Applied Mathematics and Computation最新文献

{"title":"The equivalent conditions for norm of a Hilbert-type integral operator with a combination kernel and its applications","authors":"Qiong Liu","doi":"10.1016/j.amc.2024.129076","DOIUrl":"10.1016/j.amc.2024.129076","url":null,"abstract":"<div><div>Introducing adaptation parameters <span><math><mi>σ</mi><mo>,</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, formal parameters <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>,</mo><mi>κ</mi><mo>,</mo><mi>τ</mi></math></span>, and type parameters <span><math><mi>μ</mi><mo>,</mo><mi>ν</mi></math></span>, the integration operator is defined as <span><math><mi>T</mi><mo>:</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>μ</mi><mover><mrow><mi>σ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo><mo>→</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mi>ν</mi><mover><mrow><mi>σ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></math></span>, <span><math><mi>T</mi><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub><mfrac><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup><mo>+</mo><mi>κ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup><mo>+</mo><mi>τ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup></mrow></mfrac><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>d</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. Using the weight function method, a general Hilbert-type integral inequality is obtained, thereby proving the boundedness of the operator. The constant factor of the general Hilbert-type inequality is the best possible if and only if the adaptation parameters satisfy <span><math><mi>σ</mi><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. From this, the formula for calculating the operator norm is obtained. In terms of application, some results from the references have been ","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316242","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}

{"title":"Signed total Roman domination and domatic numbers in graphs","authors":"Yubao Guo , Lutz Volkmann , Yun Wang","doi":"10.1016/j.amc.2024.129074","DOIUrl":"10.1016/j.amc.2024.129074","url":null,"abstract":"<div><div>A signed total Roman dominating function (STRDF) on a graph <em>G</em> is a function <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⟶</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span> satisfying (i) <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>x</mi><mo>∈</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mn>1</mn></math></span> for each vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and its neighborhood <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <em>G</em> and, (ii) every vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> with <span><math><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mo>−</mo><mn>1</mn></math></span>, there exists a vertex <span><math><mi>v</mi><mo>∈</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> with <span><math><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn></math></span>. The minimum number <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> among all STRDFs <em>f</em> on <em>G</em> is denoted by <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. A set <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>}</mo></math></span> of distinct STRDFs on <em>G</em> is called a signed total Roman dominating family on <em>G</em> if <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span> for each <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. We use <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> to denote the maximum number of functions among all signed total Roman dominating families on <em>G</em>. Our purpose in this paper is to examine the effects on <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> when <em>G</em> is modified by removing or subdividing an edge. In addition, we determine the number <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> for the case that <em>G</em> is a complete g","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316241","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}

{"title":"Event-triggered sampling-based singularity-free fixed-time control for nonlinear systems subject to input saturation and unknown control directions","authors":"Xiaojing Qi,&nbsp;Shengyuan Xu","doi":"10.1016/j.amc.2024.129070","DOIUrl":"10.1016/j.amc.2024.129070","url":null,"abstract":"<div><p>In this paper, the issue of event-triggered fixed-time tracking control is investigated for a class of nonlinear systems subject to unknown control directions (UCDs) and asymmetric input saturation. Firstly, to cope with the design challenge imposed by nondifferential saturation nonlinearity in the system, the asymmetric saturation function is approached by introducing a smooth nonlinear function with respect to the control input signal. Secondly, a variable separation technique lemma is developed to remove the restrictive growth conditions that must be fulfilled by the nonlinear functions, and a new practically fixed-time stability lemma with more accurate upper-bound estimate of the settling time is put forward by means of the Beta function. Then, a technical lemma regarding a class of type-B Nussbaum functions (NFs) with unique properties is introduced, which avoids specific NFs-based complex stability analysis. Moreover, in compensation for the sampling error incurred by the event-triggered mechanism under UCDs, an adaptive law is skillfully constructed to co-design the fixed-time control law and the event-triggered mechanism. The results show that the controlled system is practically fixed-time stable (PFxTS), the tracking error can converge to a small neighborhood of the origin in a fixed time, and the saturation constraint is satisfied while reducing the communication burden. Finally, the effectiveness of the practically fixed-time stability criterion and control method developed in this study are verified by two simulation examples.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238253","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}

