Pub Date : 2026-05-01Epub Date: 2025-12-04DOI: 10.1016/j.amc.2025.129882
Xiaoqi Ma, Jin Zhang, Xinyi Feng, Chunxiao Zhang
This paper investigates the supercloseness of a singularly perturbed convection diffusion problem discretized by the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical challenges involve controlling the diffusion term inside the layer, the convection term outside the layer, and the inter-element jump terms induced by the discontinuity of the numerical solution. To address these issues, we design a new composite interpolation. Outside the layer, a global projection is employed to satisfy the interface conditions imposed by the numerical flux, which helps eliminate or control the problematic terms across element interfaces. Inside the layer, the Gauß-Lobatto projection is adopted to enhance the convergence order of the diffusion term. Based on this interpolation and an appropriate choice of parameters in the numerical flux, we derive a supercloseness result of order nearly when the perturbation parameter , which improves to order in an energy norm for . Numerical experiments provided to support the theoretical findings.
{"title":"Supercloseness of the DDG method for a singularly perturbed convection diffusion problem on Shishkin mesh","authors":"Xiaoqi Ma, Jin Zhang, Xinyi Feng, Chunxiao Zhang","doi":"10.1016/j.amc.2025.129882","DOIUrl":"10.1016/j.amc.2025.129882","url":null,"abstract":"<div><div>This paper investigates the supercloseness of a singularly perturbed convection diffusion problem discretized by the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical challenges involve controlling the diffusion term inside the layer, the convection term outside the layer, and the inter-element jump terms induced by the discontinuity of the numerical solution. To address these issues, we design a new composite interpolation. Outside the layer, a global projection is employed to satisfy the interface conditions imposed by the numerical flux, which helps eliminate or control the problematic terms across element interfaces. Inside the layer, the Gauß-Lobatto projection is adopted to enhance the convergence order of the diffusion term. Based on this interpolation and an appropriate choice of parameters in the numerical flux, we derive a supercloseness result of order nearly <span><math><mrow><mi>k</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></math></span> when the perturbation parameter <span><math><mrow><mi>ϵ</mi><mo>≤</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>, which improves to order <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> in an energy norm for <span><math><mrow><mi>ϵ</mi><mo>≤</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math></span>. Numerical experiments provided to support the theoretical findings.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"516 ","pages":"Article 129882"},"PeriodicalIF":3.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685408","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 : 2026-05-01Epub Date: 2025-12-03DOI: 10.1016/j.amc.2025.129844
Yulin Gai, Yue Sun, Ming Chen, Libing Wu, Kaixiang Peng, Huanqing Wang
For a class of strict-feedback nonlinear systems, an adaptive finite-time tracking control scheme is proposed in this study. First, a fuzzy state observer is introduced to estimate the unmeasurable states. The notable innovation of this design lies in the integration of differential explosion, control law saturation, fuzzy observers and finite-time control during the controller design process. Specifically, a novel smooth approximating function is introduced to enhance the accuracy of saturation computation. Simultaneously, the scheme compensates for the adverse effect of input saturation through virtual control law saturation. Finally, the numerical simulation and single-joint robotic arm system show that the proposed scheme not only has theoretical value, but also has significant practical significance.
{"title":"Adaptive finite-time tracking control of strict-feedback nonlinear systems based on control law saturation","authors":"Yulin Gai, Yue Sun, Ming Chen, Libing Wu, Kaixiang Peng, Huanqing Wang","doi":"10.1016/j.amc.2025.129844","DOIUrl":"10.1016/j.amc.2025.129844","url":null,"abstract":"<div><div>For a class of strict-feedback nonlinear systems, an adaptive finite-time tracking control scheme is proposed in this study. First, a fuzzy state observer is introduced to estimate the unmeasurable states. The notable innovation of this design lies in the integration of differential explosion, control law saturation, fuzzy observers and finite-time control during the controller design process. Specifically, a novel smooth approximating function is introduced to enhance the accuracy of saturation computation. Simultaneously, the scheme compensates for the adverse effect of input saturation through virtual control law saturation. Finally, the numerical simulation and single-joint robotic arm system show that the proposed scheme not only has theoretical value, but also has significant practical significance.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"516 ","pages":"Article 129844"},"PeriodicalIF":3.4,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145657520","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 : 2026-04-15Epub Date: 2025-11-29DOI: 10.1016/j.amc.2025.129850
Haifeng Ma , Hongbo Chen , Predrag S. Stanimirović
This text explores characterizations of the BT inverse and proposes several methods for calculating the BT inverse. One of the representations examines the invertibility of an appropriate bordered matrix whose lower right block coincides with the BT inverse. Considerations of the BT inverse in relation to the group inverse and the standard matrix inverse are discussed. It is verified that the BT inverse solution is the unique solution to a specific class of constrained singular linear equations. Utilizing Cramer’s rule, we derive elementnwise solution of such systems. We also develop iterative methods for calculating the BT inverse and provide a criterion for the convergence of these methods. Modifications of the successive matrix square algorithm and the Newton iterative method are explored. The Singular Value Decomposition (SVD) approach for calculating the matrix BT inverse is developed. Additionally, the corresponding adopted Randomized SVD (RSVD) algorithm offers enhanced performance, making it a strong choice for large-scale data practical applications.
