Pub Date : 2026-01-15Epub Date: 2025-12-16DOI: 10.1016/j.jfranklin.2025.108316
Emílio Dolgener Cantú , Rolf Klemens Wittmann , Oliver Abdeen , Patrick Wagner , Wojciech Samek , Moritz Baier , Sebastian Lapuschkin
Quality management in semiconductor manufacturing often relies on template matching with known golden standards. For Indium-Phosphide (InP) multi-project wafer manufacturing, low production scale and high design variability lead to such golden standards being typically unavailable. Defect detection, in turn, is manual and labor-intensive. This work addresses this challenge by proposing a methodology to generate a synthetic golden standard using Deep Neural Networks, trained to simulate photo-realistic InP wafer images from CAD data. We evaluate various training objectives and assess the quality of the simulated images on both synthetic data and InP wafer photographs. Our deep-learning-based method outperforms a baseline decision-tree-based approach, enabling the use of a ‘simulated golden die’ from CAD plans in any user-defined region of a wafer for more efficient defect detection. We apply our method to a template matching procedure, to demonstrate its practical utility in surface defect detection.
{"title":"Deep learning-based multi project InP wafer simulation towards unsupervised surface defect detection","authors":"Emílio Dolgener Cantú , Rolf Klemens Wittmann , Oliver Abdeen , Patrick Wagner , Wojciech Samek , Moritz Baier , Sebastian Lapuschkin","doi":"10.1016/j.jfranklin.2025.108316","DOIUrl":"10.1016/j.jfranklin.2025.108316","url":null,"abstract":"<div><div>Quality management in semiconductor manufacturing often relies on template matching with known golden standards. For Indium-Phosphide (InP) multi-project wafer manufacturing, low production scale and high design variability lead to such golden standards being typically unavailable. Defect detection, in turn, is manual and labor-intensive. This work addresses this challenge by proposing a methodology to generate a synthetic golden standard using Deep Neural Networks, trained to simulate photo-realistic InP wafer images from CAD data. We evaluate various training objectives and assess the quality of the simulated images on both synthetic data and InP wafer photographs. Our deep-learning-based method outperforms a baseline decision-tree-based approach, enabling the use of a ‘simulated golden die’ from CAD plans in any user-defined region of a wafer for more efficient defect detection. We apply our method to a template matching procedure, to demonstrate its practical utility in surface defect detection.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108316"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837957","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 article proposes a generalized super-twisting algorithm (GSTA) for a class of perturbed sliding mode dynamic systems and further develops an adaptive integral gain strategy for the GSTA. First, a novel GSTA ensuring fixed-time stability of the system is proposed, whose parameter tuning and stability proof are addressed by means of geometrical analysis. Then, in the absence of the knowledge regarding the exact bound of the disturbance gradient, the GSTA is improved in a fixed-time adaptive scheme based on equivalent control value where the integral gain can maintain at a magnitude only marginally larger than the absolute value of the disturbance gradient during the sliding motion without yielding an origin neighborhood for decreasing the gain. Moreover, compared with adaptive strategies in the existing literature relying on equivalent control value, it achieves fixed-time adaption by employing a fixed-time filter. The effectiveness of the proposed method is evaluated through simulation analysis and comparisons.
