Pub Date : 2026-02-01Epub Date: 2026-01-11DOI: 10.1016/j.jfranklin.2026.108414
Jia Wang , Leander Hemelhof , Ivan Markovsky , Panagiotis Patrinos
This paper studies data-driven iterative learning control (ILC) for linear time-invariant (LTI) systems with unknown dynamics, output disturbances and input box-constraints. Our main contributions are: 1) using a non-parametric data-driven representation of the system dynamics, for dealing with the unknown system dynamics in the context of ILC, 2) design of a fast ILC method for dealing with output disturbances, model uncertainty and input constraints. A complete design method is given in this paper, which consists of the data-driven representation, controller formulation, acceleration strategy and convergence analysis. A batch of numerical experiments and a case study on a high-precision robotic motion system are given in the end to show the effectiveness of the proposed method.
{"title":"Fast data-driven iterative learning control for linear system with output disturbance","authors":"Jia Wang , Leander Hemelhof , Ivan Markovsky , Panagiotis Patrinos","doi":"10.1016/j.jfranklin.2026.108414","DOIUrl":"10.1016/j.jfranklin.2026.108414","url":null,"abstract":"<div><div>This paper studies data-driven iterative learning control (ILC) for linear time-invariant (LTI) systems with unknown dynamics, output disturbances and input box-constraints. Our main contributions are: 1) using a non-parametric data-driven representation of the system dynamics, for dealing with the unknown system dynamics in the context of ILC, 2) design of a fast ILC method for dealing with output disturbances, model uncertainty and input constraints. A complete design method is given in this paper, which consists of the data-driven representation, controller formulation, acceleration strategy and convergence analysis. A batch of numerical experiments and a case study on a high-precision robotic motion system are given in the end to show the effectiveness of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108414"},"PeriodicalIF":4.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-04DOI: 10.1016/j.jfranklin.2025.108382
Tianze Xie , Hui Wang , Jian Ding , Quanxin Zhu
Existing literature on input-to-state stability (ISS) primarily focuses on transient responses and robustness to external disturbances, yet it often fails to capture the inherent modeling bias in systems like those exhibiting mechanical hysteresis. To address this limitation, we introduce the concept of practical ISS for switched stochastic nonlinear time-delay systems (SSNTDSs), which provides a comprehensive framework for analyzing robustness against both internal bias and external disturbances. Acknowledging potential mismatches between the controller and subsystems, we establish less conservative criteria for practical ISS using Lyapunov-Razumikhin functions (LRFs) with indefinite differential operators. Furthermore, to accommodate mode variability and relax stringent constraints on switching signals, we develop a novel condition based on the mode-dependent average dwell time (MDADT) technique. This condition is specifically tailored for asynchronous switching and notably maintains consistency with the synchronous case, reducing to the classical condition when the switching signal delay approaches zero. The practical relevance of our work is highlighted through the extension of an exponential stability criterion and its successful application to a mechanical system with backlash hysteresis.
{"title":"Practical input-to-state stability of switched stochastic delay nonlinear systems and its application to hysteretic mechanical systems","authors":"Tianze Xie , Hui Wang , Jian Ding , Quanxin Zhu","doi":"10.1016/j.jfranklin.2025.108382","DOIUrl":"10.1016/j.jfranklin.2025.108382","url":null,"abstract":"<div><div>Existing literature on input-to-state stability (ISS) primarily focuses on transient responses and robustness to external disturbances, yet it often fails to capture the inherent modeling bias in systems like those exhibiting mechanical hysteresis. To address this limitation, we introduce the concept of practical ISS for switched stochastic nonlinear time-delay systems (SSNTDSs), which provides a comprehensive framework for analyzing robustness against both internal bias and external disturbances. Acknowledging potential mismatches between the controller and subsystems, we establish less conservative criteria for practical ISS using Lyapunov-Razumikhin functions (LRFs) with indefinite differential operators. Furthermore, to accommodate mode variability and relax stringent constraints on switching signals, we develop a novel condition based on the mode-dependent average dwell time (MDADT) technique. This condition is specifically tailored for asynchronous switching and notably maintains consistency with the synchronous case, reducing to the classical condition when the switching signal delay approaches zero. The practical relevance of our work is highlighted through the extension of an exponential stability criterion and its successful application to a mechanical system with backlash hysteresis.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108382"},"PeriodicalIF":4.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145915210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-18DOI: 10.1016/j.jfranklin.2025.108307
Zhiyuan Peng, Naifan Zhang, Yuanbo Tang, Yang Li
DNA sequences encode critical genetic information, yet their variable length and discrete nature impede direct utilization in deep learning models. Existing DNA representation schemes convert sequences into numerical vectors but fail to capture structural features of local subsequences and often suffer from limited interpretability and poor generalization on small datasets. To address these limitations, we propose Dy-mer, an interpretable and robust DNA representation scheme based on dictionary learning. Dy-mer formulates an optimization problem in tensor format, which ensures computational efficiency in batch processing. Our scheme reconstructs DNA sequences as concatenations of dynamic-length subsequences (dymers) through a convolution operation and simultaneously optimize a learnable dymer dictionary and sparse representations. Our method achieves state-of-the-art performance in downstream tasks such as DNA promoter classification and motif detection. Experiments further show that the learned dymers match known DNA motifs and clustering using Dy-mer yields semantically meaningful phylogenetic trees. These results demonstrate that the proposed approach achieves both strong predictive performance and high interpretability, making it well suited for biological research applications.
