Pub Date : 2026-01-09DOI: 10.1016/j.cnsns.2026.109662
Junqi Yang, Hao Li, Yantao Chen, Zhi Chen
The problem of output feedback state estimation is studied for weakly reconstructible Boolean control networks (BCNs) in this paper. Firstly, the reconstructibility of BCNs is categorized based on initial outputs, and an algorithm is designed to find the set of reconstructible control sequences for any initial output. Secondly, the existence condition of the output feedback state estimation controller is proposed when the control sequence is given, and the corresponding feedback matrix is obtained by designing a special algorithm. Thirdly, a set-set synchronously reachable method is developed, and the complexity of calculating reconstructible control sequences for state estimation is reduced by constructing a time-varying output feedback controller. Finally, the feasibility of the proposed method is illustrated by an example.
{"title":"Output feedback state estimation for weakly reconstructible Boolean control networks","authors":"Junqi Yang, Hao Li, Yantao Chen, Zhi Chen","doi":"10.1016/j.cnsns.2026.109662","DOIUrl":"10.1016/j.cnsns.2026.109662","url":null,"abstract":"<div><div>The problem of output feedback state estimation is studied for weakly reconstructible Boolean control networks (BCNs) in this paper. Firstly, the reconstructibility of BCNs is categorized based on initial outputs, and an algorithm is designed to find the set of reconstructible control sequences for any initial output. Secondly, the existence condition of the output feedback state estimation controller is proposed when the control sequence is given, and the corresponding feedback matrix is obtained by designing a special algorithm. Thirdly, a set-set synchronously reachable method is developed, and the complexity of calculating reconstructible control sequences for state estimation is reduced by constructing a time-varying output feedback controller. Finally, the feasibility of the proposed method is illustrated by an example.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109662"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979227","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109702
Qilong Xie , Jun You , Shoucheng Yuan , Mingliang Gu , Jun Cheng , Yu Fu , Jinde Cao
This paper addresses the load frequency control (LFC) problem of power systems operating under stochastic sampling and denial-of-service (DoS) attacks. A robust control strategy is introduced that combines a novel random switching rule with an attack compensation mechanism. The switching rule incorporates dwell time and dwell probability (DT-DP), thereby simplifying the traditional reliance on transition probabilities in Markov jump systems and reducing computational complexity. To mitigate data loss during DoS attacks, an event-triggered detection algorithm and a dynamic compensation mechanism are developed, effectively restoring damaged signals within the control loop. The controller design adopts a proportional-derivative (PD)-like structure, enabling faster response and improved control accuracy by using the derivative information of system states. Finally, a simulation study demonstrates that the proposed method achieves rapid convergence under random sampling and DoS-induced disruptions, outperforming traditional state-feedback approaches and strategies without compensation.
{"title":"Resilient load frequency control for switching power systems under stochastic sampling and denial-of-service attacks","authors":"Qilong Xie , Jun You , Shoucheng Yuan , Mingliang Gu , Jun Cheng , Yu Fu , Jinde Cao","doi":"10.1016/j.cnsns.2026.109702","DOIUrl":"10.1016/j.cnsns.2026.109702","url":null,"abstract":"<div><div>This paper addresses the load frequency control (LFC) problem of power systems operating under stochastic sampling and denial-of-service (DoS) attacks. A robust control strategy is introduced that combines a novel random switching rule with an attack compensation mechanism. The switching rule incorporates dwell time and dwell probability (DT-DP), thereby simplifying the traditional reliance on transition probabilities in Markov jump systems and reducing computational complexity. To mitigate data loss during DoS attacks, an event-triggered detection algorithm and a dynamic compensation mechanism are developed, effectively restoring damaged signals within the control loop. The controller design adopts a proportional-derivative (PD)-like structure, enabling faster response and improved control accuracy by using the derivative information of system states. Finally, a simulation study demonstrates that the proposed method achieves rapid convergence under random sampling and DoS-induced disruptions, outperforming traditional state-feedback approaches and strategies without compensation.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109702"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979706","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109638
Huihui Xian , Xindi Fan , Bin Li , Tao Jin
This paper presents a new criterion for the existence of synchronized stationary distributions for hybrid stochastic coupled systems with time delay. By investigating the convergence and uniform boundedness of the error system’s solution, the existence of the stationary distribution is obtained. Meanwhile, two main theorems are proposed, including the semi-Lyapunov-type theorem and the coefficients-type theorem, which provide the criteria to judge the synchronized stationary distribution of a hybrid stochastic coupled system. Furthermore, the theoretical results are applied to stochastic coupled oscillators with time delay, and an example with numerical simulation is given to illustrate the validity of the results developed.