{"title":"A generalized super-twisting algorithm: Parameter tuning and adaptive strategy development for integral gain","authors":"Jianheng Mao, Zhaobao Yu, Dingfeng Gao, Liaoxue Liu, Yu Guo","doi":"10.1016/j.jfranklin.2025.108367","DOIUrl":"10.1016/j.jfranklin.2025.108367","url":null,"abstract":"<div><div>This article proposes a generalized super-twisting algorithm (GSTA) for a class of perturbed sliding mode dynamic systems and further develops an adaptive integral gain strategy for the GSTA. First, a novel GSTA ensuring fixed-time stability of the system is proposed, whose parameter tuning and stability proof are addressed by means of geometrical analysis. Then, in the absence of the knowledge regarding the exact bound of the disturbance gradient, the GSTA is improved in a fixed-time adaptive scheme based on equivalent control value where the integral gain can maintain at a magnitude only marginally larger than the absolute value of the disturbance gradient during the sliding motion without yielding an origin neighborhood for decreasing the gain. Moreover, compared with adaptive strategies in the existing literature relying on equivalent control value, it achieves fixed-time adaption by employing a fixed-time filter. The effectiveness of the proposed method is evaluated through simulation analysis and comparisons.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108367"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837949","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.2025.108333
Fernando Viadero-Monasterio , Miguel Meléndez-Useros , Hui Zhang , Beatriz L. Boada , Maria Jesus L. Boada
The continuous expansion of urban areas and population growth have created an urgent need for innovative solutions in traffic management. Addressing fluctuating mobility demands and optimizing resource allocation in real time are fundamental challenges for modern cities. To address these issues, this paper introduces a low computational cost mobility-on-demand (MoD) rebalancing solution designed to dynamically adapt to varying demand across the traffic network. The proposed algorithm continuously evaluates both the current state of the traffic network and projected future demand to optimize rebalancing times. It operates using two adjustable parameters: one for requesting additional vehicles and another for allowing nodes to dispatch rebalancing vehicles. Simulation results demonstrate a significant reduction in maximum waiting times compared to scenarios without rebalancing. Additionally, the proposed solution outperforms existing methods, including reinforcement learning approaches such as deep deterministic policy gradient (DDPG), and Model Predictive Control (MPC), which require significantly longer training times. This efficiency enhances operational responsiveness, making the proposed system a more practical and scalable solution for real-world urban mobility challenges.
{"title":"Low-Cost vehicle rebalancing control for an autonomous mobility on demand system","authors":"Fernando Viadero-Monasterio , Miguel Meléndez-Useros , Hui Zhang , Beatriz L. Boada , Maria Jesus L. Boada","doi":"10.1016/j.jfranklin.2025.108333","DOIUrl":"10.1016/j.jfranklin.2025.108333","url":null,"abstract":"<div><div>The continuous expansion of urban areas and population growth have created an urgent need for innovative solutions in traffic management. Addressing fluctuating mobility demands and optimizing resource allocation in real time are fundamental challenges for modern cities. To address these issues, this paper introduces a low computational cost mobility-on-demand (MoD) rebalancing solution designed to dynamically adapt to varying demand across the traffic network. The proposed algorithm continuously evaluates both the current state of the traffic network and projected future demand to optimize rebalancing times. It operates using two adjustable parameters: one for requesting additional vehicles and another for allowing nodes to dispatch rebalancing vehicles. Simulation results demonstrate a significant reduction in maximum waiting times compared to scenarios without rebalancing. Additionally, the proposed solution outperforms existing methods, including reinforcement learning approaches such as deep deterministic policy gradient (DDPG), and Model Predictive Control (MPC), which require significantly longer training times. This efficiency enhances operational responsiveness, making the proposed system a more practical and scalable solution for real-world urban mobility challenges.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108333"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838021","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.2025.108344
Yucheng Li , Zhongxin Liu , Malika Sader
In this article, the input-output data-driven consensus problem is investigated for linear discrete-time multiagent systems (MASs) under switching communication network topologies, where the system dynamics of each agent is assumed to be completely unknown and only the input-output data of each agent are available. The distributed dynamic output feedback protocol is adopted without state data. The equivalence between the protocol and a specific static state feedback controller is established, enabling the transformation of the protocol into a feedback controller compatible with data-driven techniques. By leveraging input-output data structured as Hankel matrices, data-driven linear matrix inequalities (LMIs) are formulated to find the optimal feedback gain and the control input of each agent is calculated with the feedback gain, replicating the role of dynamic output feedback protocol. For the scenario involving noise, a regularized optimization is employed to enhance robustness. It has been demonstrated that the consensus of MASs under switching communication network topologies is guaranteed during the process of synthesizing control inputs under both noise-free and noise-corrupted conditions. Compared to the existing data-driven methods for MASs with input-state data, the application scenarios are broader with our algorithm. Finally, the efficiency of the algorithm is proven by a numerical example.
