Pub Date : 2026-03-01Epub Date: 2026-01-13DOI: 10.1016/j.jfranklin.2026.108419
Gang Chen, Arong Xue
This paper investigates the adaptive tracking control for stochastic high-order nonlinear systems with actuator faults and time-varying input delay. A novel fault-tolerant control scheme with ensured tracking performance is proposed and analyzed. More specially, the prescribed finite-time performance (PFTP) function is integrated into the controller design to achieve the prescribed transient performance. To deal with the problem of complexity explosion for the controller design, the extended high-order error compensation mechanism combined with the dynamic surface control approach is presented, which possesses enhanced robustness and broader applicability compared to existing methods. Additionally, an efficient high-order auxiliary system (HOAS) is constructed to handle the system inputs limited by faults and time delays concurrently. By combining the PFTP function with the asymptotic tracking control, the proposed control scheme first ensures that the tracking errors reach the prescribed range within the prescribed time and then achieve asymptotic convergence in probability. Finally, two simulation examples are employed to demonstrate the effectiveness of the designed control scheme.
{"title":"Adaptive control for stochastic high-order nonlinear systems with guaranteed tracking performance","authors":"Gang Chen, Arong Xue","doi":"10.1016/j.jfranklin.2026.108419","DOIUrl":"10.1016/j.jfranklin.2026.108419","url":null,"abstract":"<div><div>This paper investigates the adaptive tracking control for stochastic high-order nonlinear systems with actuator faults and time-varying input delay. A novel fault-tolerant control scheme with ensured tracking performance is proposed and analyzed. More specially, the prescribed finite-time performance (PFTP) function is integrated into the controller design to achieve the prescribed transient performance. To deal with the problem of complexity explosion for the controller design, the extended high-order error compensation mechanism combined with the dynamic surface control approach is presented, which possesses enhanced robustness and broader applicability compared to existing methods. Additionally, an efficient high-order auxiliary system (HOAS) is constructed to handle the system inputs limited by faults and time delays concurrently. By combining the PFTP function with the asymptotic tracking control, the proposed control scheme first ensures that the tracking errors reach the prescribed range within the prescribed time and then achieve asymptotic convergence in probability. Finally, two simulation examples are employed to demonstrate the effectiveness of the designed control scheme.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108419"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981579","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 : 2026-03-01Epub Date: 2026-01-18DOI: 10.1016/j.jfranklin.2026.108412
Jingqiu Li, Ruifeng Zhang, Rongni Yang
This paper explores the security control problem for discrete-time cyber-physical systems (CPSs) subject to external disturbances and periodic denial-of-service (DoS) attacks. Particularly, different from the existing results, a novel active compensation scheme is proposed for the considered CPSs, which consists of the disturbance reconstruction and one-step prediction for data loss caused by DoS attacks. First, the periodic DoS attacks are modeled via a switching strategy, such that the CPSs are characterized as a class of switched systems with stable and unstable subsystems during the silent and active intervals, respectively. Then, the augmented systems are obtained by introducing a sliding mode observer (SMO), which can achieve the real-time estimation of system states and unknown disturbances. Further, through designing the SMO and the prediction-based controller with the help of piecewise Lyapunov functions, sufficient conditions are derived to ensure the practical exponential stability of the resulting augmented systems. Finally, an application to the unmanned ground vehicle is provided to demonstrate the effectiveness and advantages of the proposed method.