{"title":"Inner synchronized stationary distribution of hybrid stochastic coupled systems with time delay","authors":"Huihui Xian , Xindi Fan , Bin Li , Tao Jin","doi":"10.1016/j.cnsns.2026.109638","DOIUrl":"10.1016/j.cnsns.2026.109638","url":null,"abstract":"<div><div>This paper presents a new criterion for the existence of synchronized stationary distributions for hybrid stochastic coupled systems with time delay. By investigating the convergence and uniform boundedness of the error system’s solution, the existence of the stationary distribution is obtained. Meanwhile, two main theorems are proposed, including the semi-Lyapunov-type theorem and the coefficients-type theorem, which provide the criteria to judge the synchronized stationary distribution of a hybrid stochastic coupled system. Furthermore, the theoretical results are applied to stochastic coupled oscillators with time delay, and an example with numerical simulation is given to illustrate the validity of the results developed.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109638"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979707","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109669
Xin-Yue Zhao, Xiao-Heng Chang, Li-Juan Cai
Currently, the role of the network in the control system is becoming increasingly crucial, making network security a topic of significant importance. This paper addresses the control problem of T-S fuzzy singular networked cascade systems by designing a novel dynamic triggering strategy that integrates privacy-preserving output mask and event-triggered mechanisms. Departing from prior research, it introduces a segmented privacy mask algorithm from a defender’s perspective and addresses the convergence issue of the privacy output mask. To further reduce communication burdens, a novel dynamic event-triggered scheme is introduced for Takagi-Sugeno (T-S) fuzzy singular networked control systems, enhancing efficiency and reducing communication resource consumption. This scheme integrates two auxiliary internal dynamic variables into the event-triggered condition, one of which is linked to the design of the finite-time privacy output mask. By constructing an appropriate Lyapunov functional, sufficient conditions are derived to guarantee system stability and performance. Finally, the effectiveness of the proposed design is verified by the main steam temperature control system.
{"title":"T -S fuzzy singular cascade networked systems with integrated privacy protection and dynamic event-triggered mechanisms","authors":"Xin-Yue Zhao, Xiao-Heng Chang, Li-Juan Cai","doi":"10.1016/j.cnsns.2026.109669","DOIUrl":"10.1016/j.cnsns.2026.109669","url":null,"abstract":"<div><div>Currently, the role of the network in the control system is becoming increasingly crucial, making network security a topic of significant importance. This paper addresses the <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> control problem of T-S fuzzy singular networked cascade systems by designing a novel dynamic triggering strategy that integrates privacy-preserving output mask and event-triggered mechanisms. Departing from prior research, it introduces a segmented privacy mask algorithm from a defender’s perspective and addresses the convergence issue of the privacy output mask. To further reduce communication burdens, a novel dynamic event-triggered scheme is introduced for Takagi-Sugeno (T-S) fuzzy singular networked control systems, enhancing efficiency and reducing communication resource consumption. This scheme integrates two auxiliary internal dynamic variables into the event-triggered condition, one of which is linked to the design of the finite-time privacy output mask. By constructing an appropriate Lyapunov functional, sufficient conditions are derived to guarantee system stability and <span><math><msub><mi>H</mi><mi>∞</mi></msub></math></span> performance. Finally, the effectiveness of the proposed design is verified by the main steam temperature control system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109669"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981811","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109656
Xuexi Zhang , Hekai Feng , Chaojie Cheng , Zhenyu Wu , Qiang Ni , Jie Tao
This article investigates anti-synchronization control for Markov jump neural networks with partially unknown probabilities under energy-constrained attacks. First, to deal with the mixed-type attacks and asynchronous phenomena, a controller based on the hidden Markov model with partially unknown probabilities is established. To conserve valuable communication resources and reduce the influence caused by denial of service attacks, a novel dynamic event-triggered scheme is developed, capable of predicting and adapting to malicious attack occurrences by weighting modulation. Sufficient conditions are then obtained to guarantee the drive and response systems achieve H∞ anti-synchronization by resorting to linear matrix inequalities. The effectiveness of the proposed anti-synchronization scheme is demonstrated through a numerical example. Finally, a secure communication system, leveraging the proposed anti-synchronization system, is constructed and its encryption security is analyzed with an image encryption example.