{"title":"Representations and computation of the BT inverse and its randomized algorithms","authors":"Haifeng Ma , Hongbo Chen , Predrag S. Stanimirović","doi":"10.1016/j.amc.2025.129850","DOIUrl":"10.1016/j.amc.2025.129850","url":null,"abstract":"<div><div>This text explores characterizations of the BT inverse and proposes several methods for calculating the BT inverse. One of the representations examines the invertibility of an appropriate bordered matrix whose lower right block coincides with the BT inverse. Considerations of the BT inverse in relation to the group inverse and the standard matrix inverse are discussed. It is verified that the BT inverse solution is the unique solution to a specific class of constrained singular linear equations. Utilizing Cramer’s rule, we derive elementnwise solution of such systems. We also develop iterative methods for calculating the BT inverse and provide a criterion for the convergence of these methods. Modifications of the successive matrix square algorithm and the Newton iterative method are explored. The Singular Value Decomposition (SVD) approach for calculating the matrix BT inverse is developed. Additionally, the corresponding adopted Randomized SVD (RSVD) algorithm offers enhanced performance, making it a strong choice for large-scale data practical applications.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129850"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145613962","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 : 2026-04-15Epub Date: 2025-11-20DOI: 10.1016/j.amc.2025.129848
Xiaonan Xia, Chen Du, Tianping Zhang, Yu Fang
An adaptive finite-time control based on command filtering and dynamic surface control (DSC) technique is developed for a class of high-order multi-agent systems (MASs) possessing input quantization and unknown time-varying input delay in this paper. A method for describing the quantization error of hysteretic uniform quantizers in high-order systems is presented in Lemma form, by which the problems of quantization error analysis in high-order systems can be solved. Command filters and the filtering error compensation signals are designed to improve the stability of control inputs, which are also capable of effectively addressing the difficulties caused by quantized input and unknown time-varying input delays. Using power reduction inequality transformation to handle high-order error terms and by constructing a Lyapunov functional applicable for high-order MASs, the difficulty of finite-time controller design under unknown input delay is overcome. Radial basis function neural networks (RBFNNs) are utilized to handle consensus errors and unknown nonlinear functions of MASs. All the signals in the closed loop systems are proved to be semi-globally finite-time practical stability (SGFPS). The validity of the proposed scheme is confirmed by means of simulation case studies.
{"title":"Finite-time dynamic surface control for uncertain high-order multi-agent systems with input quantization and unknown time-varying input delay","authors":"Xiaonan Xia, Chen Du, Tianping Zhang, Yu Fang","doi":"10.1016/j.amc.2025.129848","DOIUrl":"10.1016/j.amc.2025.129848","url":null,"abstract":"<div><div>An adaptive finite-time control based on command filtering and dynamic surface control (DSC) technique is developed for a class of high-order multi-agent systems (MASs) possessing input quantization and unknown time-varying input delay in this paper. A method for describing the quantization error of hysteretic uniform quantizers in high-order systems is presented in Lemma form, by which the problems of quantization error analysis in high-order systems can be solved. Command filters and the filtering error compensation signals are designed to improve the stability of control inputs, which are also capable of effectively addressing the difficulties caused by quantized input and unknown time-varying input delays. Using power reduction inequality transformation to handle high-order error terms and by constructing a Lyapunov functional applicable for high-order MASs, the difficulty of finite-time controller design under unknown input delay is overcome. Radial basis function neural networks (RBFNNs) are utilized to handle consensus errors and unknown nonlinear functions of MASs. All the signals in the closed loop systems are proved to be semi-globally finite-time practical stability (SGFPS). The validity of the proposed scheme is confirmed by means of simulation case studies.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129848"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145555386","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 : 2026-04-15Epub Date: 2025-11-26DOI: 10.1016/j.amc.2025.129865
Qingqing Wang , Yixian Fang , Kewen Li , Yongming Li
This article investigates the issue of the distributed fuzzy adaptive secured control for heterogeneous vehicle platoon systems (HVPS) with dynamic leaders under input saturation and denial-of-service (DoS) attacks. Then, the unknown nonlinear dynamics are approximated using fuzzy logic systems (FLSs), by introducing the compensation signal, a distributed fuzzy adaptive secure platoon controller is designed based on the Lyapunov stability theory, the developed secure control method can ensure all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the zero. Finally, the effectiveness of the proposed secure control method and theory can be validated by simulation results.