{"title":"Sliding mode observer based security control of cyber-physical systems under periodic DoS attacks: An active compensation scheme","authors":"Jingqiu Li, Ruifeng Zhang, Rongni Yang","doi":"10.1016/j.jfranklin.2026.108412","DOIUrl":"10.1016/j.jfranklin.2026.108412","url":null,"abstract":"<div><div>This paper explores the security control problem for discrete-time cyber-physical systems (CPSs) subject to external disturbances and periodic denial-of-service (DoS) attacks. Particularly, different from the existing results, a novel active compensation scheme is proposed for the considered CPSs, which consists of the disturbance reconstruction and one-step prediction for data loss caused by DoS attacks. First, the periodic DoS attacks are modeled via a switching strategy, such that the CPSs are characterized as a class of switched systems with stable and unstable subsystems during the silent and active intervals, respectively. Then, the augmented systems are obtained by introducing a sliding mode observer (SMO), which can achieve the real-time estimation of system states and unknown disturbances. Further, through designing the SMO and the prediction-based controller with the help of piecewise Lyapunov functions, sufficient conditions are derived to ensure the practical exponential stability of the resulting augmented systems. Finally, an application to the unmanned ground vehicle is provided to demonstrate the effectiveness and advantages of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108412"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025301","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 : 2026-03-01Epub Date: 2026-01-17DOI: 10.1016/j.jfranklin.2026.108435
Li Zhou , Yonghua Wang , Guanyu Lai , Yongwei Zhang
This paper proposes an adaptive optimized intelligent control strategy for nonlinear strict-feedback systems with asymmetric hysteretic actuators by integrating reinforcement learning with backstepping. Although inverse hysteresis compensation is commonly employed, its performance is inherently limited by modeling inaccuracies, leading to non-negligible residual error. To address this issue, a dual-stage control framework is developed. First, an inverse asymmetric shifted Prandtl-Ishlinskii hysteresis compensator is applied to counteract the dominant hysteresis nonlinearity. Subsequently, an optimized backstepping controller is designed using a reinforcement learning-based identifier-critic-actor architecture with the dynamic surface technique to further suppress the residual error, thereby ensuring system stability and tracking performance. The main contributions of this work are threefold: 1) A simplified reinforcement learning mechanism is established, where the weight update laws for the actor and critic networks are designed to relax the persistent excitation condition while reducing computational complexity; 2) The dynamic surface technique is introduced to effectively circumvent the “differential explosion” problem inherent in conventional backstepping; 3) Adaptive parameters are incorporated to compensate for the residual error following inverse compensation. A rigorous Lyapunov-based stability analysis demonstrates that all closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results confirm the effectiveness and robustness of the proposed controller.
{"title":"Inverse compensation-based optimized intelligent control for nonlinear systems driven by hysteretic actuators","authors":"Li Zhou , Yonghua Wang , Guanyu Lai , Yongwei Zhang","doi":"10.1016/j.jfranklin.2026.108435","DOIUrl":"10.1016/j.jfranklin.2026.108435","url":null,"abstract":"<div><div>This paper proposes an adaptive optimized intelligent control strategy for nonlinear strict-feedback systems with asymmetric hysteretic actuators by integrating reinforcement learning with backstepping. Although inverse hysteresis compensation is commonly employed, its performance is inherently limited by modeling inaccuracies, leading to non-negligible residual error. To address this issue, a dual-stage control framework is developed. First, an inverse asymmetric shifted Prandtl-Ishlinskii hysteresis compensator is applied to counteract the dominant hysteresis nonlinearity. Subsequently, an optimized backstepping controller is designed using a reinforcement learning-based identifier-critic-actor architecture with the dynamic surface technique to further suppress the residual error, thereby ensuring system stability and tracking performance. The main contributions of this work are threefold: 1) A simplified reinforcement learning mechanism is established, where the weight update laws for the actor and critic networks are designed to relax the persistent excitation condition while reducing computational complexity; 2) The dynamic surface technique is introduced to effectively circumvent the “differential explosion” problem inherent in conventional backstepping; 3) Adaptive parameters are incorporated to compensate for the residual error following inverse compensation. A rigorous Lyapunov-based stability analysis demonstrates that all closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results confirm the effectiveness and robustness of the proposed controller.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108435"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025305","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 : 2026-03-01Epub Date: 2026-01-13DOI: 10.1016/j.jfranklin.2026.108418
Lin Xiao, Yuyang Liu, Qiuyue Zuo, Mengrui Cao, Wangqiu Kuang
Sliding mode control has been extensively applied in unmanned aerial vehicle control for its robustness to nonlinear systems. However, its performance is sensitive to initial conditions and controller parameters, particularly reaching time. To address this, this paper proposes a Fuzzy Weighted Self-Allocation Sliding Mode Controller (FWSASMC) for quadrotor UAV trajectory tracking under bounded disturbances. By leveraging zeroing neural dynamics, the FWSASMC achieves fixed-time convergence through a fuzzy-weighted self-allocation scheme and an adaptive parameter. The scheme identifies varying effects of components in the conventional activation function during neural dynamics and uses fuzzy-optimized weights to coordinate them, accelerating convergence. The improved activation function is smoothed to construct a non-singular sliding surface, while the adaptive parameter refines the reaching law. Theoretical analysis and simulations verify convergence, demonstrating superior trajectory tracking performance and highlighting its potential for UAV applications, particularly in time-varying target tracking.