{"title":"Dynamic event-triggered anti-synchronization for Markov jump neural networks with partially unknown probabilities and cyber attacks","authors":"Xuexi Zhang , Hekai Feng , Chaojie Cheng , Zhenyu Wu , Qiang Ni , Jie Tao","doi":"10.1016/j.cnsns.2026.109656","DOIUrl":"10.1016/j.cnsns.2026.109656","url":null,"abstract":"<div><div>This article investigates anti-synchronization control for Markov jump neural networks with partially unknown probabilities under energy-constrained attacks. First, to deal with the mixed-type attacks and asynchronous phenomena, a controller based on the hidden Markov model with partially unknown probabilities is established. To conserve valuable communication resources and reduce the influence caused by denial of service attacks, a novel dynamic event-triggered scheme is developed, capable of predicting and adapting to malicious attack occurrences by weighting modulation. Sufficient conditions are then obtained to guarantee the drive and response systems achieve <em>H</em><sub>∞</sub> anti-synchronization by resorting to linear matrix inequalities. The effectiveness of the proposed anti-synchronization scheme is demonstrated through a numerical example. Finally, a secure communication system, leveraging the proposed anti-synchronization system, is constructed and its encryption security is analyzed with an image encryption example.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109656"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969429","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109688
Yingying Zhang , Peng Wang , Hong Sang , Ying Zhao , Georgi M. Dimirovski
In this article, a novel nonfragile bumpless transfer control (NBTC) design policy is developed for discrete-time switched positive systems (DTSPSs) that are entire composed of unstable subsystems. The core concept is to utilize the positive effect of the switching mechanism to counteract divergence of the state caused by the unstable subsystems. Furthermore, to account for the impact of uncertain parameter variations on the control strategy and to bound the control amplitude discontinuity at switching times, a time-varying nonfragile bumpless transfer controller is considered. Building upon the dwell-time and gain matrix decomposition framework, the linear vector inequalities criterion provides an opportunity to assess stability and ℓ1-gain performance. Ultimately, a communication network model is established to demonstrate the usefulness of our approach and to show the broad application.
{"title":"A novel nonfragile bumpless transfer control design for discrete-time switched positive systems under range dwell time limitation","authors":"Yingying Zhang , Peng Wang , Hong Sang , Ying Zhao , Georgi M. Dimirovski","doi":"10.1016/j.cnsns.2026.109688","DOIUrl":"10.1016/j.cnsns.2026.109688","url":null,"abstract":"<div><div>In this article, a novel nonfragile bumpless transfer control (NBTC) design policy is developed for discrete-time switched positive systems (DTSPSs) that are entire composed of unstable subsystems. The core concept is to utilize the positive effect of the switching mechanism to counteract divergence of the state caused by the unstable subsystems. Furthermore, to account for the impact of uncertain parameter variations on the control strategy and to bound the control amplitude discontinuity at switching times, a time-varying nonfragile bumpless transfer controller is considered. Building upon the dwell-time and gain matrix decomposition framework, the linear vector inequalities criterion provides an opportunity to assess stability and ℓ<sub>1</sub>-gain performance. Ultimately, a communication network model is established to demonstrate the usefulness of our approach and to show the broad application.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109688"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962062","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109675
Zhumu Fu , Yueyang Wang , Boyang Qu , Fazhan Tao
This paper proposes an aperiodic update fixed-time optimal control scheme for stochastic systems based on reinforcement learning (RL) algorithms to achieve system stability and address the problem of system resource waste, including energy resources and communication resources. Firstly, an optimal control protocol with self-learning characteristics is proposed based on optimal backstepping technique and RL iterative algorithm to obtain the optimal control solution that can balance tracking performance and system energy consumption. Secondly, by introducing the fixed-time feedback term into the optimal control protocol, the analytical framework of the Hamilton-Jacobi-Bellman (HJB) equation is reconstructed and the fixed-time optimal controller is derived to constrain the optimal control solution from infinity to a finite time interval and solve the conflict between the network learning time and the system stability time. Then, to further save resources, an event-driven aperiodic update triggered mechanism is constructed to drive the intermittent update of the system through a judgment condition composed of the differential threshold of the optimal control quantity. Finally, the effectiveness of the proposed scheme is verified by two simulations.
