Applied Mathematics and Computation最新文献

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Resilient observer-based unified state and fault estimation for nonlinear parabolic PDE systems via fuzzy approach over finite-time interval 基于弹性观测器的有限时间区间模糊非线性抛物 PDE 系统的统一状态和故障估计

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-15 DOI: 10.1016/j.amc.2024.129125

V.T. Elayabharath , P. Sozhaeswari , N. Tatar , R. Sakthivel , T. Satheesh

With the aid of a resilient fuzzy observer, this study delves into the investigation of finite-time state and fault estimation for parabolic-type nonlinear PDE systems described by fuzzy models with faults and external disturbances. Primarily, a fuzzy-dependent observer is built to offer precise estimations of the states and faults simultaneously. Therein, the fluctuations that exhibit random character are taken into account in the observer gain, which enhances the resiliency of the configured fuzzy observer. Meanwhile, the phenomenon of randomly occurring gain fluctuations is effectively characterized by utilizing a random variable that adheres to the Bernoulli distribution. Subsequently, by employing the Lyapunov stability theory and the integral-based Wirtinger's inequality, a set of adequate criteria is obtained in the form of linear matrix inequalities to ascertain that both the state and fault estimation errors are stable in a finite-time with a gratified extended passivity performance index. In the meantime, the observer gain matrices can be obtained by relying on the developed criteria. Ultimately, the simulation results of the Fisher equation are offered to emphasize the superiority of the developed resilient fuzzy observer-based approach.

借助弹性模糊观测器，本研究深入探讨了具有故障和外部扰动的模糊模型所描述的抛物线型非线性 PDE 系统的有限时间状态和故障估计。主要是建立一个模糊依赖观测器，以同时提供状态和故障的精确估计。在此过程中，观测器增益考虑了具有随机特征的波动，从而增强了所配置的模糊观测器的弹性。同时，利用符合伯努利分布的随机变量，可以有效地描述随机发生的增益波动现象。随后，通过利用 Lyapunov 稳定性理论和基于积分的 Wirtinger 不等式，以线性矩阵不等式的形式获得了一组适当的准则，以确定状态和故障估计误差在有限时间内都是稳定的，并具有令人满意的扩展被动性能指标。同时，还可以根据所制定的准则获得观测器增益矩阵。最后，提供了 Fisher 方程的仿真结果，以强调所开发的基于弹性模糊观测器方法的优越性。

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引用次数: 0

Coupled nonlinear stochastic integral equations in the general form of the predator-prey model 捕食者-猎物模型一般形式中的耦合非线性随机积分方程

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-14 DOI: 10.1016/j.amc.2024.129123

Hengameh Tamimi, Mohammad Bagher Ghaemi, Reza Saadati

This article explores the stochastic predator-prey model. This model offers a probabilistic framework for understanding the dynamics of interacting species. The stochastic predator-prey model is a practical tool for predicting the intricate balance of survival between predators and their prey in the face of nature's unpredictability. This study introduces a new measure of noncompactness and applies it to investigate solutions in nonlinear stochastic equations. Additionally, we present a numerical method using block pulse functions and demonstrate its convergence through the new measure of noncompactness for solving the system of stochastic integrals. Finally, the proposed method is employed to solve a numerical example.

本文探讨了随机捕食者-猎物模型。该模型为理解相互作用物种的动态提供了一个概率框架。面对自然界的不可预测性，随机捕食者-猎物模型是预测捕食者和猎物之间错综复杂的生存平衡的实用工具。本研究引入了一种新的非紧凑性测量方法，并将其应用于研究非线性随机方程的解。此外，我们还提出了一种使用块脉冲函数的数值方法，并通过新的非紧凑性度量证明了该方法在求解随机积分系统时的收敛性。最后，我们利用所提出的方法求解了一个数值示例。

引用次数: 0

A holistic matrix norm-based alternative solution method for Markov reward games 基于矩阵规范的马尔可夫奖赏博弈整体替代求解法

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-14 DOI: 10.1016/j.amc.2024.129124

Burhaneddin İzgi , Murat Özkaya , Nazım Kemal Üre , Matjaž Perc

In this study, we focus on examining single-agent stochastic games, especially Markov reward games represented in the form of a decision tree. We propose an alternative solution method based on the matrix norms for these games. In contrast to the existing methods such as value iteration, policy iteration, and dynamic programming, which are state-and-action-based approaches, the proposed matrix norm-based method considers the relevant stages and their actions as a whole and solves it holistically for each stage without computing the effects of each action on each state's reward individually. The new method involves a distinct transformation of the decision tree into a payoff matrix for each stage and the utilization of the matrix norm of the obtained payoff matrix. Additionally, the concept of the moving matrix is integrated into the proposed method to incorporate the impacts of all actions on the stage simultaneously, rendering the method holistic. Moreover, we present an explanatory algorithm for the implementation of the method and also provide a comprehensive solution diagram explaining the method figuratively. As a result, we offer a new and alternative perspective for solving the games with the help of the proposed method due to the simplicity of utilization of the matrix norms in addition to the existing methods. For clarification of the matrix norm-based method, we demonstrate the figurative application of the method on a benchmark Markov reward game with 2-stages and 2-actions and a comprehensive implementation of the method on a game consisting of 3-stages and 3-actions.