{"title":"Input-output data-driven consensus control of multiagent systems under switching communication network topologies","authors":"Yucheng Li , Zhongxin Liu , Malika Sader","doi":"10.1016/j.jfranklin.2025.108344","DOIUrl":"10.1016/j.jfranklin.2025.108344","url":null,"abstract":"<div><div>In this article, the input-output data-driven consensus problem is investigated for linear discrete-time multiagent systems (MASs) under switching communication network topologies, where the system dynamics of each agent is assumed to be completely unknown and only the input-output data of each agent are available. The distributed dynamic output feedback protocol is adopted without state data. The equivalence between the protocol and a specific static state feedback controller is established, enabling the transformation of the protocol into a feedback controller compatible with data-driven techniques. By leveraging input-output data structured as Hankel matrices, data-driven linear matrix inequalities (LMIs) are formulated to find the optimal feedback gain and the control input of each agent is calculated with the feedback gain, replicating the role of dynamic output feedback protocol. For the scenario involving noise, a regularized optimization is employed to enhance robustness. It has been demonstrated that the consensus of MASs under switching communication network topologies is guaranteed during the process of synthesizing control inputs under both noise-free and noise-corrupted conditions. Compared to the existing data-driven methods for MASs with input-state data, the application scenarios are broader with our algorithm. Finally, the efficiency of the algorithm is proven by a numerical example.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108344"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838024","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: 2026-01-05DOI: 10.1016/j.jfranklin.2025.108392
Shuo Wang, Shuaiming Yan, Lei Shi, Panpan Zhu
Flocking aims to induce collective aggregation through complex interactions among interconnected agents. Given the pervasive and intricate co-opetitive dynamics in multi-agent systems, realizing flocking behavior in such networks presents both practical relevance and significant challenges. This paper investigates the flocking dynamic behavior of multi-agent systems with cooperative and competitive relationships under asynchronous communication. Building on the classical Cucker-Smale (C-S) model, a distributed control protocol with asynchronous communication is designed. In this protocol, the timing of communication is determined by each agent individually, rather than being updated synchronously by a unified clock. The protocol quantifies the intensity of cooperation and competition by introducing bio-inspired nonlinear positive/negative weight functions related to interaction distances. The convergence of the dynamic model is rigorously verified through mathematical analysis using products of super-stochastic matrices, establishing an algebraic relationship between the degrees of cooperation and competition that ensures emergent flocking behavior. Finally, numerical simulations validate the effectiveness of the proposed algebraic conditions in achieving flocking behavior.
群集的目的是通过相互连接的主体之间复杂的相互作用诱导集体聚集。考虑到多智能体系统中普遍而复杂的合作竞争动态，在这种网络中实现群集行为既有现实意义，也有重大挑战。研究了异步通信条件下具有合作和竞争关系的多智能体系统的群集动态行为。在经典cucker - small （C-S）模型的基础上，设计了一种异步通信的分布式控制协议。在该协议中，通信的时间由每个代理单独决定，而不是由统一的时钟同步更新。该方案通过引入与相互作用距离相关的生物启发的非线性正/负权重函数来量化合作和竞争的强度。利用超随机矩阵的乘积，通过数学分析严格验证了动态模型的收敛性，建立了保证紧急群集行为的合作度与竞争度之间的代数关系。最后，数值模拟验证了所提出的代数条件在实现群集行为方面的有效性。
{"title":"Multi-agent flocking with asynchronous cooperative-competitive interactions","authors":"Shuo Wang, Shuaiming Yan, Lei Shi, Panpan Zhu","doi":"10.1016/j.jfranklin.2025.108392","DOIUrl":"10.1016/j.jfranklin.2025.108392","url":null,"abstract":"<div><div>Flocking aims to induce collective aggregation through complex interactions among interconnected agents. Given the pervasive and intricate co-opetitive dynamics in multi-agent systems, realizing flocking behavior in such networks presents both practical relevance and significant challenges. This paper investigates the flocking dynamic behavior of multi-agent systems with cooperative and competitive relationships under asynchronous communication. Building on the classical Cucker-Smale (C-S) model, a distributed control protocol with asynchronous communication is designed. In this protocol, the timing of communication is determined by each agent individually, rather than being updated synchronously by a unified clock. The protocol quantifies the intensity of cooperation and competition by introducing bio-inspired nonlinear positive/negative weight functions related to interaction distances. The convergence of the dynamic model is rigorously verified through mathematical analysis using products of super-stochastic matrices, establishing an algebraic relationship between the degrees of cooperation and competition that ensures emergent flocking behavior. Finally, numerical simulations validate the effectiveness of the proposed algebraic conditions in achieving flocking behavior.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108392"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926864","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: 2025-12-21DOI: 10.1016/j.jfranklin.2025.108334
Yan He , Lushuang Gao , Xiaoyu Yang , Ruijun Liu , Xuncai Zhang
The paper investigates the estimation problem for a class of nonlinear hybrid systems with aperiodic sampling. First, an aperiodic sampling mechanism is proposed using the event-triggered approach, in which a aperiodic sampling hybrid model is developed to describe the nonlinear systems. Second, the exponential stability is analyzed for the considered nonlinear hybrid model based on the Lyapunov function methods, and the stability rate is studied under different Lyapunov functions. In particular, a sufficient condition is provided to analyze the linear hybrid model. Third, an improved estimation method is proposed to derive the maximum allowable sampling interval (MASI) by constructing a new ordinary differential equation. Finally, several practical models are illustrated to verify the effectiveness of the proposed theorems.