{"title":"Aperiodic update fixed-time control for stochastic system: A self-learning optimal strategy based on reinforcement learning","authors":"Zhumu Fu , Yueyang Wang , Boyang Qu , Fazhan Tao","doi":"10.1016/j.cnsns.2026.109675","DOIUrl":"10.1016/j.cnsns.2026.109675","url":null,"abstract":"<div><div>This paper proposes an aperiodic update fixed-time optimal control scheme for stochastic systems based on reinforcement learning (RL) algorithms to achieve system stability and address the problem of system resource waste, including energy resources and communication resources. Firstly, an optimal control protocol with self-learning characteristics is proposed based on optimal backstepping technique and RL iterative algorithm to obtain the optimal control solution that can balance tracking performance and system energy consumption. Secondly, by introducing the fixed-time feedback term into the optimal control protocol, the analytical framework of the Hamilton-Jacobi-Bellman (HJB) equation is reconstructed and the fixed-time optimal controller is derived to constrain the optimal control solution from infinity to a finite time interval and solve the conflict between the network learning time and the system stability time. Then, to further save resources, an event-driven aperiodic update triggered mechanism is constructed to drive the intermittent update of the system through a judgment condition composed of the differential threshold of the optimal control quantity. Finally, the effectiveness of the proposed scheme is verified by two simulations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109675"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962517","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 : 2026-01-09DOI: 10.1016/j.cnsns.2026.109723
Haiyang Wu , Hanyao Hou , Yunlong Qiu , Dali Ge , Kai Li
Self-sustained systems utilizing active materials provide the advantage of harnessing environmental energy to maintain motion without the need for additional controllers or heavy batteries. Current self-sustained systems typically require active materials to respond quickly to match the inertial characteristic time, generating sufficient net work for sustained motion. This paper presents the design of a self-rolling rover made from a photothermally-responsive liquid crystal elastomer (LCE) fiber, a spring, a wheel, and a mass block. Experiments demonstrate that the rover can self-roll between two hollows under steady illumination, even with a lower response speed from the LCE fiber. A theoretical model for the self-rolling rover is established, from which governing equations are derived to elucidate the motion mechanisms and the critical conditions for self-rolling. Our findings reveal that the self-rolling modes and the period can be modulated by adjusting system parameters. The proposed self-rolling rover offers significant advantages, including reduced reliance on rapid response speed, and bistable mechanical stability. This research provides novel insights for the development of intelligent self-sustained systems, with potential applications in intelligent control, energy harvesting, and autonomous robotics.
{"title":"Light-powered self-rolling liquid crystal elastomer rovers between two hollows","authors":"Haiyang Wu , Hanyao Hou , Yunlong Qiu , Dali Ge , Kai Li","doi":"10.1016/j.cnsns.2026.109723","DOIUrl":"10.1016/j.cnsns.2026.109723","url":null,"abstract":"<div><div>Self-sustained systems utilizing active materials provide the advantage of harnessing environmental energy to maintain motion without the need for additional controllers or heavy batteries. Current self-sustained systems typically require active materials to respond quickly to match the inertial characteristic time, generating sufficient net work for sustained motion. This paper presents the design of a self-rolling rover made from a photothermally-responsive liquid crystal elastomer (LCE) fiber, a spring, a wheel, and a mass block. Experiments demonstrate that the rover can self-roll between two hollows under steady illumination, even with a lower response speed from the LCE fiber. A theoretical model for the self-rolling rover is established, from which governing equations are derived to elucidate the motion mechanisms and the critical conditions for self-rolling. Our findings reveal that the self-rolling modes and the period can be modulated by adjusting system parameters. The proposed self-rolling rover offers significant advantages, including reduced reliance on rapid response speed, and bistable mechanical stability. This research provides novel insights for the development of intelligent self-sustained systems, with potential applications in intelligent control, energy harvesting, and autonomous robotics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109723"},"PeriodicalIF":3.8,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979228","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 delves into the observer-based sliding mode control for switched nonlinear systems characterized by nonhomogeneous sojourn probabilities and deception attacks. In view of the inherent complexity of observing transition probabilities, the nonhomogeneous sojourn probabilities are developed with the aim of capturing the inherent randomness of switched nonlinear systems, where the variation of sojourn probabilities is meticulously controlled by a deterministic upper-level switching signal. To counteract adverse influences of deception attacks and achieve enhanced estimation performance, an innovative adaptive saturation-based observer is constructed. This observer dynamically adjusts the saturation level based on previous estimation errors. Incorporating the structural characteristics of switched systems, a novel sliding mode control strategy that properly accounts for outlier-resistant state observations is formulated. Employing Lyapunov theories, sufficient conditions for ensuring both the stochastic stability and the reachability of the designated sliding surface are provided, facilitating the design of an observer-based sliding mode controller. Finally, an automotive suspension model is applied to showcase the effectiveness and superiority of the proposed methodology.
