Applied Mathematics and Computation最新文献

{"title":"Reinforcement learning-based adaptive event-triggered control of multi-agent systems with time-varying dead-zone","authors":"Xin Li ,&nbsp;Dakuo He ,&nbsp;Qiang Zhang ,&nbsp;Hailong Liu","doi":"10.1016/j.amc.2024.129059","DOIUrl":"10.1016/j.amc.2024.129059","url":null,"abstract":"<div><p>In this paper, a novel reinforcement learning (RL)-based adaptive event-triggered control problem is studied for non-affine multi-agent systems (MASs) with time-varying dead-zone. The purpose is to design an efficient event-triggered mechanism to achieve optimal control of MASs. Compared with the existing results, an improved smooth event-triggered mechanism is proposed, which not only overcomes the design difficulties caused by discontinuous trigger signals, but also reduces the waste of communication resources. In order to achieve optimal event-triggered control, RL algorithm of the identifier-critic-actor structure based on fuzzy logic systems (FLSs) is applied to estimate system dynamics, evaluate control performance, and execute control behavior, respectively. In addition, considering time-varying dead-zone in non-affine MASs brings obstacles to controller design, which makes system applications more generalized. Through Lyapunov theory, it is proved that the optimal control performance can be achieved and the tracking error converges to a small neighborhood of the origin. Finally, simulation proves the feasibility of the proposed method.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161868","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":"Estimation-based event-triggered fixed-time fuzzy tracking control for high-order nonlinear systems","authors":"Junchang Zhai ,&nbsp;Huanqing Wang ,&nbsp;Yuping Qin ,&nbsp;Hongxia Cui","doi":"10.1016/j.amc.2024.129057","DOIUrl":"10.1016/j.amc.2024.129057","url":null,"abstract":"<div><p>This paper investigates adaptive-estimation-based dynamic event-triggered fuzzy tracking control scheme for high-order nonlinear systems in fixed-time interval. The growing assumptions of coexistence unknown nonlinear uncertainties are removed with the aid of fuzzy logic systems. Contrary to the existing results, an adaptive estimation tactic is formulated to estimate the severe coexistence uncertainties online such that no boundaries are needed for the adaptive parameters, despite approximation errors, unknown virtual control gains and time-varying disturbances. On this estimation mechanism, the virtual control gains have been relaxed to unknown, which is more applicable. In view of controller and actuator, the communication burden is reduced with the aid of dynamic event-triggered rule, and Zeno behavior can be prevented successfully during dynamic sampling and updating of the control signal. Moreover, the singularity problem has been conquered by using the inequality transformation technique and all signals are bounded in fixed-time interval. Finally, two examples are used to verify the feasibility and rationality.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0096300324005186/pdfft?md5=1e969d0c5e40f9796da50f61adc9a586&pid=1-s2.0-S0096300324005186-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161869","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}

{"title":"Pinning passivity and bipartite synchronization of fractional signed networks without gauge transformation","authors":"Yu Sun ,&nbsp;Cheng Hu ,&nbsp;Juan Yu","doi":"10.1016/j.amc.2024.129067","DOIUrl":"10.1016/j.amc.2024.129067","url":null,"abstract":"<div><p>Recently, passivity of fractional complex networks has aroused much interest, but the concerned models contain only cooperative relationships and the competitive interaction among individuals is ignored. In this article, a class of fractional complex networks with a signed graph is considered and several conditions are derived to achieve the passivity of fractional signed networks by pinning strategies designed based on M-matrix theory. Particularly, in pinning adaptive control schemes, the pinning nodes are selected only according to the cooperative relationships among nodes and the control gains can regulate automatically to meet the actual demand. In addition, without translating the signed networks into corresponding unsigned networks based on the gauge transformation, some criteria of bipartite synchronization for fractional signed networks are obtained based on the feature of the signed topology and the derived passivity results. The theoretical results are eventually verified by several illustrate examples.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161867","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":"Stable generalized finite element for two-dimensional and three-dimensional non-homogeneous interface problems","authors":"Jiajun Li,&nbsp;Ying Jiang","doi":"10.1016/j.amc.2024.129056","DOIUrl":"10.1016/j.amc.2024.129056","url":null,"abstract":"<div><p>In this paper, we propose a Stable Generalized Finite Element Method (SGFEM) to address non-homogeneous elliptic interface problems with discontinuous coefficients. Our approach utilizes the homogenization method to transform non-homogeneous interface conditions into homogeneous ones, thereby facilitating the application of the SGFEM. Specifically, we construct functions that satisfy the jump conditions, streamlining the problem-solving process. In the SGFEM, enrichment functions are used to efficiently construct these specialized functions, reducing the computational demands of the homogenization method. Notably, this method involves only calculations of additional right-hand terms near the interface, which require significantly less computation compared to the calculation of the stiffness matrix, thus avoiding any alterations to the stiffness matrix and preserving the stability and robustness of the SGFEM. We apply our method in both two-dimensional and three-dimensional scenarios, employing distinct strategies for each. In the 2D examples, the displacement homogenization method simplifies the implementation by addressing only the displacement jumps, thereby reducing the computational load. In the 3D examples, the synchronous homogenization method further simplifies numerical implementation by eliminating surface integrals on the interface. Through error analysis and numerical experiments, we demonstrate the efficiency and optimal convergence of our proposed method.