{"title":"A fuzzy weighted self-allocation sliding mode controller for UAV trajectory tracking","authors":"Lin Xiao, Yuyang Liu, Qiuyue Zuo, Mengrui Cao, Wangqiu Kuang","doi":"10.1016/j.jfranklin.2026.108418","DOIUrl":"10.1016/j.jfranklin.2026.108418","url":null,"abstract":"<div><div>Sliding mode control has been extensively applied in unmanned aerial vehicle control for its robustness to nonlinear systems. However, its performance is sensitive to initial conditions and controller parameters, particularly reaching time. To address this, this paper proposes a Fuzzy Weighted Self-Allocation Sliding Mode Controller (FWSASMC) for quadrotor UAV trajectory tracking under bounded disturbances. By leveraging zeroing neural dynamics, the FWSASMC achieves fixed-time convergence through a fuzzy-weighted self-allocation scheme and an adaptive parameter. The scheme identifies varying effects of components in the conventional activation function during neural dynamics and uses fuzzy-optimized weights to coordinate them, accelerating convergence. The improved activation function is smoothed to construct a non-singular sliding surface, while the adaptive parameter refines the reaching law. Theoretical analysis and simulations verify convergence, demonstrating superior trajectory tracking performance and highlighting its potential for UAV applications, particularly in time-varying target tracking.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108418"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969349","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 : 2026-03-01Epub Date: 2026-01-25DOI: 10.1016/j.jfranklin.2026.108452
Li-Ying Hao, Lin-Fan Liu, Huiying Liu
Traditional trajectory tracking control methods rely excessively on precise models of unmanned marine vehicles (UMVs). However, due to complex marine environmental disturbances, it is challenging to obtain accurate models for UMVs. Therefore, a data-driven approach is employed for UMVs trajectory tracking control. An improved prediction compensation method is proposed, which incorporates an arctangent function for pseudo Jacobian matrix updating to achieve more accurate predictions compared to traditional methods. Moreover, an event-triggered (ET) mechanism incorporating a dead-zone operator is designed. Compared to fixed triggering conditions, this mechanism balances system performance and triggering frequency by adjusting the parameter of the dead-zone operator, thereby enhancing triggering flexibility. In addition, an improved extended state observer (ESO) is designed by integrating the successfully transmitted output and the predicted output. It effectively addresses the impact of hybrid attacks and ET on the ESO in the disturbed system, enabling the estimation of lumped disturbances. This paper introduces a novel secure control strategy that integrates an attack compensation mechanism with an improved ESO, ensuring that UMVs can reliably track the desired trajectory despite external disturbances and hybrid attacks. The entire design process relies on input/output data only, and simulation comparisons validate the effectiveness of the proposed methods.
