制方案。具体而言，与现有的高阶FAS容错控制结果不同，该方法即使在执行器存在故障的情况下也能确保轨迹跟踪和性能优化，同时避免了对持续激励条件的需要。考虑滑模控制（SMC）具有鲁棒性强、响应速度快的优点，通过建立（n-1）阶滑模曲面，实现多变量同步快速跟踪和最优控制。通过严密的理论分析，证明了闭环系统中所有信号的有界性。最后，通过数值仿真和航天器姿态系统实例验证了所提控制方法的有效性。

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引用次数: 0

A two-stage parallel iteration method for nonlinear complementarity problems 非线性互补问题的两阶段并行迭代法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-13 DOI: 10.1016/j.amc.2025.129777

Wenxiu Guo , Hua Zheng , Xiaoping Lu , Yongxiong Zhang , Seakweng Vong

To solve a class of large-scale sparse nonlinear complementarity problems, this paper proposes a modulus-based synchronous two-stage multisplitting iteration method. The method utilizes matrix splitting iteration in its inner iterations. Under the assumption that the system matrix is an

H

-matrix, the convergence analysis of the new method is provided. The efficiency of the proposed method is demonstrated through numerical examples using the OpenACC parallel framework.

针对一类大规模稀疏非线性互补问题，提出了一种基于模的同步两阶段多分裂迭代方法。该方法在内部迭代中采用矩阵分裂迭代。在系统矩阵为h矩阵的假设下，给出了新方法的收敛性分析。通过OpenACC并行框架的数值算例验证了该方法的有效性。

引用次数: 0

A subspace-orbit randomized algorithm for quaternion tensor singular value decomposition based on Qt-product 基于qt积的四元数张量奇异值分解子空间-轨道随机化算法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-15 DOI: 10.1016/j.amc.2025.129780

Yonghe Liu, Fengsheng Wu, Jifei Miao, Chaoqian Li

Based on a subspace-orbit random projection method and a randomized block Krylov iteration approach, we propose a subspace-orbit randomized algorithm with the block Krylov iteration for third-order quaternion tensor singular value decomposition based on Qt-product. The deterministic and expected approximation error bounds for the proposed randomized algorithm are given. Numerical experiments using synthetic data and color video data are presented to demonstrate its feasibility and effectiveness.

基于子空间轨道随机投影法和随机分块Krylov迭代法，提出了一种基于qt积的三阶四元数张量奇异值分解的子空间轨道随机分块Krylov迭代算法。给出了随机化算法的确定性和期望近似误差界。利用合成数据和彩色视频数据进行了数值实验，验证了该方法的可行性和有效性。

引用次数: 0

Two-disjoint-cycle-cover vertex bipancyclicity of bubble-sort star graphs 泡状星图的两不相交环盖顶点双环性

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2026-03-01 Epub Date: 2025-10-17 DOI: 10.1016/j.amc.2025.129787

Hanle Dai , Yan-Quan Feng , Young Soo Kwon , Da-Wei Yang

Let

r_{1}

and

r_{2}

denote two positive integers satisfying

r_{1} \leq r_{2}

. A bipartite graph

G

is defined as two-disjoint-cycle-cover (abbreviated as 2-DCC) vertex

[r_{1}, r_{2}]

-bipancyclic if, for its any pair of distinct vertices

u, v

and any even integer

ℓ

within the range

r_{1} \leq ℓ \leq r_{2}

, there exist two cycles

C_{1}

of length

ℓ

and

C_{2}

of length

| V (G) | - ℓ

G

, such that

V (C_{1}) \cap V (C_{2}) = \emptyset

u \in V (C_{1})

and

v \in V (C_{2})

. In this work, we establish that an

n

-dimensional bubble-sort star graph

B S_{n}

is 2-DCC

[4, \frac{n!}{2}]

-bipancyclic for

n \geq 4

. This finding generalizes a result given by Zhang et al. (2023) and is optimal, given that

B S_{n}

is bipartite and contains

n!

vertices.

令r1和r2表示满足r1≤r2的两个正整数。定义二部图G为双不相交环-覆盖（简称2-DCC）顶点[r1，r2]-双环，如果其在r1≤r≤r范围内的任意对不同的顶点u，v和任意偶数r，在G中存在长度为r的环C1和长度为| v (G)|−r的环C2，使得v (C1)∩v (C2)=∅,u∈v (C1),v∈v （C2）。在这项工作中，我们建立了一个n维气泡排序星图BSn是2-DCC [4，n!][2]对于n≥4 -双环。这一发现推广了Zhang等人（2023）给出的结果，并且是最优的，因为BSn是二部的并且包含n！顶点。

引用次数: 0

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Applied Mathematics and Computation

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