Pub Date : 2025-02-17DOI: 10.1016/j.amc.2025.129346
Rui Ding , Shujuan Cao , Binying Cai , Yongming Zou , Fang-xiang Wu
Alzheimer's disease (AD) is a neurological disorder with complicated pathogenesis. The approved AD drugs cannot block or reverse the pathologic progression of AD. In this study, a method based on Logistic Matrix Factorization and Similarity Network Fusion (MLMFSNF) is proposed for screening out the Traditional Chinese medicines (TCMs) and active ingredients targeting AD targets. Firstly, TCMs for AD are obtained from the AD drug reviews, the active ingredients and related targets are collected from various databases. Secondly, the similarity networks are constructed by an improved Gaussian interaction profile kernel and other metrics for active ingredients and targets. The synthesized similarity networks are integrated based on similarity network fusion (SNF). The filling of missing activity ingredient-target associations is achieved by the logistic matrix factorization. Finally, the association scores between active ingredients and targets are calculated and ranked. We screen out TCMs for AD by the logistic function transformation. The results demonstrated that the MLMFSNF algorithm is effective for association prediction.
{"title":"Traditional Chinese medicine studies for AD based on Logistic Matrix Factorization and Similarity Network Fusion","authors":"Rui Ding , Shujuan Cao , Binying Cai , Yongming Zou , Fang-xiang Wu","doi":"10.1016/j.amc.2025.129346","DOIUrl":"10.1016/j.amc.2025.129346","url":null,"abstract":"<div><div>Alzheimer's disease (AD) is a neurological disorder with complicated pathogenesis. The approved AD drugs cannot block or reverse the pathologic progression of AD. In this study, a method based on Logistic Matrix Factorization and Similarity Network Fusion (MLMFSNF) is proposed for screening out the Traditional Chinese medicines (TCMs) and active ingredients targeting AD targets. Firstly, TCMs for AD are obtained from the AD drug reviews, the active ingredients and related targets are collected from various databases. Secondly, the similarity networks are constructed by an improved Gaussian interaction profile kernel and other metrics for active ingredients and targets. The synthesized similarity networks are integrated based on similarity network fusion (SNF). The filling of missing activity ingredient-target associations is achieved by the logistic matrix factorization. Finally, the association scores between active ingredients and targets are calculated and ranked. We screen out TCMs for AD by the logistic function transformation. The results demonstrated that the MLMFSNF algorithm is effective for association prediction.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129346"},"PeriodicalIF":3.5,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428215","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}
Pub Date : 2025-02-17DOI: 10.1016/j.amc.2025.129354
Yaxin Jiang, Yujun Yang
For any two vertices u and v of a connected graph G, the resistance distance between u and v is defined as the effective resistance between them in the corresponding electrical network created by placing a unit resistor on each edge of G. The Kirchhoff index of G is defined as the sum of resistance distances between all pairs of vertices in G. Let be the graph obtained from the complete graph by deleting an edge. In this paper, we consider two classes of graphs formed by , namely the string graph of and the ring graph of , which are denoted by and , respectively. By using combinatorial and electrical network approaches, we obtain the formulae for resistance distances and Kirchhoff indices of and , which generalizes the results by Sardar et al. (2024) [25].