{"title":"Dy-mer: An explainable DNA sequence representation scheme using dictionary learning","authors":"Zhiyuan Peng, Naifan Zhang, Yuanbo Tang, Yang Li","doi":"10.1016/j.jfranklin.2025.108307","DOIUrl":"10.1016/j.jfranklin.2025.108307","url":null,"abstract":"<div><div>DNA sequences encode critical genetic information, yet their variable length and discrete nature impede direct utilization in deep learning models. Existing DNA representation schemes convert sequences into numerical vectors but fail to capture structural features of local subsequences and often suffer from limited interpretability and poor generalization on small datasets. To address these limitations, we propose <strong>Dy-mer</strong>, an interpretable and robust DNA representation scheme based on dictionary learning. Dy-mer formulates an optimization problem in tensor format, which ensures computational efficiency in batch processing. Our scheme reconstructs DNA sequences as concatenations of dynamic-length subsequences (dymers) through a convolution operation and simultaneously optimize a learnable dymer dictionary and sparse representations. Our method achieves state-of-the-art performance in downstream tasks such as DNA promoter classification and motif detection. Experiments further show that the learned dymers match known DNA motifs and clustering using Dy-mer yields semantically meaningful phylogenetic trees. These results demonstrate that the proposed approach achieves both strong predictive performance and high interpretability, making it well suited for biological research applications.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108307"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-18DOI: 10.1016/j.jfranklin.2025.108364
Ning Zhang , Yugang Niu , Wenhai Qi
This paper considers the problem of model-free adaptive sliding mode control (MFASMC) for nonlinear networked control systems (NCSs), in which both random deception attacks and intermittent denial-of-service (DoS) attacks may occur in the data transmission channel from sensor to controller. Based on the partial format dynamic linearization (PFDL) model, a dual-observer structure consisting of an adaptive observer and a sliding mode disturbance observer is constructed. The adaptive observer is proposed to estimate the unavailable system output under DoS attacks, meanwhile, the composite disturbance that includes external disturbance and unmodeled dynamics is estimated via a sliding mode disturbance observer. Under this dual-observer frame, the designed MFASMC law can be updated in real time to mitigate the impact of the attacks and the composite disturbance with unknown boundary such that the boundedness of the desired output tracking error can be ensured. Finally, the proposed MFASMC strategy is verified by two examples.
