Pub Date : 2026-01-15DOI: 10.1016/j.cnsns.2026.109743
Henghui Tang, Daopeng Yin, Xiaohao Zhang, Liquan Mei
This paper presents a novel high-order time discretization scheme on the time complex plane for parabolic equations. The innovation of this method lies in its ability to straightforwardly construct temporal discretization schemes of arbitrary order while achieving stability comparable to explicit Runge-Kutta methods, and simultaneously enhancing computational efficiency without compromising stability. By employing a matrix construction method, we unify the characterization of the stability region for both ordinary differential equations and partial differential equations. We prove the L2 stability and arbitrary-order convergence of the method. Numerical experiments demonstrate that, compared to explicit Runge-Kutta methods, the proposed scheme improves computational efficiency. This method offers an efficient and accurate solution for applications with stringent precision.
{"title":"Implicit-explicit time discretization with complex time for parabolic equations","authors":"Henghui Tang, Daopeng Yin, Xiaohao Zhang, Liquan Mei","doi":"10.1016/j.cnsns.2026.109743","DOIUrl":"10.1016/j.cnsns.2026.109743","url":null,"abstract":"<div><div>This paper presents a novel high-order time discretization scheme on the time complex plane for parabolic equations. The innovation of this method lies in its ability to straightforwardly construct temporal discretization schemes of arbitrary order while achieving stability comparable to explicit Runge-Kutta methods, and simultaneously enhancing computational efficiency without compromising stability. By employing a matrix construction method, we unify the characterization of the stability region for both ordinary differential equations and partial differential equations. We prove the <em>L</em><sup>2</sup> stability and arbitrary-order convergence of the method. Numerical experiments demonstrate that, compared to explicit Runge-Kutta methods, the proposed scheme improves computational efficiency. This method offers an efficient and accurate solution for applications with stringent precision.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109743"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145982096","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 : 2026-01-15DOI: 10.1016/j.cnsns.2026.109730
Huihui Song , Zezhou Fan , Yitong Liu , Xin Zhang
This paper investigates the inner synchronized stationary distribution of delayed signed networks with Markovian switching (DMSNs) by investigating convergence and uniform boundedness of the solution of the error system. The Lyapunov method and the signed digraph theory are applied to investigating the existence of stationary distribution, which avoids the difficulty of constructing the Lyapunov function construction directly. Then two synchronized stationary distribution criteria which ensure DMSNs exist stationary distribution are presented. Finally, the proposed theoretical results are applied to Chua’s circuit, and through corresponding numerical simulations, the validity of the theoretical results is verified.
{"title":"Synchronized stationary distribution of Markovian switching stochastic delayed signed networks with application to Chua’s circuits","authors":"Huihui Song , Zezhou Fan , Yitong Liu , Xin Zhang","doi":"10.1016/j.cnsns.2026.109730","DOIUrl":"10.1016/j.cnsns.2026.109730","url":null,"abstract":"<div><div>This paper investigates the inner synchronized stationary distribution of delayed signed networks with Markovian switching (DMSNs) by investigating convergence and uniform boundedness of the solution of the error system. The Lyapunov method and the signed digraph theory are applied to investigating the existence of stationary distribution, which avoids the difficulty of constructing the Lyapunov function construction directly. Then two synchronized stationary distribution criteria which ensure DMSNs exist stationary distribution are presented. Finally, the proposed theoretical results are applied to Chua’s circuit, and through corresponding numerical simulations, the validity of the theoretical results is verified.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109730"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145982094","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 : 2026-01-14DOI: 10.1016/j.cnsns.2026.109664
Zenghui Hu , Jiamin Liu , Yiming Wang , Lijie You
The almost surely exponential stability (ES a.s.) is investigated for nonlinear systems subject to the effects of stochastic noises and random impulses. The randomness of impulsive effects is considered in two aspects: impulsive intensity and density. In detail, the impulsive instants and jumps are respectively impelled by a renewal process and a Markov chain. By analyzing the coupling effect among stochastic noise, randomly impulsive intensity and density, novel criteria of ES a.s. are obtained by employing Lyapunov-based approach. The proposed results not only capture the positive effect of stochastic noise, but also remove the non-zero property of solution required in existing works. As an application, the synchronization problem of master-slave stochastic chaotic systems is solved by applying the randomly impulsive control method. Two examples are provided to illustrate the effectiveness and application of the proposed results.