在本研究中，我们重点研究了单代理随机博弈，尤其是以决策树形式表示的马尔可夫奖励博弈。我们针对这些博弈提出了一种基于矩阵规范的替代求解方法。与价值迭代、策略迭代和动态编程等基于状态和行动的现有方法相比，我们提出的基于矩阵规范的方法将相关阶段及其行动视为一个整体，并对每个阶段进行整体求解，而无需单独计算每个行动对每个状态奖励的影响。新方法包括将决策树转化为每个阶段的报酬矩阵，并利用所得报酬矩阵的矩阵规范。此外，我们还将移动矩阵的概念融入到所提出的方法中，以便同时考虑所有行动对阶段的影响，从而使该方法具有整体性。此外，我们还提出了实现该方法的解释性算法，并提供了一个综合解图，形象地解释了该方法。因此，由于在现有方法的基础上简单地利用矩阵规范，我们提出的方法为解决博弈问题提供了一个新的替代视角。为了说明基于矩阵规范的方法，我们演示了该方法在一个具有 2 个阶段和 2 个行动的基准马尔可夫奖励博弈中的具象应用，以及该方法在一个由 3 个阶段和 3 个行动组成的博弈中的全面实施。

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引用次数: 0

Distributed adaptive moving horizon estimation for multi-sensor networks subject to quantization effects 受量化效应影响的多传感器网络分布式自适应移动地平线估计

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-14 DOI: 10.1016/j.amc.2024.129126

Yuan-Wei Lv , Guang-Hong Yang , Georgi Marko Dimirovski

This paper investigates the distributed state estimation problem for multi-sensor networks with quantized measurements. Within the Bayesian framework, a distributed adaptive moving horizon estimation algorithm is developed. Unlike the existing methods regarding quantized errors roughly as bounded uncertainties, the posterior distributions of the errors are demanded to be derived. To overcome the difficulty of evaluating the posterior distributions for series of the states and quantized errors jointly, the variational Bayesian methodology is adopted to approximate the true distributions. Based on the fixed-point iteration method, the update rules are analytically derived, with the convergence criterion provided. Furthermore, by incorporating the average consensus algorithm into the prediction process, all sensors can achieve consensus on their estimates in a distributed manner. Finally, a numerical example of target tracking under logarithmic and uniform quantization effects is given to illustrate the validity of the proposed algorithm.

本文研究了具有量化测量的多传感器网络的分布式状态估计问题。在贝叶斯框架内，开发了一种分布式自适应移动地平线估计算法。与将量化误差大致视为有界不确定性的现有方法不同，本文要求推导误差的后验分布。为了克服联合评估状态序列和量化误差后验分布的困难，采用了变分贝叶斯方法来逼近真实分布。基于定点迭代法，分析得出了更新规则，并提供了收敛标准。此外，通过将平均共识算法纳入预测过程，所有传感器都能以分布式方式就其估计值达成共识。最后，给出了一个在对数和均匀量化效应下进行目标跟踪的数值示例，以说明所提算法的有效性。

引用次数: 0

Data-driven predictor of control-affine nonlinear dynamics: Finite discrete-time bilinear approximation of koopman operator 控制-非线性非线性动力学的数据驱动预测器：库普曼算子的有限离散时间双线性近似值

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-12 DOI: 10.1016/j.amc.2024.129068

Sara Iman, Mohammad-Reza Jahed-Motlagh

This paper introduces a novel and efficient data-driven approach for approximating a finite discrete-time bilinear model of control affine nonlinear dynamical systems with a tunable parameter that balances model dimension and prediction accuracy. An approximation of the Koopman operator based on the evolutions of the nonlinear system measurements used to lift a control-affine nonlinear system to a higher dimensional model. However, higher dimensional spaces can result in a long learning time and the curse of dimensionality in control analysis. The proposed approach addresses these challenges by introducing a convex optimization which identifies informative observable functions. This technique allows for the adjustment of a parameter to strike a balance between model dimension and accuracy in prediction. The main contribution of this study is to introduce a reduced dimensional bilinear model for a nonlinear complex system. This achievement is made possible by implementing convex sparse optimization, enabling the exploration of informative estimated Koopman eigenfunctions while minimizing the number of system measurements required. The optimization problem is solved using the alternating direction method of multipliers. The effectiveness of the proposed method is evaluated on three different nonlinear systems: a numerical nonlinear system, a Van der Pol oscillator, and a Duffing oscillator. In the last simulation, an estimation of the Koopman linear model is considered as a special case, and the policy iteration algorithm is employed to evaluate optimal control designed for different reduced-dimensional models.