{"title":"Event-triggered data-driven secure control for unmanned marine vehicles under hybrid attacks","authors":"Li-Ying Hao, Lin-Fan Liu, Huiying Liu","doi":"10.1016/j.jfranklin.2026.108452","DOIUrl":"10.1016/j.jfranklin.2026.108452","url":null,"abstract":"<div><div>Traditional trajectory tracking control methods rely excessively on precise models of unmanned marine vehicles (UMVs). However, due to complex marine environmental disturbances, it is challenging to obtain accurate models for UMVs. Therefore, a data-driven approach is employed for UMVs trajectory tracking control. An improved prediction compensation method is proposed, which incorporates an arctangent function for pseudo Jacobian matrix updating to achieve more accurate predictions compared to traditional methods. Moreover, an event-triggered (ET) mechanism incorporating a dead-zone operator is designed. Compared to fixed triggering conditions, this mechanism balances system performance and triggering frequency by adjusting the parameter of the dead-zone operator, thereby enhancing triggering flexibility. In addition, an improved extended state observer (ESO) is designed by integrating the successfully transmitted output and the predicted output. It effectively addresses the impact of hybrid attacks and ET on the ESO in the disturbed system, enabling the estimation of lumped disturbances. This paper introduces a novel secure control strategy that integrates an attack compensation mechanism with an improved ESO, ensuring that UMVs can reliably track the desired trajectory despite external disturbances and hybrid attacks. The entire design process relies on input/output data only, and simulation comparisons validate the effectiveness of the proposed methods.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108452"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190053","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}
This paper tackles the challenge of identifying parameters in a linear auto-regressive exogenous (ARX) model, particularly when using multiple sensors with unknown noise variances. To address this, we have expanded the multitask maximum likelihood (MTML) identification method into a robust multitask expectation maximization (MEM) approach. This new method not only estimates the model parameters and unknown noise variances but also determines analytical weights simultaneously. Our proposed MEM method outperforms the MTML in terms of accuracy, benefiting from the integration of multiple unknown noise variances and its adaptability to fluctuating noise conditions. The effectiveness of the MEM method is demonstrated through a numerical example and a case study involving a continuous fermentor, showcasing its superior identification capabilities and adaptability.
{"title":"Identification for ARX models with multiple unknown noise variances: A multitask expectation maximization approach","authors":"Yixuan Chu , Xiaojing Ping , Shunyi Zhao , Chengxi Zhang , Ruomu Tan","doi":"10.1016/j.jfranklin.2025.108399","DOIUrl":"10.1016/j.jfranklin.2025.108399","url":null,"abstract":"<div><div>This paper tackles the challenge of identifying parameters in a linear auto-regressive exogenous (ARX) model, particularly when using multiple sensors with unknown noise variances. To address this, we have expanded the multitask maximum likelihood (MTML) identification method into a robust multitask expectation maximization (MEM) approach. This new method not only estimates the model parameters and unknown noise variances but also determines analytical weights simultaneously. Our proposed MEM method outperforms the MTML in terms of accuracy, benefiting from the integration of multiple unknown noise variances and its adaptability to fluctuating noise conditions. The effectiveness of the MEM method is demonstrated through a numerical example and a case study involving a continuous fermentor, showcasing its superior identification capabilities and adaptability.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108399"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170882","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 : 2026-03-01Epub Date: 2026-01-22DOI: 10.1016/j.jfranklin.2026.108433
Yi Chang , Yiqi Wang , Zhiguang Feng , Ruifeng Zhu
This paper studies the spatial trajectory tracking control issue for an underactuated autonomous underwater vehicle (AUV) with disturbances. Firstly, by performing coordinate transformation, a strict-feedback form of error variables is constructed, which facilitates the design of the scheme using the backstepping method. Secondly, neural networks are introduced to approximate the disturbances and the complex dynamic of AUV, which not only reduces the requirement for model accuracy in the backstepping method, but also simplifies the design process. At the same time, the inevitable problem of “computational explosion” in the backstepping method is solved by the command filter, and combined with the adaptive control method, the weights of the neural networks are adjusted online to complete the design of the adaptive neural networks command filter controllers. Lyapunov theory analysis demonstrates that all signals are ultimately bounded, and the tracking error converges to a small neighborhood near the origin. Finally, a comparative simulation is provided to validate the effectiveness and superiority of the designed control scheme.