{"title":"Almost surely exponential stability of nonlinear stochastic systems with random impulses and its application in chaos synchronization","authors":"Zenghui Hu , Jiamin Liu , Yiming Wang , Lijie You","doi":"10.1016/j.cnsns.2026.109664","DOIUrl":"10.1016/j.cnsns.2026.109664","url":null,"abstract":"<div><div>The almost surely exponential stability (ES a.s.) is investigated for nonlinear systems subject to the effects of stochastic noises and random impulses. The randomness of impulsive effects is considered in two aspects: impulsive intensity and density. In detail, the impulsive instants and jumps are respectively impelled by a renewal process and a Markov chain. By analyzing the coupling effect among stochastic noise, randomly impulsive intensity and density, novel criteria of ES a.s. are obtained by employing Lyapunov-based approach. The proposed results not only capture the positive effect of stochastic noise, but also remove the non-zero property of solution required in existing works. As an application, the synchronization problem of master-slave stochastic chaotic systems is solved by applying the randomly impulsive control method. Two examples are provided to illustrate the effectiveness and application of the proposed results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109664"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962060","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 : 2026-01-13DOI: 10.1016/j.cnsns.2026.109698
Jing Wang, Likui Wang, Qianling Wang
This paper investigates the problem of observer design for positive T-S fuzzy systems. Two methods are provided to design the observer. First, the augmented system matrices are divided into blocks, and the observer is designed by using these blocks with a switching strategy. Then, for a special case that output system matrices are the same, less conservative design conditions are obtained by applying singular value decomposition (SVD) and second-order forms of the system states. Finally, the relationship of the two methods is discussed and two examples are given to verify the effectiveness of the results in this paper.
{"title":"Fuzzy observer design for positive T-S fuzzy systems","authors":"Jing Wang, Likui Wang, Qianling Wang","doi":"10.1016/j.cnsns.2026.109698","DOIUrl":"10.1016/j.cnsns.2026.109698","url":null,"abstract":"<div><div>This paper investigates the problem of observer design for positive T-S fuzzy systems. Two methods are provided to design the observer. First, the augmented system matrices are divided into blocks, and the observer is designed by using these blocks with a switching strategy. Then, for a special case that output system matrices are the same, less conservative design conditions are obtained by applying singular value decomposition (SVD) and second-order forms of the system states. Finally, the relationship of the two methods is discussed and two examples are given to verify the effectiveness of the results in this paper.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109698"},"PeriodicalIF":3.8,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962061","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 : 2026-01-13DOI: 10.1016/j.cnsns.2026.109722
Luis T. Aguilar
In this paper, we analyze the stability of an open-loop subcutaneous insulin kinetics model for type 1 diabetes. The contribution of the proposed study relies on developing a semi-autonomous strategy for delivering insulin in the body, minimizing the risks of overdoses. The model comprises a pair of nonlinear partial differential equations (PDEs): one representing hexameric insulin and the other modeling dimeric insulin. We investigate the solutions and the stability properties of both the local and global models. Additionally, we propose a boundary control strategy for the system. The stability analysis is conducted within the framework of Lyapunov functions, and the theoretical findings are further validated through simulation results.
{"title":"Analysis and boundary control of subcutaneous insulin kinetics PDE model for type one diabetes","authors":"Luis T. Aguilar","doi":"10.1016/j.cnsns.2026.109722","DOIUrl":"10.1016/j.cnsns.2026.109722","url":null,"abstract":"<div><div>In this paper, we analyze the stability of an open-loop subcutaneous insulin kinetics model for type 1 diabetes. The contribution of the proposed study relies on developing a semi-autonomous strategy for delivering insulin in the body, minimizing the risks of overdoses. The model comprises a pair of nonlinear partial differential equations (PDEs): one representing hexameric insulin and the other modeling dimeric insulin. We investigate the solutions and the stability properties of both the local and global models. Additionally, we propose a boundary control strategy for the system. The stability analysis is conducted within the framework of Lyapunov functions, and the theoretical findings are further validated through simulation results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109722"},"PeriodicalIF":3.8,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962516","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 : 2026-01-12DOI: 10.1016/j.cnsns.2026.109754
Wanjin Guo , Ru Li , Qianhui Li , Yuxiang Tian , Chuqing Cao , Lijun Zhao
In order to solve the issue of relatively noticeable end deformation due to the weak rigidity structures in a highly dexterous 3T2R industrial robot, a composite index-based method of quasi-static robot stiffness optimization and deformation error compensation is proposed. The proposed method aims to enhance the quasi-static stiffness performance and reduce the quasi-static end deformation for this weak rigidity industrial robot. First, structural characteristics of the weak rigidity industrial robot are analyzed, and a quasi-static robot stiffness model is established. Second, a quasi-static robot stiffness identification approach is presented, considering weakly rigid joint transmission chains and flexible rod of the studied robot. The effects of the weakly rigid joint transmission chains and the flexible rod on the robot end deformation are investigated. Quasi-static robot stiffness identification experiment is conducted to obtain the quasi-static stiffness of each joint of the studied robot. Third, a composite stiffness index is constructed by using a compliance ellipsoid, incorporating both quasi-static normal stiffness evaluation index and quasi-static plane stiffness evaluation index. And a composite index-based method of quasi-static robot stiffness optimization and deformation error compensation is proposed to minimize the quasi-static robot end deformation of the studied weak rigidity industrial robot. Finally, the effectiveness of the presented quasi-static robot stiffness identification approach, and the effectiveness of the proposed composite index-based method of quasi-static robot stiffness optimization and deformation error compensation, are validated experimentally. Experimental results indicate that the error rates between the measured comprehensive robot end deformations and the theoretical counterparts at 4 kg, 8 kg, and 16 kg quasi-static loads are 10.61%, 11.82%, and 8.89%, respectively. The comprehensive position deformation is reduced by 23.43% before and after the quasi-static robot stiffness optimization. After performing quasi-static robot end deformation error compensation for parallelogram, triangle, and rectilinear segment, the reduced comprehensive position deformations range from 28.61% to 81.61%.