{"title":"Computation of resistance distances and Kirchhoff indices for two classes of graphs","authors":"Yaxin Jiang, Yujun Yang","doi":"10.1016/j.amc.2025.129354","DOIUrl":"10.1016/j.amc.2025.129354","url":null,"abstract":"<div><div>For any two vertices <em>u</em> and <em>v</em> of a connected graph <em>G</em>, the resistance distance between <em>u</em> and <em>v</em> is defined as the effective resistance between them in the corresponding electrical network created by placing a unit resistor on each edge of <em>G</em>. The Kirchhoff index of <em>G</em> is defined as the sum of resistance distances between all pairs of vertices in <em>G</em>. Let <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> be the graph obtained from the complete graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> by deleting an edge. In this paper, we consider two classes of graphs formed by <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, namely the string graph of <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> and the ring graph of <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, which are denoted by <span><math><mi>S</mi><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><mi>R</mi><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><mi>n</mi><mo>)</mo></math></span>, respectively. By using combinatorial and electrical network approaches, we obtain the formulae for resistance distances and Kirchhoff indices of <span><math><mi>S</mi><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><mi>R</mi><mo>(</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>,</mo><mi>n</mi><mo>)</mo></math></span>, which generalizes the results by Sardar et al. (2024) <span><span>[25]</span></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129354"},"PeriodicalIF":3.5,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428216","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}
Pub Date : 2025-02-14DOI: 10.1016/j.amc.2025.129355
Yunhua Zeng , Zhijun Tan
Considering the initial singularity, a fully discrete two-grid finite element method (FEM) on nonuniform temporal meshes is constructed for the semilinear time-fractional variable coefficient diffusion equations (TF-VCDEs) with Caputo-Hadamard derivative. The nonuniform L formula and two-grid method are employed to discretize the time and space directions, respectively. Through strict theoretical proof, the α-robust stability and optimal -norm and -norm error analysis for the fully discrete FEM and the two-grid method are obtained, where the error bound does not blow up as . To reduce computational costs, a fast two-grid method is constructed by approximating the kernel function with an effective sum-of-exponentials (SOE) technique. Finally, the accuracy and effectiveness of the two-grid method and its associated fast algorithm are verified through two numerical examples.
{"title":"An α-robust two-grid finite element method with nonuniform L2-1σ scheme for the semilinear Caputo-Hadamard time-fractional diffusion equations involving initial singularity","authors":"Yunhua Zeng , Zhijun Tan","doi":"10.1016/j.amc.2025.129355","DOIUrl":"10.1016/j.amc.2025.129355","url":null,"abstract":"<div><div>Considering the initial singularity, a fully discrete two-grid finite element method (FEM) on nonuniform temporal meshes is constructed for the semilinear time-fractional variable coefficient diffusion equations (TF-VCDEs) with Caputo-Hadamard derivative. The nonuniform L<span><math><msub><mrow></mrow><mrow><mi>log</mi><mo></mo><mo>,</mo><mn>2</mn><mo>−</mo><msub><mrow><mn>1</mn></mrow><mrow><mi>σ</mi></mrow></msub></mrow></msub></math></span> formula and two-grid method are employed to discretize the time and space directions, respectively. Through strict theoretical proof, the <em>α</em>-robust stability and optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm error analysis for the fully discrete FEM and the two-grid method are obtained, where the error bound does not blow up as <span><math><mi>α</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span>. To reduce computational costs, a fast two-grid method is constructed by approximating the kernel function with an effective sum-of-exponentials (SOE) technique. Finally, the accuracy and effectiveness of the two-grid method and its associated fast algorithm are verified through two numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129355"},"PeriodicalIF":3.5,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418580","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}
Pub Date : 2025-02-14DOI: 10.1016/j.amc.2025.129360
Shengdi Wang, Tingfu Ma, Lili Wu, Xiaojia Yang
In this paper, two numerical methods for solving the initial boundary value problem of one-dimensional nonlinear Generalized Benjamin-Borne-Mahony-Burgers equation are presented. Both methods utilize a fourth-order backward difference scheme for the discretization of the first-order derivative in the time direction, and apply a fourth-order compact difference scheme and a fourth-order Padé scheme to discretize the second-order and first-order spatial derivatives, respectively. The primary difference between the two methods lies in their distinct linearization strategies for the nonlinear term, which results in the formation of two linear systems. Both methods achieve fourth-order convergence in time and space. Subsequently, theoretical proofs are provided for the conservation property, stability and the existence and uniqueness of the numerical solution of the proposed numerical scheme. Finally, numerical experiments are conducted to verify the reliability and effectiveness of both methods.