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161866","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":"Zero-determinant strategy of finite games with implementation errors and its application into group decision-making","authors":"Zhipeng Zhang ,&nbsp;Xiaotong Jiang ,&nbsp;Chengyi Xia","doi":"10.1016/j.amc.2024.129055","DOIUrl":"10.1016/j.amc.2024.129055","url":null,"abstract":"<div><p>The zero-determinant (ZD) strategy provides a new perspective for describing the interaction between players, and the errors among them will be an important role in designing ZD strategy, which attracts a lot of researches in various fields. This paper investigates how to design ZD strategy for multiplayer two-strategy repeated finite game under implementation errors. First, the implementation errors can be introduced by breaking down the probabilities of different possible cases, and the model of strategy transition process can be constructed with the semi-tensor product (STP) of matrices. Second, through the classical ZD strategy acquisition method, the step for designing ZD strategy for multiplayer two-strategy repeated finite games under implementation errors is presented. Then, the sufficient and necessary conditions for checking the effectiveness of ZD strategy under implementation errors are studied. In addition, by distinguishing the focal player's neighbors, the current approach is extended to networked evolutionary game (NEG) under implementation errors for group decision-making, and an intelligent algorithm is also provided. Finally, we use two examples to demonstrate the validity of our proposed method.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142143972","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":"A payoff equality perspective for evolutionary games: Mental accounting and cooperation promotion","authors":"Yandi Liu ,&nbsp;Yonghui Li","doi":"10.1016/j.amc.2024.129039","DOIUrl":"10.1016/j.amc.2024.129039","url":null,"abstract":"<div><p>The secret behind cooperation with the present profit-pursuing nature has been unveiled via the Evolutionary Game Theory and models. However, the payoff equality is not sufficiently explored. This paper proposes a simple but efficient way to focus on the synergetic behaviors of payoff equality and cooperation improvement. Herein, the classical Evolutional Game model is re-evaluated from the perspective of payoff equality. By assuming the similarity between the value function in “mental accounting effect” and the inverse of the Lorenz curve, the “rank strategy” is introduced in the form of a slightly alternated Fermi strategy which focuses on the rank difference on the wealth (payoff) distribution curve along the calculation of the Gini coefficient. Such introduction opens up a new perspective to the cross section between economics and the evolutionary game theory. Compared with the original Fermi strategy adoption (named payoff strategy), the rank strategy significantly aids the system to survive a higher benefit with a faster recovery after the enduring period. The reason behind this can be discussed from the formation of giant clusters, which also indicates a spillover effect in both cooperation and payoff equality improvement. A further breakdown in the population also suggests the leading role of rich players who help poor players in improving the payoff equality among them. The rank strategy is further evaluated in a broad parameter range with different combinations of the ratio of initial cooperators, the benefit (b) and the fitness (K). In most cases, the rank strategy shows a better performance in both the fraction of cooperators and the Gini coefficient, which concludes that the mental accounting effect could be the more realistic factor that may be critical to consider. The resolution in the cooperative mechanism may also be linked to wealth equality. Simulation results in this work suggest a close relationship between cooperation improvement and the payoff equality which is not extensively explored in earlier works. Simulations with Gini distribution explain “A good deed is never lost” in a numerical way.