{"title":"Analysis of α-fractal functions without boundary point conditions on the Sierpiński gasket","authors":"Gurubachan ,&nbsp;V.V.M.S. Chandramouli ,&nbsp;S. Verma","doi":"10.1016/j.amc.2024.129072","DOIUrl":"10.1016/j.amc.2024.129072","url":null,"abstract":"<div><p>This note aims to manifest the existence of a class of <em>α</em>-fractal interpolation functions (<em>α</em>-FIFs) without boundary point conditions at the <em>m</em>-th level in the space consisting of continuous functions on the Sierpiński gasket (<em>SG</em>). Furthermore, we add the existence of the same class in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> space and energy space on <em>SG</em>. Under certain hypotheses, we show the existence of <em>α</em>-FIFs without boundary point conditions in the Hölder space and oscillation space on <em>SG</em>, and also calculate the fractal dimensions of their graphs.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238254","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}

{"title":"Efficient finite element strategy using enhanced high-order and second-derivative-free variants of Newton's method","authors":"Aymen Laadhari ,&nbsp;Helmi Temimi","doi":"10.1016/j.amc.2024.129058","DOIUrl":"10.1016/j.amc.2024.129058","url":null,"abstract":"<div><p>In this work, we propose a stable finite element approximation by extending higher-order Newton's method to the multidimensional case for solving nonlinear systems of partial differential equations. This approach relies solely on the evaluation of Jacobian matrices and residuals, eliminating the need for computing higher-order derivatives. Achieving third and fifth-order convergence, it ensures stability and allows for significantly larger time steps compared to explicit methods. We thoroughly address accuracy and convergence, focusing on the singular <em>p</em>-Laplacian problem and the time-dependent lid-driven cavity benchmark. A globalized variant incorporating a continuation technique is employed to effectively handle high Reynolds number regimes. Through two-dimensional and three-dimensional numerical experiments, we demonstrate that the improved cubically convergent variant outperforms others, leading to substantial computational savings, notably halving the computational cost for the lid-driven cavity test at large Reynolds numbers.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228735","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}

{"title":"On the dynamics of a linear-hyperbolic population model with Allee effect and almost sure extinction","authors":"J.S. Cánovas,&nbsp;M. Muñoz-Guillermo","doi":"10.1016/j.amc.2024.129005","DOIUrl":"10.1016/j.amc.2024.129005","url":null,"abstract":"<div><p>This paper considers a biological model in which two stages of the population, adults and preadults, are modeled by a Beverton-Holt type function and a logistic-type function. Two new models are proposed, each with an additional parameter representing the compensation. This new parameter is introduced in adult and juvenile populations. As a result, the Allee effect is observed in both models. The scenario of almost sure extinction can appear when the dynamic is chaotic enough.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173692","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}

{"title":"The guidance of neutral human populations maintains cooperation in the prisoner's dilemma game","authors":"Tao You ,&nbsp;Linjiang Yang ,&nbsp;Jian Wang ,&nbsp;Peng Zhang ,&nbsp;Jinchao Chen ,&nbsp;Ying Zhang","doi":"10.1016/j.amc.2024.129071","DOIUrl":"10.1016/j.amc.2024.129071","url":null,"abstract":"<div><p>In game theory, the emergence and maintenance of cooperative behavior within a group is a significant topic in evolutionary game theory and complex network theory. However, the limitations of a single mechanism in traditional networks restrict a thorough analysis of the sustenance and development of cooperative behavior, given the challenges posed by the diversity of social groups. To address this issue, this paper combines reinforcement learning game strategies with traditional prisoner's dilemma strategies based on two-layer coupled network to investigate the transmission of cooperative behavior among individuals in games. In our research, we study the evolutionary pattern and phase transitions using the Monte Carlo method. We use the prisoner's dilemma game as a mathematical model, establishing two subpopulations in each layer, with mutually payoff-neutral players between different subpopulations. This configuration results in intriguing spatiotemporal dynamics and patterns, leading to the spontaneous emergence of a cyclic dominance, where defectors from one group become prey for cooperators in another group, and vice versa. By simulating game evolution, we explore individual strategy changes and the impact of individual abilities on cooperative behavior in reinforcement learning. Extensive validations indicate that, in social dilemmas, adjusting the abilities of groups through effective guidance can sustain cooperative behavior. This guidance enables us to comprehend the stability of cooperation under adverse conditions. Simultaneously, the coexistence of two subpopulations greatly amplifies the complexity of evolutionary dynamics, causing a increase in cooperation rate.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173693","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}