{"title":"Two high-order compact finite difference schemes for solving the nonlinear generalized Benjamin-Bona-Mahony-Burgers equation","authors":"Shengdi Wang, Tingfu Ma, Lili Wu, Xiaojia Yang","doi":"10.1016/j.amc.2025.129360","DOIUrl":"10.1016/j.amc.2025.129360","url":null,"abstract":"<div><div>In this paper, two numerical methods for solving the initial boundary value problem of one-dimensional nonlinear Generalized Benjamin-Borne-Mahony-Burgers equation are presented. Both methods utilize a fourth-order backward difference scheme for the discretization of the first-order derivative in the time direction, and apply a fourth-order compact difference scheme and a fourth-order Padé scheme to discretize the second-order and first-order spatial derivatives, respectively. The primary difference between the two methods lies in their distinct linearization strategies for the nonlinear term, which results in the formation of two linear systems. Both methods achieve fourth-order convergence in time and space. Subsequently, theoretical proofs are provided for the conservation property, stability and the existence and uniqueness of the numerical solution of the proposed numerical scheme. Finally, numerical experiments are conducted to verify the reliability and effectiveness of both methods.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129360"},"PeriodicalIF":3.5,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418579","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}
Pub Date : 2025-02-14DOI: 10.1016/j.amc.2025.129343
Herbert Jodlbauer , Matthias Dehmer , Frank Emmert-Streib
Demand-Driven Material Requirement Planning (DDMRP) represents a combination of traditional Material Requirements Planning (MRP) and the reorder point method. A key consideration in DDMRP revolves around determining the optimal position of decoupling points, also referred to as strategic inventory positions. This article addresses the question of where these decoupling points should be strategically positioned, utilizing a directed universal graph derived from the Bill of Materials (BOM) to formalize the optimal decoupling point setting problem. To address this challenge, analytical formulas are developed. The analytical formulas utilize parameters such as delivery time, demand variance, replenishment time, lot sizes, holding costs, and service levels. These formulas provide insights into key characteristics of optimal decoupling points. The obtained results can be categorized into arguments advocating for decoupling points to be positioned either more upstream or more downstream. Furthermore, we derive specific characteristics that an optimal decoupling point position should possess. This research contributes valuable knowledge for practitioners seeking to enhance the efficiency and effectiveness of their DDMRP implementation.
{"title":"Aspects on the optimal decoupling point setting problem","authors":"Herbert Jodlbauer , Matthias Dehmer , Frank Emmert-Streib","doi":"10.1016/j.amc.2025.129343","DOIUrl":"10.1016/j.amc.2025.129343","url":null,"abstract":"<div><div>Demand-Driven Material Requirement Planning (DDMRP) represents a combination of traditional Material Requirements Planning (MRP) and the reorder point method. A key consideration in DDMRP revolves around determining the optimal position of decoupling points, also referred to as strategic inventory positions. This article addresses the question of where these decoupling points should be strategically positioned, utilizing a directed universal graph derived from the Bill of Materials (BOM) to formalize the optimal decoupling point setting problem. To address this challenge, analytical formulas are developed. The analytical formulas utilize parameters such as delivery time, demand variance, replenishment time, lot sizes, holding costs, and service levels. These formulas provide insights into key characteristics of optimal decoupling points. The obtained results can be categorized into arguments advocating for decoupling points to be positioned either more upstream or more downstream. Furthermore, we derive specific characteristics that an optimal decoupling point position should possess. This research contributes valuable knowledge for practitioners seeking to enhance the efficiency and effectiveness of their DDMRP implementation.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129343"},"PeriodicalIF":3.5,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-13DOI: 10.1016/j.amc.2025.129344
Philip P. Forrier , Joan Gimeno , Àngel Jorba
In this note we study the behavior of the coefficients of the Taylor method when computing the numerical solution of stiff Ordinary Differential Equations. First, we derive an asymptotic formula for the growth of the stability region w.r.t. the order of the Taylor method. Then, we analyze the behavior of the Taylor coefficients of the solution when the equation is stiff. Using jet transport, we show that the coefficients computed with a floating point arithmetic of arbitrary precision have an absolute error that depends on the variational equations of the solution, which can have a dominant exponential growth in stiff problems. This is naturally related to the characterization of stiffness presented by Söderlind et al. [32], and allows to discuss why explicit solvers need a stepsize reduction when dealing with stiff systems. We explore how high-order methods can alleviate this restriction when high precision computations are required. We provide numerical experiments with classical stiff problems and perform extended precision computations to demonstrate this behavior.