{"title":"Model-free adaptive sliding mode security control under hybrid attacks: A dual-observer approach via partial format dynamic linearization","authors":"Ning Zhang , Yugang Niu , Wenhai Qi","doi":"10.1016/j.jfranklin.2025.108364","DOIUrl":"10.1016/j.jfranklin.2025.108364","url":null,"abstract":"<div><div>This paper considers the problem of model-free adaptive sliding mode control (MFASMC) for nonlinear networked control systems (NCSs), in which both random deception attacks and intermittent denial-of-service (DoS) attacks may occur in the data transmission channel from sensor to controller. Based on the partial format dynamic linearization (PFDL) model, a dual-observer structure consisting of an adaptive observer and a sliding mode disturbance observer is constructed. The adaptive observer is proposed to estimate the unavailable system output under DoS attacks, meanwhile, the composite disturbance that includes external disturbance and unmodeled dynamics is estimated via a sliding mode disturbance observer. Under this dual-observer frame, the designed MFASMC law can be updated in real time to mitigate the impact of the attacks and the composite disturbance with unknown boundary such that the boundedness of the desired output tracking error can be ensured. Finally, the proposed MFASMC strategy is verified by two examples.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108364"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-17DOI: 10.1016/j.jfranklin.2025.108332
Raziyeh Erfanifar, Masoud Hajarian
Many scientific disciplines, from basic sciences to engineering, frequently encounter the challenge of solving systems of nonlinear problems. Addressing this challenge demands the development of accurate and efficient computational methods. In this work, we propose a novel multi-step iterative method that achieves an exceptional convergence order of , where m ≥ 3 denotes the number of iterative steps. This method significantly enhances computational efficiency without compromising accuracy, as it requires only a single evaluation and inversion of the Jacobian matrix per iteration cycle. To further optimize performance, the linear systems arising at every step are solved via LU decomposition, bypassing the computational burden of direct matrix inversion. As a result, the proposed method attains a higher convergence order than existing multi-step methods while maintaining comparable computational costs. Its efficiency makes it particularly well-suited for large-scale problems, where computational overhead is a critical concern. To validate the method’s effectiveness, we conducted comprehensive numerical experiments, assessing its efficiency, accuracy, and the geometry of its basins of attraction. The results consistently aligned with theoretical predictions, demonstrating the method’s superior performance over conventional approaches. Additionally, the method to solve standard nonlinear systems commonly arising in science and engineering is applied. Finally, we extended its application to image processing tasks, where it effectively addressed systems of nonlinear problem. The numerical outcomes underscored the method’s robustness, stability, and potential to outperform traditional iterative methods.
{"title":"An efficient high-order iterative method to solve systems of nonlinear equations with applications to differential equations and image processing","authors":"Raziyeh Erfanifar, Masoud Hajarian","doi":"10.1016/j.jfranklin.2025.108332","DOIUrl":"10.1016/j.jfranklin.2025.108332","url":null,"abstract":"<div><div>Many scientific disciplines, from basic sciences to engineering, frequently encounter the challenge of solving systems of nonlinear problems. Addressing this challenge demands the development of accurate and efficient computational methods. In this work, we propose a novel multi-step iterative method that achieves an exceptional convergence order of <span><math><mrow><mn>3</mn><mi>m</mi><mo>+</mo><mn>2</mn></mrow></math></span>, where <em>m</em> ≥ 3 denotes the number of iterative steps. This method significantly enhances computational efficiency without compromising accuracy, as it requires only a single evaluation and inversion of the Jacobian matrix per iteration cycle. To further optimize performance, the linear systems arising at every step are solved via LU decomposition, bypassing the computational burden of direct matrix inversion. As a result, the proposed method attains a higher convergence order than existing multi-step methods while maintaining comparable computational costs. Its efficiency makes it particularly well-suited for large-scale problems, where computational overhead is a critical concern. To validate the method’s effectiveness, we conducted comprehensive numerical experiments, assessing its efficiency, accuracy, and the geometry of its basins of attraction. The results consistently aligned with theoretical predictions, demonstrating the method’s superior performance over conventional approaches. Additionally, the method to solve standard nonlinear systems commonly arising in science and engineering is applied. Finally, we extended its application to image processing tasks, where it effectively addressed systems of nonlinear problem. The numerical outcomes underscored the method’s robustness, stability, and potential to outperform traditional iterative methods.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108332"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-19DOI: 10.1016/j.jfranklin.2025.108325
Qiliang Zhang , Ze Wang , Jianfang Jiao , Yongyuan Yu
This paper develops a robust optimal control method to study the finite-time set stabilization (FTSS) of probabilistic Boolean control networks (PBCNs). First, an efficient algorithm is proposed to determine the solvability of the FTSS of PBCNs by constructing index vectors. Then, a pre-step cost function is introduced, which is based on the largest control invariant subset of PBCNs. By applying the dynamic programming theory, an algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state. Compared with existing results, the proposed robust optimal control method transforms the FTSS of PBCNs into an optimization problem and significantly reduces the time complexity from O(γN3M) to O(γN2M). Finally, an illustrative example involving a biological system validates the effectiveness of the proposed approach, demonstrating significant improvements in computational efficiency.