{"title":"Composite index-based stiffness optimization and deformation error compensation for a weak rigidity industrial robot","authors":"Wanjin Guo , Ru Li , Qianhui Li , Yuxiang Tian , Chuqing Cao , Lijun Zhao","doi":"10.1016/j.cnsns.2026.109754","DOIUrl":"10.1016/j.cnsns.2026.109754","url":null,"abstract":"<div><div>In order to solve the issue of relatively noticeable end deformation due to the weak rigidity structures in a highly dexterous 3T2R industrial robot, a composite index-based method of quasi-static robot stiffness optimization and deformation error compensation is proposed. The proposed method aims to enhance the quasi-static stiffness performance and reduce the quasi-static end deformation for this weak rigidity industrial robot. First, structural characteristics of the weak rigidity industrial robot are analyzed, and a quasi-static robot stiffness model is established. Second, a quasi-static robot stiffness identification approach is presented, considering weakly rigid joint transmission chains and flexible rod of the studied robot. The effects of the weakly rigid joint transmission chains and the flexible rod on the robot end deformation are investigated. Quasi-static robot stiffness identification experiment is conducted to obtain the quasi-static stiffness of each joint of the studied robot. Third, a composite stiffness index is constructed by using a compliance ellipsoid, incorporating both quasi-static normal stiffness evaluation index and quasi-static plane stiffness evaluation index. And a composite index-based method of quasi-static robot stiffness optimization and deformation error compensation is proposed to minimize the quasi-static robot end deformation of the studied weak rigidity industrial robot. Finally, the effectiveness of the presented quasi-static robot stiffness identification approach, and the effectiveness of the proposed composite index-based method of quasi-static robot stiffness optimization and deformation error compensation, are validated experimentally. Experimental results indicate that the error rates between the measured comprehensive robot end deformations and the theoretical counterparts at 4 kg, 8 kg, and 16 kg quasi-static loads are 10.61%, 11.82%, and 8.89%, respectively. The comprehensive position deformation is reduced by 23.43% before and after the quasi-static robot stiffness optimization. After performing quasi-static robot end deformation error compensation for parallelogram, triangle, and rectilinear segment, the reduced comprehensive position deformations range from 28.61% to 81.61%.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109754"},"PeriodicalIF":3.8,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957143","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 paper aims to develop a novel adaptive dynamic programming (ADP) based fault-tolerant control (FTC) framework for nonlinear systems, which can effectively handle actuator failures and full-state time-varying constraints while reducing resource consumption through a dynamic event-triggered mechanism (DETM). In order to deal with full-state time-varying constrained problems, a novel control barrier function (CBF) has been proposed that transforms the original system into an unconstrained system. To address unknown faults in the actuator, a fault observer is proposed that compensates for the observed faults. In addition, a new DETM is designed, and optimal control rules can be approximated by constructing a single-critic neural network (NN). A prioritized experience replay strategy based on recency is integrated with the empirical replay technique to relax the persistent excitation (PE) condition so that the weights are updated with more attention to the most recent post-weighting data in the updating process. Lyapunov theory is used to ensure that the nonlinear system state and the critic NN weight are uniformly ultimately bounded (UUB). The effectiveness of the proposed method is verified through simulation results.