{"title":"Estimation of maximum allowable sampling interval for hybrid systems with aperiodic sampling using the event-triggered approach","authors":"Yan He , Lushuang Gao , Xiaoyu Yang , Ruijun Liu , Xuncai Zhang","doi":"10.1016/j.jfranklin.2025.108334","DOIUrl":"10.1016/j.jfranklin.2025.108334","url":null,"abstract":"<div><div>The paper investigates the estimation problem for a class of nonlinear hybrid systems with aperiodic sampling. First, an aperiodic sampling mechanism is proposed using the event-triggered approach, in which a aperiodic sampling hybrid model is developed to describe the nonlinear systems. Second, the exponential stability is analyzed for the considered nonlinear hybrid model based on the Lyapunov function methods, and the stability rate is studied under different Lyapunov functions. In particular, a sufficient condition is provided to analyze the linear hybrid model. Third, an improved estimation method is proposed to derive the maximum allowable sampling interval (MASI) by constructing a new ordinary differential equation. Finally, several practical models are illustrated to verify the effectiveness of the proposed theorems.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108334"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881062","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: 2025-11-26DOI: 10.1016/j.jfranklin.2025.108274
Tao Zhang , Peixuan Song , Jia Long , Qian Kang , Peng Li , Dengxiu Yu
In this paper, an off-policy hierarchical reinforcement learning (HRL) algorithm is proposed to solve the collision avoidance problem for a class of multi-agent systems. The collision avoidance refers to maintaining a predefined formation pattern and avoiding collisions with obstacles while driving each agent to the target state, which is formulated as a differential game. We leverage the idea of divide and conquer to artificially decompose the problem into three corresponding subtasks: target state attraction, neighbor agent repulsion, and static obstacle repulsion, to cope with the complex external environment. The off-policy HRL algorithm is designed based on the original policy iteration algorithm and implemented in real-time using only measured data to cope with the problem of completely unknown system information. Compared with the traditional least-square and gradient descent approach, critic and action neural networks of each subtask are simultaneously added to a broad learning system (BLS). It is worth noting that the pseudo-inverse operation of BLS allows us to achieve a faster and better approximate solution of the weight using global data online. The uniform ultimate bounded stability of the closed-loop system is proved based on the Lyapunov approach. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithm.