{"title":"Finite-time set stabilization of probabilistic boolean control networks: A robust optimal control approach","authors":"Qiliang Zhang , Ze Wang , Jianfang Jiao , Yongyuan Yu","doi":"10.1016/j.jfranklin.2025.108325","DOIUrl":"10.1016/j.jfranklin.2025.108325","url":null,"abstract":"<div><div>This paper develops a robust optimal control method to study the finite-time set stabilization (FTSS) of probabilistic Boolean control networks (PBCNs). First, an efficient algorithm is proposed to determine the solvability of the FTSS of PBCNs by constructing index vectors. Then, a pre-step cost function is introduced, which is based on the largest control invariant subset of PBCNs. By applying the dynamic programming theory, an algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state. Compared with existing results, the proposed robust optimal control method transforms the FTSS of PBCNs into an optimization problem and significantly reduces the time complexity from <em>O</em>(<em>γN</em><sup>3</sup><em>M</em>) to <em>O</em>(<em>γN</em><sup>2</sup><em>M</em>). Finally, an illustrative example involving a biological system validates the effectiveness of the proposed approach, demonstrating significant improvements in computational efficiency.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108325"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-17DOI: 10.1016/j.jfranklin.2025.108365
Sara Fakih, Laetitia Perez, Laurent Autrique
This study aims to maintain a thermal system, whose evolution is modeled by a parabolic partial differential equation, close to a target state while mitigating disturbances caused by a moving fan. To do this, an additional actuator (a constant-flow heat source) is added and a quasi-online conjugate gradient method (CGM) is developed to determine its trajectory in order to track and reject fan disturbances. The method extends the classical offline CGM to a sliding interval formulation that allows real-time identification of the actuator’s trajectory in order to best reject the disturbance. In addition, the proposed approach provides a strategy for selecting the most sensitive sensors over time in order to determine the control law under the best conditions.
{"title":"Strategic sensors selection for the quasi online heat source trajectory control in 2D mobile disturbance rejection","authors":"Sara Fakih, Laetitia Perez, Laurent Autrique","doi":"10.1016/j.jfranklin.2025.108365","DOIUrl":"10.1016/j.jfranklin.2025.108365","url":null,"abstract":"<div><div>This study aims to maintain a thermal system, whose evolution is modeled by a parabolic partial differential equation, close to a target state while mitigating disturbances caused by a moving fan. To do this, an additional actuator (a constant-flow heat source) is added and a quasi-online conjugate gradient method (CGM) is developed to determine its trajectory in order to track and reject fan disturbances. The method extends the classical offline CGM to a sliding interval formulation that allows real-time identification of the actuator’s trajectory in order to best reject the disturbance. In addition, the proposed approach provides a strategy for selecting the most sensitive sensors over time in order to determine the control law under the best conditions.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108365"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-20DOI: 10.1016/j.jfranklin.2025.108349
Qian Zhang, Ximei Liu
This paper investigates computationally efficient identification methods for multivariable autoregressive output-error autoregressive moving-average systems. To tackle high-dimensional parameter estimation challenges, the multivariable system is decomposed into several subsystems. Furthermore, each subsystem identification model is decomposed into two small-scale sub-identification models to reduce the computational burden. Based on the hierarchical identification principle, a two-stage auxiliary model maximum likelihood least squares-based iterative algorithm is proposed. The analysis of floating point operations shows that the proposed algorithm achieves higher computational efficiency than the existing auxiliary model maximum likelihood least squares-based iterative algorithm. Simulation results demonstrate that the proposed algorithm is effective and achieves high parameter estimation accuracy.
{"title":"Two-stage auxiliary model maximum likelihood least squares-based iterative estimation method for general stochastic multivariable systems","authors":"Qian Zhang, Ximei Liu","doi":"10.1016/j.jfranklin.2025.108349","DOIUrl":"10.1016/j.jfranklin.2025.108349","url":null,"abstract":"<div><div>This paper investigates computationally efficient identification methods for multivariable autoregressive output-error autoregressive moving-average systems. To tackle high-dimensional parameter estimation challenges, the multivariable system is decomposed into several subsystems. Furthermore, each subsystem identification model is decomposed into two small-scale sub-identification models to reduce the computational burden. Based on the hierarchical identification principle, a two-stage auxiliary model maximum likelihood least squares-based iterative algorithm is proposed. The analysis of floating point operations shows that the proposed algorithm achieves higher computational efficiency than the existing auxiliary model maximum likelihood least squares-based iterative algorithm. Simulation results demonstrate that the proposed algorithm is effective and achieves high parameter estimation accuracy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108349"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-20DOI: 10.1016/j.jfranklin.2025.108366
Lei Fu , Shang Cui , Huilan Liu
This paper presents a novel event-triggered mechanism (ETM) with adaptive triggering thresholds and develops a distributed cooperative load frequency control (LFC) framework for cyber-physical power systems (CPPS) subject to hybrid attacks. By integrating uncertain saturated nonlinearities inherent in turbine and governor dynamics of the CPPS, this paper establishes a Takagi-Sugeno (T-S) fuzzy system framework to characterize nonlinear features and devises a fuzzy distributed cooperative proportional-integral (PI) controller that explicitly accounts for actuator faults. Through the construction of a two-sided closed-loop Lyapunov-Krasovskii functional (LKF) incorporating delay-dependent matrices, an asymptotic stability criterion with enhanced H∞ performance is rigorously derived. Illustrative examples involving a one-area and a three-area CPPS validate the effectiveness of the methodology in improving dynamic performance and cyber-resilience.