{"title":"ADP-based dynamic event-triggered fault-tolerant control for nonlinear systems with actuator failures and full-state time-varying constraints","authors":"Chunbin Qin, Mingyu Pang, Zhongwei Wang, Suyang Hou, Qian Qiu","doi":"10.1016/j.cnsns.2026.109676","DOIUrl":"10.1016/j.cnsns.2026.109676","url":null,"abstract":"<div><div>This paper aims to develop a novel adaptive dynamic programming (ADP) based fault-tolerant control (FTC) framework for nonlinear systems, which can effectively handle actuator failures and full-state time-varying constraints while reducing resource consumption through a dynamic event-triggered mechanism (DETM). In order to deal with full-state time-varying constrained problems, a novel control barrier function (CBF) has been proposed that transforms the original system into an unconstrained system. To address unknown faults in the actuator, a fault observer is proposed that compensates for the observed faults. In addition, a new DETM is designed, and optimal control rules can be approximated by constructing a single-critic neural network (NN). A prioritized experience replay strategy based on recency is integrated with the empirical replay technique to relax the persistent excitation (PE) condition so that the weights are updated with more attention to the most recent post-weighting data in the updating process. Lyapunov theory is used to ensure that the nonlinear system state and the critic NN weight are uniformly ultimately bounded (UUB). The effectiveness of the proposed method is verified through simulation results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109676"},"PeriodicalIF":3.8,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957175","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 : 2026-01-12DOI: 10.1016/j.cnsns.2026.109710
Jinpeng Kuang, Yunfei Mu, Xianghui Qin, Yingchun Wang, Ruiwang Sun
This work focuses on the problem of observer-based preview sliding mode control (SMC) for discrete-time T-S fuzzy systems under Round-Robin (RR) protocol. For the phenomenon that the system is subject to RR protocol, a compensation strategy is proposed. A fuzzy observer is designed for original system. Meanwhile, an augmented system (AS) with discrete-time integrators and a previewable reference signal is developed, and then the tracking problem is transformed into the stability of ASs. A linear sliding surface and a preview SMC law are presented for ASs, which can guarantee the input-to-state stable (ISS) of the quasi-sliding motion and the reachability of the sliding region. Finally, the validity of the obtained theory is verified by an example.
{"title":"Observer-based sliding mode control for discrete-time T-S fuzzy systems under Round-Robin protocol via a preview target mechanism","authors":"Jinpeng Kuang, Yunfei Mu, Xianghui Qin, Yingchun Wang, Ruiwang Sun","doi":"10.1016/j.cnsns.2026.109710","DOIUrl":"https://doi.org/10.1016/j.cnsns.2026.109710","url":null,"abstract":"This work focuses on the problem of observer-based preview sliding mode control (SMC) for discrete-time T-S fuzzy systems under Round-Robin (RR) protocol. For the phenomenon that the system is subject to RR protocol, a compensation strategy is proposed. A fuzzy observer is designed for original system. Meanwhile, an augmented system (AS) with discrete-time integrators and a previewable reference signal is developed, and then the tracking problem is transformed into the stability of ASs. A linear sliding surface and a preview SMC law are presented for ASs, which can guarantee the input-to-state stable (ISS) of the quasi-sliding motion and the reachability of the sliding region. Finally, the validity of the obtained theory is verified by an example.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"259 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957149","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 : 2026-01-12DOI: 10.1016/j.cnsns.2026.109752
Xiangwen Meng , Hao Wang , Fan Zou
In the realm of underwater acoustic communication, the multipath characteristic of the channel significantly reduces communication efficiency, so it is necessary to estimate the channel and then compensate for it. However, traditional estimation methods struggle to accurately estimate channels polluted by noise and require a significant number of pilot signals. Currently, Orthogonal matching pursuit (OMP) is widely used for channel estimation, but it is susceptible to noise interference and lacks self-adaptive sparsity. In underwater acoustic communication, the signal-to-noise ratio (SNR) is often low, and the actual sparsity is unknown, necessitating a more effective estimation method with self-adaptive sparsity. This paper proposes an adaptive simultaneous forecast orthogonal matching pursuit (ASFOMP) for estimating the underwater acoustic channel. ASFOMP, which is improved from OMP, incorporates a forecast step and a self-adaptation function. In the forecast step, the selection of the current tap is determined not only by the correlation between the residual and the atom at the present step, but also by predicting the residual magnitude over several subsequent iterations after selecting that atom. This mechanism helps prevent the erroneous selection of taps that may be influenced by noise or interference. In the self-adaptation function, the residual gradient directly reflects the gain effect of the current newly added tap on channel compensation. When the residual gradient is very small, it indicates that the main taps of the channel have been estimated. Therefore, using the residual gradient as an indicator for adaptive channel estimation can effectively solve the problem of unknown number of channel taps. In the Rayleigh channel case, when SNR is 10 dB, the channel error of ASFOMP is only -51.474 dB, and its BER is 4.218%, which is superior to other methods. Compared to OMP, it reduces the channel estimation error by 39.973 dB and decreases the BER by 0.277%. In the Bellhop-generated channel case, it also achieves performance gains, with channel error reduced by 35.393 dB, and corresponding BER reduction of 0.304%.