{"title":"Observer-based sliding mode control for switched nonlinear systems and application to automotive suspension","authors":"Changchun Shen , Tianfeng Tang , Shoucheng Yuan , Jun Cheng , Yonghong Chen","doi":"10.1016/j.cnsns.2026.109660","DOIUrl":"10.1016/j.cnsns.2026.109660","url":null,"abstract":"<div><div>This paper delves into the observer-based sliding mode control for switched nonlinear systems characterized by nonhomogeneous sojourn probabilities and deception attacks. In view of the inherent complexity of observing transition probabilities, the nonhomogeneous sojourn probabilities are developed with the aim of capturing the inherent randomness of switched nonlinear systems, where the variation of sojourn probabilities is meticulously controlled by a deterministic upper-level switching signal. To counteract adverse influences of deception attacks and achieve enhanced estimation performance, an innovative adaptive saturation-based observer is constructed. This observer dynamically adjusts the saturation level based on previous estimation errors. Incorporating the structural characteristics of switched systems, a novel sliding mode control strategy that properly accounts for outlier-resistant state observations is formulated. Employing Lyapunov theories, sufficient conditions for ensuring both the stochastic stability and the reachability of the designated sliding surface are provided, facilitating the design of an observer-based sliding mode controller. Finally, an automotive suspension model is applied to showcase the effectiveness and superiority of the proposed methodology.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109660"},"PeriodicalIF":3.8,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979297","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 : 2026-01-08DOI: 10.1016/j.cnsns.2025.109634
Qunzhi Jin , Xin Zhang , Jihong Shen , Yuanfeng Jin
This paper proposes a hybrid numerical method based on the ADI scheme and adaptive weights, aiming at minimizing the piecewise constant Mumford-Shah energy function in image segmentation. The method is unconditionally stable and further enhances segmentation accuracy and flexibility by introducing adaptive weights for the background and object regions. Specifically, this study optimizes the limitations of traditional multigrid methods in sizing domains, overcoming the deficiencies of previous methods to segment complex regions. The proposed model is based on the Allen-Cahn equation and uses operator splitting techniques for numerical solutions. Through numerical experiments, we verify the second-order convergence of the proposed difference scheme in time and space and prove its unconditional stability. Experimental results show that, compared to classical methods, our method not only performs efficient image segmentation on arbitrary domains but also significantly improves computational efficiency.
{"title":"An efficient hybrid numerical method based on the ADI scheme and adaptive weights for image segmentation","authors":"Qunzhi Jin , Xin Zhang , Jihong Shen , Yuanfeng Jin","doi":"10.1016/j.cnsns.2025.109634","DOIUrl":"10.1016/j.cnsns.2025.109634","url":null,"abstract":"<div><div>This paper proposes a hybrid numerical method based on the ADI scheme and adaptive weights, aiming at minimizing the piecewise constant Mumford-Shah energy function in image segmentation. The method is unconditionally stable and further enhances segmentation accuracy and flexibility by introducing adaptive weights for the background and object regions. Specifically, this study optimizes the limitations of traditional multigrid methods in sizing domains, overcoming the deficiencies of previous methods to segment complex regions. The proposed model is based on the Allen-Cahn equation and uses operator splitting techniques for numerical solutions. Through numerical experiments, we verify the second-order convergence of the proposed difference scheme in time and space and prove its unconditional stability. Experimental results show that, compared to classical methods, our method not only performs efficient image segmentation on arbitrary domains but also significantly improves computational efficiency.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"156 ","pages":"Article 109634"},"PeriodicalIF":3.8,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979705","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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