{"title":"Research on adaptive neural networks spatial trajectory tracking control problem of an underactuated AUV under disturbances","authors":"Yi Chang , Yiqi Wang , Zhiguang Feng , Ruifeng Zhu","doi":"10.1016/j.jfranklin.2026.108433","DOIUrl":"10.1016/j.jfranklin.2026.108433","url":null,"abstract":"<div><div>This paper studies the spatial trajectory tracking control issue for an underactuated autonomous underwater vehicle (AUV) with disturbances. Firstly, by performing coordinate transformation, a strict-feedback form of error variables is constructed, which facilitates the design of the scheme using the backstepping method. Secondly, neural networks are introduced to approximate the disturbances and the complex dynamic of AUV, which not only reduces the requirement for model accuracy in the backstepping method, but also simplifies the design process. At the same time, the inevitable problem of “computational explosion” in the backstepping method is solved by the command filter, and combined with the adaptive control method, the weights of the neural networks are adjusted online to complete the design of the adaptive neural networks command filter controllers. Lyapunov theory analysis demonstrates that all signals are ultimately bounded, and the tracking error converges to a small neighborhood near the origin. Finally, a comparative simulation is provided to validate the effectiveness and superiority of the designed control scheme.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108433"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079780","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 : 2026-03-01Epub Date: 2026-01-06DOI: 10.1016/j.jfranklin.2026.108405
Yanming Liang , Yongfeng Guo , Qingzeng Song
Abnormal directional propagation of neural signals, as observed in epilepsy, cannot be fully captured by traditional single layer neuronal models driven by Gaussian noise. Departing from prior studies that emphasized Gaussian perturbations or single layer topologies, this work investigates how localized non-Gaussian Lévy noise influences cross-layer synchronization and directional information flow in a multilayer neuronal network. We construct a two-layer FitzHugh-Nagumo (FHN) system with non-local coupling in which only the first layer is exposed to Lévy noise, thereby mimicking focal pathological discharges and enabling the study of interlayer transmission through diffusive coupling. Using transfer entropy (TE) as a directional measure of information flow, we systematically analyze how the noise intensity, stability index, and skewness regulate interlayer communication and synchronization dynamics. The results show that Lévy noise not only induces chimera and solitary states but also drives symmetry breaking in interlayer information flow, with the noise driven layer exerting the dominant regulatory influence. The stability index organizes transitions among synchronized, chimera, and desynchronized regimes, whereas skewness modulates the prevailing direction of information transfer. Notably, directional TE remains elevated even under global desynchronization, indicating persistent causal influence in pathological conditions. These findings reveal a noise induced mechanism for asymmetric information transfer and provide a physiologically grounded framework for modeling epileptic brain dynamics.
{"title":"Directional Information Flow and Chimera States in a Multi-layer FitzHugh–Nagumo Neuronal Network Excited by Local Lévy Noise","authors":"Yanming Liang , Yongfeng Guo , Qingzeng Song","doi":"10.1016/j.jfranklin.2026.108405","DOIUrl":"10.1016/j.jfranklin.2026.108405","url":null,"abstract":"<div><div>Abnormal directional propagation of neural signals, as observed in epilepsy, cannot be fully captured by traditional single layer neuronal models driven by Gaussian noise. Departing from prior studies that emphasized Gaussian perturbations or single layer topologies, this work investigates how localized non-Gaussian Lévy noise influences cross-layer synchronization and directional information flow in a multilayer neuronal network. We construct a two-layer FitzHugh-Nagumo (FHN) system with non-local coupling in which only the first layer is exposed to Lévy noise, thereby mimicking focal pathological discharges and enabling the study of interlayer transmission through diffusive coupling. Using transfer entropy (TE) as a directional measure of information flow, we systematically analyze how the noise intensity, stability index, and skewness regulate interlayer communication and synchronization dynamics. The results show that Lévy noise not only induces chimera and solitary states but also drives symmetry breaking in interlayer information flow, with the noise driven layer exerting the dominant regulatory influence. The stability index organizes transitions among synchronized, chimera, and desynchronized regimes, whereas skewness modulates the prevailing direction of information transfer. Notably, directional TE remains elevated even under global desynchronization, indicating persistent causal influence in pathological conditions. These findings reveal a noise induced mechanism for asymmetric information transfer and provide a physiologically grounded framework for modeling epileptic brain dynamics.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 4","pages":"Article 108405"},"PeriodicalIF":4.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146170836","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: 2026-01-08DOI: 10.1016/j.jfranklin.2026.108403
Cong Li , Qingling Wang
This paper investigates the distributed aggregative optimization (DAO) problem for high-order nonlinear multi-agent systems over time-varying graphs. We first introduce a new class of aggregative regulation variables that integrate sampled neighbor data during each sampling period, these variables are upgraded through an auxiliary function. By leveraging the C-step consensus contraction method alongside these variables, we reformulate the time-varying graphs DAO problem as a regulation problem, thereby facilitating the use of classical control techniques to address complex nonlinear dynamics. Additionally, we propose a control law that incorporates performance functions and aggregative regulation variables to solve the DAO problem for high-order nonlinear agents with state delays. Numerical simulations demonstrate the validity of the proposed framework.