{"title":"Adaptive simultaneous forecast orthogonal matching pursuit applied in underwater acoustic channel estimation","authors":"Xiangwen Meng , Hao Wang , Fan Zou","doi":"10.1016/j.cnsns.2026.109752","DOIUrl":"10.1016/j.cnsns.2026.109752","url":null,"abstract":"<div><div>In the realm of underwater acoustic communication, the multipath characteristic of the channel significantly reduces communication efficiency, so it is necessary to estimate the channel and then compensate for it. However, traditional estimation methods struggle to accurately estimate channels polluted by noise and require a significant number of pilot signals. Currently, Orthogonal matching pursuit (OMP) is widely used for channel estimation, but it is susceptible to noise interference and lacks self-adaptive sparsity. In underwater acoustic communication, the signal-to-noise ratio (SNR) is often low, and the actual sparsity is unknown, necessitating a more effective estimation method with self-adaptive sparsity. This paper proposes an adaptive simultaneous forecast orthogonal matching pursuit (ASFOMP) for estimating the underwater acoustic channel. ASFOMP, which is improved from OMP, incorporates a forecast step and a self-adaptation function. In the forecast step, the selection of the current tap is determined not only by the correlation between the residual and the atom at the present step, but also by predicting the residual magnitude over several subsequent iterations after selecting that atom. This mechanism helps prevent the erroneous selection of taps that may be influenced by noise or interference. In the self-adaptation function, the residual gradient directly reflects the gain effect of the current newly added tap on channel compensation. When the residual gradient is very small, it indicates that the main taps of the channel have been estimated. Therefore, using the residual gradient as an indicator for adaptive channel estimation can effectively solve the problem of unknown number of channel taps. In the Rayleigh channel case, when SNR is 10 dB, the channel error of ASFOMP is only -51.474 dB, and its BER is 4.218%, which is superior to other methods. Compared to OMP, it reduces the channel estimation error by 39.973 dB and decreases the BER by 0.277%. In the Bellhop-generated channel case, it also achieves performance gains, with channel error reduced by 35.393 dB, and corresponding BER reduction of 0.304%.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109752"},"PeriodicalIF":3.8,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957144","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 : 2026-01-12DOI: 10.1016/j.cnsns.2026.109725
Hyunjin Ahn
We propose and analyze a multi-agent controlled system on Riemannian manifolds for the design of a competitive flag pursuit game. In this system, agents are subject to mutual repulsion forces while pursuing a given flag, with the goal of one agent successfully capturing the flag while the others fail. To achieve this, we first provide appropriate energy estimates for the mutual repulsion forces between agents using a Lyapunov-based approach. These estimates, along with various bounded estimates, are used to show that, under certain sufficient conditions, one agent can successfully capture the flag while the others are unable to do so. The primary objective of this work is to identify suitable admissible data, concerning initial data, system parameters, kernel functions, and the given flag (whether moving or fixed), that allow one agent to be arbitrarily chosen to win the game by capturing the flag, while ensuring the failure of all other agents.
{"title":"Competitive flag pursuit with mutual repulsion in a multi-agent system on Riemannian Manifolds","authors":"Hyunjin Ahn","doi":"10.1016/j.cnsns.2026.109725","DOIUrl":"10.1016/j.cnsns.2026.109725","url":null,"abstract":"<div><div>We propose and analyze a multi-agent controlled system on Riemannian manifolds for the design of a competitive flag pursuit game. In this system, agents are subject to mutual repulsion forces while pursuing a given flag, with the goal of one agent successfully capturing the flag while the others fail. To achieve this, we first provide appropriate energy estimates for the mutual repulsion forces between agents using a Lyapunov-based approach. These estimates, along with various bounded estimates, are used to show that, under certain sufficient conditions, one agent can successfully capture the flag while the others are unable to do so. The primary objective of this work is to identify suitable admissible data, concerning initial data, system parameters, kernel functions, and the given flag (whether moving or fixed), that allow one agent to be arbitrarily chosen to win the game by capturing the flag, while ensuring the failure of all other agents.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109725"},"PeriodicalIF":3.8,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957148","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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