Pub Date : 2026-02-10DOI: 10.1016/j.jfranklin.2026.108493
Liu Liu, Di Jin
State estimation provides the foundation for the safe and autonomous operation of quadrotors by delivering reliable pose and velocity information under noisy and incomplete sensor measurements, but it is insufficient for complex missions. As its temporal extension, trajectory prediction underpins key functions such as path planning, obstacle avoidance, and decision-making control directly. Classical estimation methods are inadequate for long-horizon prediction, while deep learning models, despite their strong nonlinear representational capacity, lack real-time correction mechanisms compatible with state estimation principles. To overcome these limitations, this paper proposes a TCN-MLP trajectory prediction model enhanced with a hybrid-correction (HC) mechanism. By dynamically incorporating partial ground-truth observations during training, the HC mechanism effectively mitigates error accumulation. Experimental results on real-world quadrotor flight datasets demonstrate that the proposed method achieves superior long-term prediction accuracy and robustness compared with mainstream baselines.
{"title":"Enhancing quadrotor trajectory prediction via hybrid-corrected TCN-MLP network","authors":"Liu Liu, Di Jin","doi":"10.1016/j.jfranklin.2026.108493","DOIUrl":"10.1016/j.jfranklin.2026.108493","url":null,"abstract":"<div><div>State estimation provides the foundation for the safe and autonomous operation of quadrotors by delivering reliable pose and velocity information under noisy and incomplete sensor measurements, but it is insufficient for complex missions. As its temporal extension, trajectory prediction underpins key functions such as path planning, obstacle avoidance, and decision-making control directly. Classical estimation methods are inadequate for long-horizon prediction, while deep learning models, despite their strong nonlinear representational capacity, lack real-time correction mechanisms compatible with state estimation principles. To overcome these limitations, this paper proposes a TCN-MLP trajectory prediction model enhanced with a hybrid-correction (HC) mechanism. By dynamically incorporating partial ground-truth observations during training, the HC mechanism effectively mitigates error accumulation. Experimental results on real-world quadrotor flight datasets demonstrate that the proposed method achieves superior long-term prediction accuracy and robustness compared with mainstream baselines.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108493"},"PeriodicalIF":4.2,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172561","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 : 2026-02-10DOI: 10.1016/j.jfranklin.2026.108512
Jesús Sandoval , Luis Cervantes-Pérez , Isaac Gandarilla , Víctor Santibáñez , César Higuera , Marco Castro-Liera
The control of a class of electromechanical systems electrically-driven by brushed Direct Current (DC) motors of permanent magnet is addressed in this paper. An energy shaping approach is used for the voltage controller design, which achieves position/speed regulation of underactuated mechanical systems –those systems with more actuators than degrees of freedom– actuated by DC motors. The main contribution is a control law in terms of voltage feeding each DC motor instead of a torque/force input, which does not need voltage or armature current feedback, but only position measurements and speed. The proposed voltage controller is useful for this class of electrically-driven mechanical systems used in experimental workbenches found in numerous automatic control laboratories. The effectiveness of the proposed controller is demonstrated through two underactuated mechanical systems: the disk-on-disk and the self-balancing robot. For the disk-on-disk system, numerical simulations are provided, whereas for the self-balancing robot, real-time experimental results are displayed.