{"title":"Distributed fuzzy adaptive secured control for heterogeneous vehicle platoons under denial-of-Service attacks","authors":"Qingqing Wang , Yixian Fang , Kewen Li , Yongming Li","doi":"10.1016/j.amc.2025.129865","DOIUrl":"10.1016/j.amc.2025.129865","url":null,"abstract":"<div><div>This article investigates the issue of the distributed fuzzy adaptive secured control for heterogeneous vehicle platoon systems (HVPS) with dynamic leaders under input saturation and denial-of-service (DoS) attacks. Then, the unknown nonlinear dynamics are approximated using fuzzy logic systems (FLSs), by introducing the compensation signal, a distributed fuzzy adaptive secure platoon controller is designed based on the Lyapunov stability theory, the developed secure control method can ensure all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the zero. Finally, the effectiveness of the proposed secure control method and theory can be validated by simulation results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129865"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145598932","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 : 2026-04-15Epub Date: 2025-11-25DOI: 10.1016/j.amc.2025.129862
Huaihe Huang , Ye Ye , Wei Bao , Yue Zhang , Nenggang Xie
In evolutionary game theory, zero-determinant (ZD) strategies have become a breakthrough in the study of the Prisoner’s Dilemma due to their ability to unilaterally control payoffs. However, traditional ZD strategies—such as extortion (E) and generosity (G) strategies—suffer from imbalanced interests and limited adaptability. This paper proposes a dynamically switching PERG strategy (Poverty-Extortion, Richness-Generosity), which adaptively switches between E and G based on state-dependent mechanisms to balance the payoffs of both parties. By constructing a seven-strategy model including PERG, TFT, WSLS, E, G, C, and D, we systematically reveal the evolutionary dynamics in well-mixed populations, synthetic networks, and real-world networks. Computational simulations show that in well-mixed populations, benevolent strategies like PERG have evolutionary advantages. Smaller extortion and generosity factors can suppress the spread of the D strategy, and lower cooperation costs may weaken the incentive effect of payoffs on cooperation. In synthetic networks and real-world networks, PERG, WSLS, and G strategies rapidly invade other strategies. The benefit parameter has little impact on the distribution of dominant strategies in synthetic networks, and in BA scale-free networks, the proportion of the PERG strategy shows an upward or downward trend as specific parameters change.
{"title":"An evolutionary game analysis of a dynamically switching zero-determinant strategy","authors":"Huaihe Huang , Ye Ye , Wei Bao , Yue Zhang , Nenggang Xie","doi":"10.1016/j.amc.2025.129862","DOIUrl":"10.1016/j.amc.2025.129862","url":null,"abstract":"<div><div>In evolutionary game theory, zero-determinant (ZD) strategies have become a breakthrough in the study of the Prisoner’s Dilemma due to their ability to unilaterally control payoffs. However, traditional ZD strategies—such as extortion (E) and generosity (G) strategies—suffer from imbalanced interests and limited adaptability. This paper proposes a dynamically switching PERG strategy (Poverty-Extortion, Richness-Generosity), which adaptively switches between E and G based on state-dependent mechanisms to balance the payoffs of both parties. By constructing a seven-strategy model including PERG, TFT, WSLS, E, G, C, and D, we systematically reveal the evolutionary dynamics in well-mixed populations, synthetic networks, and real-world networks. Computational simulations show that in well-mixed populations, benevolent strategies like PERG have evolutionary advantages. Smaller extortion and generosity factors can suppress the spread of the D strategy, and lower cooperation costs may weaken the incentive effect of payoffs on cooperation. In synthetic networks and real-world networks, PERG, WSLS, and G strategies rapidly invade other strategies. The benefit parameter has little impact on the distribution of dominant strategies in synthetic networks, and in BA scale-free networks, the proportion of the PERG strategy shows an upward or downward trend as specific parameters change.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129862"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145598936","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 : 2026-04-15Epub Date: 2025-11-21DOI: 10.1016/j.amc.2025.129846
Ziwei Wu , Ning Xu , Liang Zhang , Ning Zhao , Guangjing Song
In this paper, a dynamic event-triggered bipartite consensus control strategy is proposed for a class of nonlinear multi-agent systems (MAS) with mismatched disturbances. The core idea of this strategy is to divide the subjects into two groups. In order to avoid the leakage of system information, a privacy preservation mechanism is introduced. By constructing a mask function, the state of the system is protected to enhance data confidentiality while guaranteeing system stability. Meanwhile, a disturbance observer is constructed to estimate the composite disturbance term consisting of mismatched external disturbances and approximation errors, which ensures system performances. In addition, due to limited communication bandwidth of the networked nonlinear system, a distributed event-triggered mechanism is introduced to reduce the communication burden, and the Zeno behavior is excluded. It is shown from stability analysis that signals of the overall closed-loop system can be guaranteed to be bounded. Finally, the effectiveness of the proposed strategy is verified by a numerical example.