{"title":"Multiple exponential stability for short memory fractional impulsive Cohen-Grossberg neural networks with time delays","authors":"Jinsen Zhang,&nbsp;Xiaobing Nie","doi":"10.1016/j.amc.2024.129066","DOIUrl":"10.1016/j.amc.2024.129066","url":null,"abstract":"<div><p>Different from the existing multiple asymptotic stability or multiple Mittag-Leffler stability, the multiple exponential stability with explicit and faster convergence rate is addressed in this paper for short memory fractional-order impulsive Cohen-Grossberg neural networks with time delay. Firstly, <span><math><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><mn>2</mn><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></math></span> total equilibrium points of such <em>n</em>-neuron neural networks can be ensured via the known fixed point theorem. Then, by means of the theory of fractional-order differential equations, the methods of average impulsive interval and Lyapunov function, a series of sufficient conditions for determining the locally exponential stability of <span><math><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></math></span> equilibrium points are obtained based on maximum norm, 1-norm and general <em>q</em>-norm (<span><math><mi>q</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span>), respectively. This paper's research reveals the effects of impulsive function, impulsive interval, fractional order and time delay on the dynamic behaviors. Finally, four examples are proposed to demonstrate the effectiveness of theoretic achievements.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169042","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}

{"title":"Numerical integration of mechanical forces in center-based models for biological cell populations","authors":"Per Lötstedt,&nbsp;Sonja Mathias","doi":"10.1016/j.amc.2024.129069","DOIUrl":"10.1016/j.amc.2024.129069","url":null,"abstract":"<div><p>Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to many thousands or more, these models have to be numerically efficient, while being reasonably accurate on the level of individual cell trajectories. In this work, we increase the robustness, accuracy, and efficiency of the simulation of center-based models by choosing the time steps adaptively in the numerical method and comparing five different integration methods. We investigate the gain in using single rate time stepping based on local estimates of the numerical errors for the forward and backward Euler methods of first order accuracy and a Runge-Kutta method and the trapezoidal method of second order accuracy. Properties of the analytical solution such as convergence to steady state and conservation of the center of gravity are inherited by the numerical solutions. Furthermore, we propose a multirate time stepping scheme that simulates regions with high local force gradients (e.g. as they happen after cell division) with multiple smaller time steps within a larger single time step for regions with smoother forces. These methods are compared for a model system in numerical experiments. We conclude, for example, that the multirate forward Euler method performs better than the Runge-Kutta method for low accuracy requirements but for higher accuracy the latter method is preferred. Only with frequent cell divisions the method with a fixed time step is the best choice.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169040","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}

{"title":"Fixed-time active fault-tolerant control for dynamical systems with intermittent faults and unknown disturbances","authors":"Xuanrui Cheng ,&nbsp;Ming Gao ,&nbsp;Wuxiang Huai ,&nbsp;Yichun Niu ,&nbsp;Li Sheng","doi":"10.1016/j.amc.2024.129054","DOIUrl":"10.1016/j.amc.2024.129054","url":null,"abstract":"<div><p>In this article, the problem of fixed-time active fault-tolerant control is investigated for dynamical linear systems with intermittent faults and unknown disturbances. Unlike traditional active fault-tolerant control, fixed-time control is taken into account in this article since intermittent faults appear and disappear within a certain period of time. The entire active fault-tolerant control framework is composed of fault detection, fault isolation, fault and state estimation as well as the reconfigurable controller. Using the homogeneity-based observers, states and faults are well estimated and a fault diagnosis scheme is proposed for the sake of detecting and isolating intermittent faults in a fixed time. The fault-tolerant controller, which provides global practical fixed-time stability of the closed-loop system, has two switching states corresponding to the appearance and disappearance of intermittent faults. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, two examples are exploited to demonstrate the effectiveness of theoretical results.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169043","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}