本文介绍了一种新颖、高效的数据驱动方法，利用一个可调参数来近似控制仿射非线性动态系统的有限离散时间双线性模型，从而在模型维度和预测精度之间取得平衡。基于非线性系统测量演化的 Koopman 算子近似值用于将控制仿射非线性系统提升到高维模型。然而，高维空间会导致学习时间过长，以及控制分析中的维度诅咒。所提出的方法通过引入凸优化来确定信息可观测函数，从而解决了这些难题。这种技术可以调整参数，在模型维度和预测精度之间取得平衡。本研究的主要贡献在于为非线性复杂系统引入了一个降维双线性模型。这一成果是通过实施凸稀疏优化得以实现的，在最大限度减少所需的系统测量次数的同时，还能探索信息丰富的估计 Koopman 特征函数。优化问题采用交替乘法求解。我们在三个不同的非线性系统上评估了所提方法的有效性：一个数值非线性系统、一个范德波尔振荡器和一个达芬振荡器。在最后一个仿真中，库普曼线性模型的估计被视为一个特例，并采用策略迭代算法来评估为不同降维模型设计的最优控制。

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引用次数: 0

Non-cospectral equienergetic trees of diameter at most four 直径至多为 4 的非谱系等能树

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129104

Fenjin Liu , Ke Su , Wei Wang , Hao Zhang

No general method differing from computer search has been discovered for finding noncospectral equienergetic trees. We first utilize techniques of spectral graph theory and Diophantine Equation to analyze the energy of two families of short-diameter trees. Seven infinite families noncospectral equienergetic trees are obtained of which six pairs of them have equal number vertices. This contributes to an open problem posed by Li, Shi and Gutman for constructing noncospectral equienergetic trees.

在寻找非谱等能树方面，还没有发现不同于计算机搜索的通用方法。我们首先利用谱图理论和二重方程技术分析了两个短径树族的能量。我们得到了七个无穷族非谱等能树，其中六对顶点数相等。这有助于解决 Li、Shi 和 Gutman 提出的构建非谱等能树的未决问题。

引用次数: 0

Perfect matching cover indices of generalized rotation snarks 广义旋转星痕的完美匹配覆盖指数

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129101

Wenjuan Zhou, Rong-Xia Hao, Yilun Luo

Let Γ be a 3-regular bridgeless graph and

τ (Γ)

be the perfect matching cover index of Γ. It is conjectured by Berge that

τ (Γ) \leq 5

. Esperet and Mazzuoccolo (2013) [4] proved that deciding whether Γ satisfies

τ (Γ) \leq 4

is NP-complete. Máčajová and Škoviera (2021) [13] gave a family

R = {R_{k} : k \geq 4}

of rotation snarks. We construct a family

FR = {F R_{2 n + 1} : n \geq 1}

of generalized rotation snarks. In this paper, we show that each

F R_{2 n + 1}

satisfies

τ (F R_{2 n + 1}) = 4

. As a corollary, each

R_{k}

satisfies

τ (R_{k}) = 4

设 Γ 是一个三规则无桥图，τ(Γ) 是 Γ 的完全匹配覆盖指数。根据 Berge 的猜想，τ(Γ)≤5。Esperet 和 Mazzuoccolo (2013) [4] 证明，判断 Γ 是否满足 τ(Γ)≤4 是 NP-完全的。Máčajová 和 Škoviera (2021) [13] 给出了一个旋转星痕族 R={Rk:k≥4}。我们构建了一个广义旋转夸克族 FR={FR2n+1:n≥1}。在本文中，我们证明每个 FR2n+1 都满足 τ(FR2n+1)=4 的条件。作为推论，每个 Rk 满足 τ(Rk)=4 。

引用次数: 0

Graphs with burning number three 燃烧数字 3 的图表

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129100

Yinkui Li , Guiyu Shi , Xiaoxiao Qin

Recently, Bonato et al. proposed the concept of the burning number of a graph to measure the speed of contagion spread on a network. They pointed out that the burning number of graph G is

b (G) \geq 2

and showed that the graph G with burning number 2 if and only if G has maximum degree

| V (G) | - 1

| V (G) | - 2

. Consider the problem of finding the maximum degree of a graph is solvable in polynomial time, graphs with burning number 2 can be recognized in polynomial time and thus the lower bound of burning number be improved to 3. In this paper, we characterize graphs with burning number 3 in terms of maximum degree and diameter.