{"title":"Off-policy hierarchical reinforcement learning for collision avoidance via broad learning system","authors":"Tao Zhang , Peixuan Song , Jia Long , Qian Kang , Peng Li , Dengxiu Yu","doi":"10.1016/j.jfranklin.2025.108274","DOIUrl":"10.1016/j.jfranklin.2025.108274","url":null,"abstract":"<div><div>In this paper, an off-policy hierarchical reinforcement learning (HRL) algorithm is proposed to solve the collision avoidance problem for a class of multi-agent systems. The collision avoidance refers to maintaining a predefined formation pattern and avoiding collisions with obstacles while driving each agent to the target state, which is formulated as a differential game. We leverage the idea of divide and conquer to artificially decompose the problem into three corresponding subtasks: target state attraction, neighbor agent repulsion, and static obstacle repulsion, to cope with the complex external environment. The off-policy HRL algorithm is designed based on the original policy iteration algorithm and implemented in real-time using only measured data to cope with the problem of completely unknown system information. Compared with the traditional least-square and gradient descent approach, critic and action neural networks of each subtask are simultaneously added to a broad learning system (BLS). It is worth noting that the pseudo-inverse operation of BLS allows us to achieve a faster and better approximate solution of the weight using global data online. The uniform ultimate bounded stability of the closed-loop system is proved based on the Lyapunov approach. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithm.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108274"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798745","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.2025.108353
Xiangyang Cao , Daduan Zhao , Yan Li , Chao Wu
This paper is concerned with the finite-time H∞ consensus control problem of a class of nonlinear multi-agent systems (MASs) with dynamic event-triggered mechanism (DETM) and multiple cyber attacks including denial-of-service (DoS) attack and random deception attack. First, a new networked switched model is formulated for appropriately characterizing the initial MASs with the impacts of multiple cyber attacks and physical constraint of actuator saturation. Second, by means of switched system theory and iterative technique, the event-triggered finite-time secure consensus is achieved, providing that the frequency and duration of DoS attack satisfy certain conditions. Particularly, the developed dynamic event-triggered control scheme has the advantages of simultaneously alleviating the computation/transmission burdens and resisting cyber attacks. Then, to suppress the influence of external disturbance on consensus regulation performance, an event-triggered H∞ consensus criterion is established, which achieves secure consensus in finite-time interval while guaranteeing a prescribed H∞ performance index. The corresponding control gain is derived based on the linear matrix inequality approach. Finally, two circuit simulations are exemplified to illustrate the effectiveness of the theoretical results.
{"title":"Finite-time H∞ consensus control of multi-agent systems with dynamic event-triggered mechanism and multiple cyber attacks","authors":"Xiangyang Cao , Daduan Zhao , Yan Li , Chao Wu","doi":"10.1016/j.jfranklin.2025.108353","DOIUrl":"10.1016/j.jfranklin.2025.108353","url":null,"abstract":"<div><div>This paper is concerned with the finite-time <em>H</em><sub>∞</sub> consensus control problem of a class of nonlinear multi-agent systems (MASs) with dynamic event-triggered mechanism (DETM) and multiple cyber attacks including denial-of-service (DoS) attack and random deception attack. First, a new networked switched model is formulated for appropriately characterizing the initial MASs with the impacts of multiple cyber attacks and physical constraint of actuator saturation. Second, by means of switched system theory and iterative technique, the event-triggered finite-time secure consensus is achieved, providing that the frequency and duration of DoS attack satisfy certain conditions. Particularly, the developed dynamic event-triggered control scheme has the advantages of simultaneously alleviating the computation/transmission burdens and resisting cyber attacks. Then, to suppress the influence of external disturbance on consensus regulation performance, an event-triggered <em>H</em><sub>∞</sub> consensus criterion is established, which achieves secure consensus in finite-time interval while guaranteeing a prescribed <em>H</em><sub>∞</sub> performance index. The corresponding control gain is derived based on the linear matrix inequality approach. Finally, two circuit simulations are exemplified to illustrate the effectiveness of the theoretical results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108353"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837877","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: 2025-12-12DOI: 10.1016/j.jfranklin.2025.108304
Peng-qi Wu, Jian-wei Liu, Jia-yi Han
Given the complex feature dependencies of time-series data, learning and integrating local features with global features is crucial for long-term time series forecasting. Although CNN-based methods have significant advantages in modeling local features, they are generally unable to capture the global features of time series through simple model structures or low model complexity, as many MLP networks do. Additionally, research on modeling dependencies in time-series data by combining frequency domain information remains limited, particularly in learning local periodic features using frequency domain information. To address the above issues, we propose FTMixer, which models and integrates local periodic variations in the frequency domain and global features in the time domain using an improved CNN structure and MLP networks. Unlike conventional methods, FTMixer directly extracts intra-local and inter-local periodic change features in a single-scale manner, thus forecasting the time series in the perspective of the local periodicity. Our experiments on eight benchmark datasets demonstrate that FTMixer outperforms previous state-of-the-art methods. In multivariate forecasting experiments, compared with the state-of-the-art methods and the best MLP-based baseline model, FTMixer achieves relative MSE reductions of 6.1 % and 27.1 %. FTMixer also achieves significantly better predictive performance than the best CNN-based methods. Furthermore, FTMixer exhibits higher capabilities and training efficiency in capturing temporal information. These results highlight the effectiveness of combining global and local features, time domain information and frequency domain information for LTSF. We will make our code and model publicly available.