{"title":"A note on the local behavior of the Taylor method for stiff ODEs","authors":"Philip P. Forrier , Joan Gimeno , Àngel Jorba","doi":"10.1016/j.amc.2025.129344","DOIUrl":"10.1016/j.amc.2025.129344","url":null,"abstract":"<div><div>In this note we study the behavior of the coefficients of the Taylor method when computing the numerical solution of stiff Ordinary Differential Equations. First, we derive an asymptotic formula for the growth of the stability region w.r.t. the order of the Taylor method. Then, we analyze the behavior of the Taylor coefficients of the solution when the equation is stiff. Using jet transport, we show that the coefficients computed with a floating point arithmetic of arbitrary precision have an absolute error that depends on the variational equations of the solution, which can have a dominant exponential growth in stiff problems. This is naturally related to the characterization of stiffness presented by Söderlind et al. <span><span>[32]</span></span>, and allows to discuss why explicit solvers need a stepsize reduction when dealing with stiff systems. We explore how high-order methods can alleviate this restriction when high precision computations are required. We provide numerical experiments with classical stiff problems and perform extended precision computations to demonstrate this behavior.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129344"},"PeriodicalIF":3.5,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394465","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}
Pub Date : 2025-02-13DOI: 10.1016/j.amc.2025.129359
Wei Tang, Da Xu
In this article, a direct method for the numerical solution of multi-term fractional differential equations is proposed. The method is based on transforming the original equation into an equivalent system of multi-order fractional equations. This system is discretized by fractional derivatives of Riesz spline wavelets and the collocation method. Then the original problem is transformed into a system of algebraic equations and can be easily solved. Finally, several numerical examples and comparisons with other methods are provided to demonstrate the efficiency and accuracy of our approach.
{"title":"Numerical solution of nonlinear multi-term fractional differential equations based on spline Riesz wavelets","authors":"Wei Tang, Da Xu","doi":"10.1016/j.amc.2025.129359","DOIUrl":"10.1016/j.amc.2025.129359","url":null,"abstract":"<div><div>In this article, a direct method for the numerical solution of multi-term fractional differential equations is proposed. The method is based on transforming the original equation into an equivalent system of multi-order fractional equations. This system is discretized by fractional derivatives of Riesz spline wavelets and the collocation method. Then the original problem is transformed into a system of algebraic equations and can be easily solved. Finally, several numerical examples and comparisons with other methods are provided to demonstrate the efficiency and accuracy of our approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129359"},"PeriodicalIF":3.5,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403629","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}
Pub Date : 2025-02-11DOI: 10.1016/j.amc.2025.129347
Yuliang Cai , Youtong Wang , Hanguang Su , Lianyan Fu , Qiang He
This paper addresses the bipartite leader-following consensus problem for general linear multi-agent systems (MASs) with unknown disturbances under directed communication topology. A novel control strategy is proposed to effectively mitigate disturbances and reduce unnecessary triggering actions, thereby conserving resources. The strategy consists of double dynamic event-triggered mechanisms (DDETM) that operate independently: one governs inter-agent communication, while the other determines controller updates. To prevent Zeno behavior, additional constants are introduced into the triggering mechanisms. Moreover, a simplified parameter selection method is developed, eliminating the need for verifying solutions to specific matrix inequalities. Finally, comprehensive simulation experiments are conducted to demonstrate the effectiveness and practicality of the proposed approach.
{"title":"Bipartite leader-following consensus of linear multi-agent systems with unknown disturbances under directed graphs by double dynamic event-triggered mechanism","authors":"Yuliang Cai , Youtong Wang , Hanguang Su , Lianyan Fu , Qiang He","doi":"10.1016/j.amc.2025.129347","DOIUrl":"10.1016/j.amc.2025.129347","url":null,"abstract":"<div><div>This paper addresses the bipartite leader-following consensus problem for general linear multi-agent systems (MASs) with unknown disturbances under directed communication topology. A novel control strategy is proposed to effectively mitigate disturbances and reduce unnecessary triggering actions, thereby conserving resources. The strategy consists of double dynamic event-triggered mechanisms (DDETM) that operate independently: one governs inter-agent communication, while the other determines controller updates. To prevent Zeno behavior, additional constants are introduced into the triggering mechanisms. Moreover, a simplified parameter selection method is developed, eliminating the need for verifying solutions to specific matrix inequalities. Finally, comprehensive simulation experiments are conducted to demonstrate the effectiveness and practicality of the proposed approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129347"},"PeriodicalIF":3.5,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143388414","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}
Pub Date : 2025-02-10DOI: 10.1016/j.amc.2025.129316
Yingxue Hou , Yan-Jun Liu , Shaocheng Tong
This paper is devoted to solving the finite-time fault-tolerant tracking control problem based on event-triggered control (ETC) strategy for multi-input-multi-output (MIMO) switched nonlinear systems, which are simultaneously subject to unknown sensor and actuator faults. A switched state observer with fault estimation is designed to compensate unknown sensor fault parameter and unavailable states online, while fuzzy logic systems (FLSs) are employed to identify the uncertainties. The shortcoming of “explosion of complexity” is mitigated by fusing backstepping control and command filter. To trade off the communication resources and the system performance, a event-triggered finite-time fault-tolerant control (FTC) scheme with adaptive parameter compensation mechanism is developed, which can alleviate the impact of actuator and sensor faults by designing different parameter adaptive laws, and ensures all signals are semiglobal practical finite-time stable (SGPFS). Furthermore, a mass spring damper system is applied to verify the performance of the proposed control method.