最近，Bonato 等人提出了图的燃烧数概念，用以衡量网络中传染扩散的速度。他们指出图 G 的燃烧数为 b(G)≥2，并证明当且仅当 G 具有最大度 |V(G)|-1 或 |V(G)|-2 时，图 G 的燃烧数为 2。考虑到求一个图的最大度的问题可以在多项式时间内求解，燃烧数为 2 的图可以在多项式时间内识别，因此燃烧数的下界可以提高到 3。

引用次数: 0

Parameter estimation method for separable fractional-order Hammerstein nonlinear systems based on the on-line measurements 基于在线测量的可分离分数阶哈默斯坦非线性系统参数估计方法

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129102

Junwei Wang , Weili Xiong , Feng Ding , Yihong Zhou , Erfu Yang

This paper investigates the problem of parameter estimation for fractional-order Hammerstein nonlinear systems. To handle the identification difficulty of the parameters of the system and the order, the maximum likelihood and hierarchical identification principles are combined to derive a maximum likelihood gradient-based iterative algorithm. Moreover, to achieve the higher estimation accuracy, the multi-innovation identification theory is introduced, based on which the residual can be formulated as a linear combination of the innovation. Then, a multi-innovation maximum likelihood gradient-based iterative algorithm is proposed, which further improves the innovation utilization. Meanwhile, the computational cost of the proposed algorithm is assessed through the use of flops, which is less than those of its peers. Finally, the convergence analysis and simulation examples demonstrate the efficacy and robustness of the proposed algorithms.

本文研究了分数阶哈默斯坦非线性系统的参数估计问题。为了解决系统参数和阶次的识别难题，本文结合最大似然和分层识别原理，推导出一种基于最大似然梯度的迭代算法。此外，为了实现更高的估计精度，还引入了多创新识别理论，在此基础上，残差可被表述为创新的线性组合。然后，提出了一种基于多创新最大似然梯度的迭代算法，进一步提高了创新利用率。同时，通过翻转次数评估了所提算法的计算成本，其计算成本低于同类算法。最后，收敛分析和仿真实例证明了所提算法的有效性和鲁棒性。

引用次数: 0

Disjoint path covers of star graphs 星形图的相邻路径覆盖

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2024-10-10 DOI: 10.1016/j.amc.2024.129098

Hongwei Qiao, Jixiang Meng

Given a graph G, let S and T be two vertex-disjoint subsets of equal size k of G. A k-disjoint path cover of G corresponding to S and T is the union of k vertex-disjoint paths among S and T that spans G. If every vertex of S should be joined to a prescribed vertex in T, it is defined to be paired, otherwise it is unpaired. Let

S T_{n}

be a star graph with bipartition

V_{0}

and

V_{1}

. Let

S \subseteq V_{0}

and

T \subseteq V_{1}

be two vertex subsets of equal size k. It is shown in this paper that

S T_{n}

admits an unpaired k-disjoint path cover between S and T, where

k \leq n - 2

and

n \geq 4

. In view of the degree of

S T_{n}

, this result is optimal.

给定一个图 G，设 S 和 T 是 G 的两个大小相等的 k 个顶点相交子集。与 S 和 T 相对应的 G 的 k 个相交路径覆盖是 S 和 T 之间跨越 G 的 k 个顶点相交路径的联合。假设 STn 是一个星形图，具有双分区 V0 和 V1。本文证明了 STn 在 S 和 T 之间允许一个非配对的 k 叉路径覆盖，其中 k≤n-2 且 n≥4。考虑到 STn 的度数，这一结果是最优的。

{"title":"Disjoint path covers of star graphs","authors":"Hongwei Qiao, Jixiang Meng","doi":"10.1016/j.amc.2024.129098","DOIUrl":"10.1016/j.amc.2024.129098","url":null,"abstract":"<div><div>Given a graph <em>G</em>, let <em>S</em> and <em>T</em> be two vertex-disjoint subsets of equal size <em>k</em> of <em>G</em>. A <em>k</em>-disjoint path cover of <em>G</em> corresponding to <em>S</em> and <em>T</em> is the union of <em>k</em> vertex-disjoint paths among <em>S</em> and <em>T</em> that spans <em>G</em>. If every vertex of <em>S</em> should be joined to a prescribed vertex in <em>T</em>, it is defined to be paired, otherwise it is unpaired. Let <span><math><mi>S</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be a star graph with bipartition <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. Let <span><math><mi>S</mi><mo>⊆</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><mi>T</mi><mo>⊆</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> be two vertex subsets of equal size <em>k</em>. It is shown in this paper that <span><math><mi>S</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> admits an unpaired <em>k</em>-disjoint path cover between <em>S</em> and <em>T</em>, where <span><math><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>2</mn></math></span> and <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. In view of the degree of <span><math><mi>S</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, this result is optimal.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129098"},"PeriodicalIF":3.5,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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