{"title":"Privacy preservation-based dynamic event-triggered bipartite consensus strategy for nonlinear multi-agent systems with unknown mismatched disturbances","authors":"Ziwei Wu , Ning Xu , Liang Zhang , Ning Zhao , Guangjing Song","doi":"10.1016/j.amc.2025.129846","DOIUrl":"10.1016/j.amc.2025.129846","url":null,"abstract":"<div><div>In this paper, a dynamic event-triggered bipartite consensus control strategy is proposed for a class of nonlinear multi-agent systems (MAS) with mismatched disturbances. The core idea of this strategy is to divide the subjects into two groups. In order to avoid the leakage of system information, a privacy preservation mechanism is introduced. By constructing a mask function, the state of the system is protected to enhance data confidentiality while guaranteeing system stability. Meanwhile, a disturbance observer is constructed to estimate the composite disturbance term consisting of mismatched external disturbances and approximation errors, which ensures system performances. In addition, due to limited communication bandwidth of the networked nonlinear system, a distributed event-triggered mechanism is introduced to reduce the communication burden, and the Zeno behavior is excluded. It is shown from stability analysis that signals of the overall closed-loop system can be guaranteed to be bounded. Finally, the effectiveness of the proposed strategy is verified by a numerical example.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129846"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145555390","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 : 2026-04-15Epub Date: 2025-11-20DOI: 10.1016/j.amc.2025.129854
Gerasim V. Krivovichev , Ksenia I. Semina
This paper is devoted to the construction and analysis of gradient methods based on the explicit second-order Runge–Kutta method with a non-standard finite difference. The application of this type of finite difference provides the possibility to use the function of step instead of the step value (like in standard gradient descent) and add new parameters for the improvement of stability and convergence rate. The preconditioned gradient descent method and its version with momentum (heavy ball method) are constructed. Theorems on convergence conditions for a strongly convex quadratic function and its perturbation are formulated.
The numerical approaches for obtaining optimal parameters for two methods are proposed. Optimal convergence rates are compared with the optimal rates for well-known first-order methods with constant parameters (standard gradient descent, Polyak’s heavy ball method, and Nesterov’s accelerated methods). Theoretical analysis is supported by the numerical experiments carried out on problems from different applications (2D and 3D Dirichlet problems for the Poisson equation, minimization of integral functional, problem for nonlinear integro-differential equation, and regularized logistic regression). It is demonstrated that the preconditioned method with momentum performs better than well-known methods with constant parameters, used for comparison.
{"title":"Application of Runge–Kutta method with non-standard finite difference for the construction of preconditioned gradient methods","authors":"Gerasim V. Krivovichev , Ksenia I. Semina","doi":"10.1016/j.amc.2025.129854","DOIUrl":"10.1016/j.amc.2025.129854","url":null,"abstract":"<div><div>This paper is devoted to the construction and analysis of gradient methods based on the explicit second-order Runge–Kutta method with a non-standard finite difference. The application of this type of finite difference provides the possibility to use the function of step instead of the step value (like in standard gradient descent) and add new parameters for the improvement of stability and convergence rate. The preconditioned gradient descent method and its version with momentum (heavy ball method) are constructed. Theorems on convergence conditions for a strongly convex quadratic function and its perturbation are formulated.</div><div>The numerical approaches for obtaining optimal parameters for two methods are proposed. Optimal convergence rates are compared with the optimal rates for well-known first-order methods with constant parameters (standard gradient descent, Polyak’s heavy ball method, and Nesterov’s accelerated methods). Theoretical analysis is supported by the numerical experiments carried out on problems from different applications (2D and 3D Dirichlet problems for the Poisson equation, minimization of integral functional, problem for nonlinear integro-differential equation, and regularized logistic regression). It is demonstrated that the preconditioned method with momentum performs better than well-known methods with constant parameters, used for comparison.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129854"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145555387","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}
This study proposes an innovative switching ET (event-triggered) control framework for parabolic partial differential equation (PDE) systems under dual uncertainties from unknown dynamics and external disturbances. First, a dual-scale decomposition integrating multilayer neural networks and Galerkin spectral methods to decouple PDE dynamics into relatively accurate slow/fast subsystems and enable model-free nonlinearity identification via Levenberg-Marquardt algorithm. Second, a dwell-time-regulated switching ET mechanism significantly reducing communication frequency compared to conventional periodic sampling or static ET while guaranteeing to avoid Zeno behavior through time-domain constraints. Third, sub-optimal H∞ performance is achieved via an iterative algorithm based on the alternating optimization of convex linear matrix inequality subproblems. Finally, validated through two numerical simulations: catalytic reactor and traffic flow, the framework establishes a new paradigm for industrial thermal-chemical processes requiring reliability under communication constraints.