{"title":"Event-triggered fault-compensation-based fuzzy finite-time FTC for MIMO switched nonlinear systems","authors":"Yingxue Hou , Yan-Jun Liu , Shaocheng Tong","doi":"10.1016/j.amc.2025.129316","DOIUrl":"10.1016/j.amc.2025.129316","url":null,"abstract":"<div><div>This paper is devoted to solving the finite-time fault-tolerant tracking control problem based on event-triggered control (ETC) strategy for multi-input-multi-output (MIMO) switched nonlinear systems, which are simultaneously subject to unknown sensor and actuator faults. A switched state observer with fault estimation is designed to compensate unknown sensor fault parameter and unavailable states online, while fuzzy logic systems (FLSs) are employed to identify the uncertainties. The shortcoming of “explosion of complexity” is mitigated by fusing backstepping control and command filter. To trade off the communication resources and the system performance, a event-triggered finite-time fault-tolerant control (FTC) scheme with adaptive parameter compensation mechanism is developed, which can alleviate the impact of actuator and sensor faults by designing different parameter adaptive laws, and ensures all signals are semiglobal practical finite-time stable (SGPFS). Furthermore, a mass spring damper system is applied to verify the performance of the proposed control method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"496 ","pages":"Article 129316"},"PeriodicalIF":3.5,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376735","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}
Pub Date : 2025-02-07DOI: 10.1016/j.amc.2025.129337
Wen-Biao Gao
The two-dimensional fractional Fourier transform (FrFT) has very important applications in applied mathematics and signal processing. The polar coordinate form can not only enables the definitions of instantaneous amplitude, instantaneous phase, and the instantaneous frequency of a signal, but also extract some features that cannot be directly observed in the real signal. In this paper, we study the problem of correlation theorem and applications in the FrFT domain based on the polar coordinates. First, shift theorem and product theorem associated with the FrFT are exploited. Then, a correlation theorem of the FrFT is achieved according to the shift theorem. Furthermore, the relationship between the product theorem and the correlation theorem for the FrFT is established. Finally, we explored the possible applications of the obtained results of the FrFT on time-frequency representation, equation solving, and fast algorithm.
{"title":"Correlation theorem and applications associated with the fractional Fourier transform in polar coordinates","authors":"Wen-Biao Gao","doi":"10.1016/j.amc.2025.129337","DOIUrl":"10.1016/j.amc.2025.129337","url":null,"abstract":"<div><div>The two-dimensional fractional Fourier transform (FrFT) has very important applications in applied mathematics and signal processing. The polar coordinate form can not only enables the definitions of instantaneous amplitude, instantaneous phase, and the instantaneous frequency of a signal, but also extract some features that cannot be directly observed in the real signal. In this paper, we study the problem of correlation theorem and applications in the FrFT domain based on the polar coordinates. First, shift theorem and product theorem associated with the FrFT are exploited. Then, a correlation theorem of the FrFT is achieved according to the shift theorem. Furthermore, the relationship between the product theorem and the correlation theorem for the FrFT is established. Finally, we explored the possible applications of the obtained results of the FrFT on time-frequency representation, equation solving, and fast algorithm.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129337"},"PeriodicalIF":3.5,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143242667","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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