{"title":"Event-triggered control for T-S fuzzy multi-area cyber-physical power system under hybrid attacks","authors":"Lei Fu , Shang Cui , Huilan Liu","doi":"10.1016/j.jfranklin.2025.108366","DOIUrl":"10.1016/j.jfranklin.2025.108366","url":null,"abstract":"<div><div>This paper presents a novel event-triggered mechanism (ETM) with adaptive triggering thresholds and develops a distributed cooperative load frequency control (LFC) framework for cyber-physical power systems (CPPS) subject to hybrid attacks. By integrating uncertain saturated nonlinearities inherent in turbine and governor dynamics of the CPPS, this paper establishes a Takagi-Sugeno (T-S) fuzzy system framework to characterize nonlinear features and devises a fuzzy distributed cooperative proportional-integral (PI) controller that explicitly accounts for actuator faults. Through the construction of a two-sided closed-loop Lyapunov-Krasovskii functional (LKF) incorporating delay-dependent matrices, an asymptotic stability criterion with enhanced <em>H</em><sub>∞</sub> performance is rigorously derived. Illustrative examples involving a one-area and a three-area CPPS validate the effectiveness of the methodology in improving dynamic performance and cyber-resilience.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108366"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-15Epub Date: 2025-12-16DOI: 10.1016/j.jfranklin.2025.108345
Ziwen Shen , Tao Dong , Tingwen Huang , Huaqing Li
This article addresses the intelligent prescribed-time bipartite synchronization (BS) control problem of complex networks (CNs) with cooperative-competitive relationships. Firstly, based on the interaction of cooperation and competition among nodes, a state error system is constructed. A novel performance value function is proposed, which contains state error, synchronization accuracy, and prescribed time. Different from the existing performance value function that only contains state error, the proposed performance value function contains more control parameters, which can more accurately reflect the diversified needs in actual control. By solving the Hamilton-Jacobi-Bellman (HJB) equation based on the performance value function, the optimal prescribed-time control policy is obtained. Then, a fuzzy actor-critic framework is used to implement the control policy. In addition, the convergence of the algorithm is analyzed, which shows that the proposed algorithm can make the state error converge to a prescribed accuracy within a prescribed time. Finally, two numerical simulation examples are used to verify the effectiveness of the algorithm.
{"title":"Intelligent prescribed-time bipartite synchronization control of complex networks with cooperative-competitive relationships via fuzzy reinforcement learning","authors":"Ziwen Shen , Tao Dong , Tingwen Huang , Huaqing Li","doi":"10.1016/j.jfranklin.2025.108345","DOIUrl":"10.1016/j.jfranklin.2025.108345","url":null,"abstract":"<div><div>This article addresses the intelligent prescribed-time bipartite synchronization (BS) control problem of complex networks (CNs) with cooperative-competitive relationships. Firstly, based on the interaction of cooperation and competition among nodes, a state error system is constructed. A novel performance value function is proposed, which contains state error, synchronization accuracy, and prescribed time. Different from the existing performance value function that only contains state error, the proposed performance value function contains more control parameters, which can more accurately reflect the diversified needs in actual control. By solving the Hamilton-Jacobi-Bellman (HJB) equation based on the performance value function, the optimal prescribed-time control policy is obtained. Then, a fuzzy actor-critic framework is used to implement the control policy. In addition, the convergence of the algorithm is analyzed, which shows that the proposed algorithm can make the state error converge to a prescribed accuracy within a prescribed time. Finally, two numerical simulation examples are used to verify the effectiveness of the algorithm.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108345"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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