{"title":"Switching event-triggered control of nonlinear parabolic PDE systems via Galerkin/neural-network-based modeling approach","authors":"Xiaoyu Sun , Chuan Zhang , Huai-Ning Wu , Xianfu Zhang","doi":"10.1016/j.amc.2025.129833","DOIUrl":"10.1016/j.amc.2025.129833","url":null,"abstract":"<div><div>This study proposes an innovative switching ET (event-triggered) control framework for parabolic partial differential equation (PDE) systems under dual uncertainties from unknown dynamics and external disturbances. First, a dual-scale decomposition integrating multilayer neural networks and Galerkin spectral methods to decouple PDE dynamics into relatively accurate slow/fast subsystems and enable model-free nonlinearity identification via Levenberg-Marquardt algorithm. Second, a dwell-time-regulated switching ET mechanism significantly reducing communication frequency compared to conventional periodic sampling or static ET while guaranteeing to avoid Zeno behavior through time-domain constraints. Third, sub-optimal <em>H</em><sub>∞</sub> performance is achieved via an iterative algorithm based on the alternating optimization of convex linear matrix inequality subproblems. Finally, validated through two numerical simulations: catalytic reactor and traffic flow, the framework establishes a new paradigm for industrial thermal-chemical processes requiring reliability under communication constraints.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129833"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145592981","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 : 2026-04-15Epub Date: 2025-11-26DOI: 10.1016/j.amc.2025.129863
Xiaozhou Feng , Yang Lei , Fei Xie , Changtong Li , Yuzhen Wang , Xiaojia Wang , Tingting Li
This paper investigates a time-delayed fractional SIR epidemic model incorporating a saturated incidence rate. First, the existence of endemic equilibria is investigated under different conditions, and the basic reproduction number is calculated utilizing the next-generation matrix method. Then, the global and local asymptotic stability of equilibrium points are analyzed. For the time delay , global asymptotic stability conditions are obtained by constructing a Lyapunov function. Finally, through Hopf bifurcation analysis, the influence of the fractional order on the system’s dynamic behavior is discussed. This study provides epidemiological insights that inform practical measures for managing infectious disease outbreaks: (i) During the initial epidemic stage, it is crucial to minimize the response delay to prevent exceeding the critical bifurcation threshold; (ii) The stability of epidemic containment systems can be significantly enhanced by adjusting the fractional order appropriately.
{"title":"Stability analysis and Hopf bifurcation in a time-delayed fractional epidemic model","authors":"Xiaozhou Feng , Yang Lei , Fei Xie , Changtong Li , Yuzhen Wang , Xiaojia Wang , Tingting Li","doi":"10.1016/j.amc.2025.129863","DOIUrl":"10.1016/j.amc.2025.129863","url":null,"abstract":"<div><div>This paper investigates a time-delayed fractional SIR epidemic model incorporating a saturated incidence rate. First, the existence of endemic equilibria is investigated under different conditions, and the basic reproduction number is calculated utilizing the next-generation matrix method. Then, the global and local asymptotic stability of equilibrium points are analyzed. For the time delay <span><math><mrow><mi>τ</mi><mo>=</mo><mn>0</mn></mrow></math></span>, global asymptotic stability conditions are obtained by constructing a Lyapunov function. Finally, through Hopf bifurcation analysis, the influence of the fractional order on the system’s dynamic behavior is discussed. This study provides epidemiological insights that inform practical measures for managing infectious disease outbreaks: (i) During the initial epidemic stage, it is crucial to minimize the response delay to prevent exceeding the critical bifurcation threshold; (ii) The stability of epidemic containment systems can be significantly enhanced by adjusting the fractional order appropriately.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"515 ","pages":"Article 129863"},"PeriodicalIF":3.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145598933","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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