{"title":"Long-term time series forecasting by combining local periodic change features in frequency domain and global features in time domain","authors":"Peng-qi Wu, Jian-wei Liu, Jia-yi Han","doi":"10.1016/j.jfranklin.2025.108304","DOIUrl":"10.1016/j.jfranklin.2025.108304","url":null,"abstract":"<div><div>Given the complex feature dependencies of time-series data, learning and integrating local features with global features is crucial for long-term time series forecasting. Although CNN-based methods have significant advantages in modeling local features, they are generally unable to capture the global features of time series through simple model structures or low model complexity, as many MLP networks do. Additionally, research on modeling dependencies in time-series data by combining frequency domain information remains limited, particularly in learning local periodic features using frequency domain information. To address the above issues, we propose FTMixer, which models and integrates local periodic variations in the frequency domain and global features in the time domain using an improved CNN structure and MLP networks. Unlike conventional methods, FTMixer directly extracts intra-local and inter-local periodic change features in a single-scale manner, thus forecasting the time series in the perspective of the local periodicity. Our experiments on eight benchmark datasets demonstrate that FTMixer outperforms previous state-of-the-art methods. In multivariate forecasting experiments, compared with the state-of-the-art methods and the best MLP-based baseline model, FTMixer achieves relative MSE reductions of 6.1 % and 27.1 %. FTMixer also achieves significantly better predictive performance than the best CNN-based methods. Furthermore, FTMixer exhibits higher capabilities and training efficiency in capturing temporal information. These results highlight the effectiveness of combining global and local features, time domain information and frequency domain information for LTSF. We will make our code and model publicly available.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108304"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837876","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.2025.108358
Kai Zong , Xiaochen Xie , Zhaoji Ling , Jing Dai , Ka-Wai Kwok
In this paper, the concept of periodic discrete-time high-order control barrier function (P-DHOCBF) is developed. The proposed P-DHOCBF is utilized to ensure the forward invariance of the safety set for discrete-time systems with periodic characteristics in system states of any relative degree. Focusing on the periodic forward walking problem of bipedal robots based on the variable-height inverted pendulum model, a periodic model predictive control optimization problem incorporating P-DHOCBF is formulated, and periodicity-related constraints are established. Compared to the existing discrete-time control barrier function, the proposed P-DHOCBF significantly reduces the conservatism of safety, thereby enhancing the system safety by promptly preventing unsafe occurrences. An illustrative example and simulation results based on a 12-degree-of-freedom (DOF) bipedal robot verify the effectiveness of the proposed approach.
{"title":"Safety guarantee via periodic discrete-time high-order control barrier function: Application to bipedal robots","authors":"Kai Zong , Xiaochen Xie , Zhaoji Ling , Jing Dai , Ka-Wai Kwok","doi":"10.1016/j.jfranklin.2025.108358","DOIUrl":"10.1016/j.jfranklin.2025.108358","url":null,"abstract":"<div><div>In this paper, the concept of periodic discrete-time high-order control barrier function (P-DHOCBF) is developed. The proposed P-DHOCBF is utilized to ensure the forward invariance of the safety set for discrete-time systems with periodic characteristics in system states of any relative degree. Focusing on the periodic forward walking problem of bipedal robots based on the variable-height inverted pendulum model, a periodic model predictive control optimization problem incorporating P-DHOCBF is formulated, and periodicity-related constraints are established. Compared to the existing discrete-time control barrier function, the proposed P-DHOCBF significantly reduces the conservatism of safety, thereby enhancing the system safety by promptly preventing unsafe occurrences. An illustrative example and simulation results based on a 12-degree-of-freedom (DOF) bipedal robot verify the effectiveness of the proposed approach.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108358"},"PeriodicalIF":4.2,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837890","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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