{"title":"Distributed aggregative optimization for nonlinear multi-agent systems with state delays under time-varying graphs using sampling technology","authors":"Cong Li , Qingling Wang","doi":"10.1016/j.jfranklin.2026.108403","DOIUrl":"10.1016/j.jfranklin.2026.108403","url":null,"abstract":"<div><div>This paper investigates the distributed aggregative optimization (DAO) problem for high-order nonlinear multi-agent systems over time-varying graphs. We first introduce a new class of aggregative regulation variables that integrate sampled neighbor data during each sampling period, these variables are upgraded through an auxiliary function. By leveraging the C-step consensus contraction method alongside these variables, we reformulate the time-varying graphs DAO problem as a regulation problem, thereby facilitating the use of classical control techniques to address complex nonlinear dynamics. Additionally, we propose a control law that incorporates performance functions and aggregative regulation variables to solve the DAO problem for high-order nonlinear agents with state delays. Numerical simulations demonstrate the validity of the proposed framework.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108403"},"PeriodicalIF":4.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981006","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: 2026-01-05DOI: 10.1016/j.jfranklin.2025.108400
Vipin Kumar, Roberto Guglielmi
This paper explores the concept of exponential synchronization in neutral-type neural networks with mixed delays over arbitrary time domains. We employ a state feedback controller and formulate the problem using the time scales approach, allowing us to address hybrid time domains that include both continuous and discrete-time domains as a special case. Our approach relies on a combination of time scale calculus and the Banach fixed-point theorem, and leads to less restrictive assumptions compared to other techniques. Importantly, the synchronization criterion derived through this approach reduces to a simple, easy-to-verify linear scalar inequality. Furthermore, we present various special cases of the system under consideration and engage in a comprehensive discussion to highlight the advantages of our findings compared to existing results. We validate the effectiveness of our results through simulated numerical examples over different time domains, including an application to secure communication.
{"title":"Exponential synchronization of neutral-type neural networks with leakage and mixed delays on time scales","authors":"Vipin Kumar, Roberto Guglielmi","doi":"10.1016/j.jfranklin.2025.108400","DOIUrl":"10.1016/j.jfranklin.2025.108400","url":null,"abstract":"<div><div>This paper explores the concept of exponential synchronization in neutral-type neural networks with mixed delays over arbitrary time domains. We employ a state feedback controller and formulate the problem using the time scales approach, allowing us to address hybrid time domains that include both continuous and discrete-time domains as a special case. Our approach relies on a combination of time scale calculus and the Banach fixed-point theorem, and leads to less restrictive assumptions compared to other techniques. Importantly, the synchronization criterion derived through this approach reduces to a simple, easy-to-verify linear scalar inequality. Furthermore, we present various special cases of the system under consideration and engage in a comprehensive discussion to highlight the advantages of our findings compared to existing results. We validate the effectiveness of our results through simulated numerical examples over different time domains, including an application to secure communication.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108400"},"PeriodicalIF":4.2,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981011","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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