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142143973","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 reputation-based reward mechanism promotes the evolution of fairness","authors":"Lili Deng ,&nbsp;Rugen Wang ,&nbsp;Ying Liao ,&nbsp;Ronghua Xu ,&nbsp;Cheng Wang","doi":"10.1016/j.amc.2024.129042","DOIUrl":"10.1016/j.amc.2024.129042","url":null,"abstract":"<div><p>In real life, a good reputation generally brings positive returns to individuals. For example, merchants with numerous good reviews usually gain higher profits. Considering this in the ultimatum game, we propose a reputation-based reward mechanism to investigate the evolution of fairness. Specifically, individuals' reputations evolve dynamically based on the outcomes of games. At the same time, we set a reputation threshold in the population. When individuals' reputations exceed the reputation threshold, they are considered excellent. Otherwise, they are ordinary. The excellent individuals can receive extra rewards compared to the ordinary ones. Finally, individuals' total payoffs determine their fitness within the population. Based on these settings, this paper mainly explores how reputation threshold, weight factor and reward strength affect the evolution of fairness. Through a series of simulations, the reputation-based rewards mechanism is proved to effectively promote the fairness in the population. To be specific, we find that higher reputation thresholds and smaller values of weight factor significantly enhance the promotion effect of reward on fairness. Simultaneously, there is a specific correspondence between the reputation threshold and the weight factor. When reward strength is fixed, for different reputation thresholds, the optimal value of weight factor to achieve maximum fairness levels also varies. Additionally, increasing reward strength can significantly promote fairness.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142128503","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":"Linear programming with infinite, finite, and infinitesimal values in the right-hand side","authors":"Marco Cococcioni,&nbsp;Lorenzo Fiaschi","doi":"10.1016/j.amc.2024.129044","DOIUrl":"10.1016/j.amc.2024.129044","url":null,"abstract":"<div><p>The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron becomes more complex, since its vertices can be represented by non-purely finite coordinates, and so is the optimum of the problem. The introduction of such constraints enlarges the class of linear programs, where those described by finite values only become a special case. To tackle optimization problems over such polyhedra, there is a need for an ad-hoc solving routine: this work proposes a generalization of the Simplex algorithm, which is able to solve common linear programs as corner cases. Finally, the study presents three relevant applications that can benefit from the use of these novel constraints, making the use of the extended Simplex algorithm essential. For each application, an exemplifying benchmark is solved, showing the effectiveness of the proposed routine.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0096300324005058/pdfft?md5=12dfb5dd72877b7d0a19e0b9fcbd8f75&pid=1-s2.0-S0096300324005058-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142128502","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}

{"title":"Second-order non-uniform and fast two-grid finite element methods for non-linear time-fractional mobile/immobile equations with weak regularity","authors":"Zhijun Tan","doi":"10.1016/j.amc.2024.129043","DOIUrl":"10.1016/j.amc.2024.129043","url":null,"abstract":"<div><p>This paper introduces a novel temporal second-order fully discrete approach of finite element method (FEM) and its fast two-grid FEM on non-uniform meshes, which aims to solve non-linear time-fractional variable coefficient mobile/immobile (MIM) equations with a solution exhibiting weak regularity. The proposed method utilizes the averaged L1 formula on graded meshes in the temporal domain to handle the weak initial singularity. In the spatial domain, a two-grid approach based on FEM and its associated fast algorithm are employed to optimize computational efficiency. To ensure fast and accurate calculations of kernels, an innovative algorithm is developed. The stability and optimal error estimates in <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 are rigorously established for the non-uniform averaged L1-based FEM, two-grid FEM and their associated fast algorithms, respectively. The numerical findings clearly showcase the validity of our theoretical discoveries, highlighting the enhanced effectiveness of our two-grid approach in contrast to the conventional approach. An important point to mention is that this work is the pioneering effort in addressing both <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-stability and second-order <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm error analysis for the fractional MIM problem with weak regularity, as well as temporal second-order approaches of two-grid for the fractional MIM equation with a weakly singular solution.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122748","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":"Some identities on degenerate harmonic and degenerate higher-order harmonic numbers","authors":"Taekyun Kim ,&nbsp;Dae San Kim","doi":"10.1016/j.amc.2024.129045","DOIUrl":"10.1016/j.amc.2024.129045","url":null,"abstract":"<div><p>The harmonic numbers and higher-order harmonic numbers appear frequently in several areas which are related to combinatorial identities, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this paper is to study the degenerate harmonic and degenerate higher-order harmonic numbers, which are respectively degenerate versions of the harmonic and higher-order harmonic numbers, in connection with the degenerate zeta and degenerate Hurwitz zeta function. Here the degenerate zeta and degenerate Hurwitz zeta function are respectively degenerate versions of the Riemann zeta and Hurwitz zeta function. We show that several infinite sums involving the degenerate higher-order harmonic numbers can be expressed in terms of the degenerate zeta function. Furthermore, we demonstrate that an infinite sum involving finite sums of products of the degenerate harmonic numbers can be represented by using the degenerate Hurwitz zeta function.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122845","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}