{"title":"Voltage control of a class of underactuated electromechanical systems via an energy shaping approach","authors":"Jesús Sandoval , Luis Cervantes-Pérez , Isaac Gandarilla , Víctor Santibáñez , César Higuera , Marco Castro-Liera","doi":"10.1016/j.jfranklin.2026.108512","DOIUrl":"10.1016/j.jfranklin.2026.108512","url":null,"abstract":"<div><div>The control of a class of electromechanical systems electrically-driven by brushed Direct Current (DC) motors of permanent magnet is addressed in this paper. An energy shaping approach is used for the voltage controller design, which achieves position/speed regulation of underactuated mechanical systems –those systems with more actuators than degrees of freedom– actuated by DC motors. The main contribution is a control law in terms of voltage feeding each DC motor instead of a torque/force input, which does not need voltage or armature current feedback, but only position measurements and speed. The proposed voltage controller is useful for this class of electrically-driven mechanical systems used in experimental workbenches found in numerous automatic control laboratories. The effectiveness of the proposed controller is demonstrated through two underactuated mechanical systems: the disk-on-disk and the self-balancing robot. For the disk-on-disk system, numerical simulations are provided, whereas for the self-balancing robot, real-time experimental results are displayed.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108512"},"PeriodicalIF":4.2,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172571","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 : 2026-02-10DOI: 10.1016/j.jfranklin.2026.108479
Jinlan Liu , Helei Kang , Renyun Liu , Dongpo Xu
Global optimization is essential for addressing complex real-world problems characterized by non-convexity and numerous local minima. Traditional gradient-based methods often struggle in such scenarios due to poor convergence to local optima rather than the global solution. To overcome this limitation, we propose a novel parameter-free filled function, an auxiliary construct designed to enhance global optimization algorithms by escaping local optima. The proposed function introduces an inverse cosine component to create a continuously differentiable and completely parameter-free formulation that effectively overcomes the common limitations of false smoothing and numerical instability found in existing filled function methods. Theoretical analysis demonstrates the function’s continuous differentiability and its effectiveness in escaping local optima. Building on this formulation, we develop the Non-Parametric Filled Function algorithm (NPFFF), which alternately minimizes the original objective function and the filled function to traverse the search space. NPFFF eliminates the need for manual parameter tuning, simplifying implementation and enhancing robustness. Complexity analysis indicates that constructing the filled function requires only linear time. Experimental results on standard benchmark functions demonstrate that NPFFF achieves faster convergence and higher accuracy than existing methods. Furthermore, NPFFF successfully solves nonlinear systems of equations by transforming them into global optimization tasks.
{"title":"A novel parameter-free filled function method for global optimization and solving nonlinear equation systems","authors":"Jinlan Liu , Helei Kang , Renyun Liu , Dongpo Xu","doi":"10.1016/j.jfranklin.2026.108479","DOIUrl":"10.1016/j.jfranklin.2026.108479","url":null,"abstract":"<div><div>Global optimization is essential for addressing complex real-world problems characterized by non-convexity and numerous local minima. Traditional gradient-based methods often struggle in such scenarios due to poor convergence to local optima rather than the global solution. To overcome this limitation, we propose a novel parameter-free filled function, an auxiliary construct designed to enhance global optimization algorithms by escaping local optima. The proposed function introduces an inverse cosine component to create a continuously differentiable and completely parameter-free formulation that effectively overcomes the common limitations of false smoothing and numerical instability found in existing filled function methods. Theoretical analysis demonstrates the function’s continuous differentiability and its effectiveness in escaping local optima. Building on this formulation, we develop the Non-Parametric Filled Function algorithm (NPFFF), which alternately minimizes the original objective function and the filled function to traverse the search space. NPFFF eliminates the need for manual parameter tuning, simplifying implementation and enhancing robustness. Complexity analysis indicates that constructing the filled function requires only linear time. Experimental results on standard benchmark functions demonstrate that NPFFF achieves faster convergence and higher accuracy than existing methods. Furthermore, NPFFF successfully solves nonlinear systems of equations by transforming them into global optimization tasks.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108479"},"PeriodicalIF":4.2,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172573","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 : 2026-02-10DOI: 10.1016/j.jfranklin.2026.108494
Wanning Peng , Chen Chen , Zhengrong Xiang
In this article, a practical prescribed-time (PPT) formation control strategy is proposed for multiple nonholonomic mobile robots (NMRs). Due to the limited communication range of devices and the physical size of robots, the connectivity maintenance and collision avoidance are considered. Firstly, a bounded and differentiable saturated prescribed-time adjustment (SPTA) function is introduced, allowing users to specify the settling time. Subsequently, a virtual multi-robot system is constructed by employing a potential function that incorporates both the communication range and the safe distance, which generates reference trajectories for the actual mobile robots. Additionally, fuzzy logic systems (FLSs) are employed to approximate the unknown dynamics of the NMR model. In particular, adaptive techniques are further introduced to compensate for the approximation errors, thus improving the accuracy of the approximation. The control scheme ensures that multiple NMRs achieve a desired formation pattern within a prescribed time while satisfying the connectivity and collision avoidance requirements. Finally, simulations are conducted to validate the effectiveness of the proposed control method.
{"title":"Practical prescribed-time formation control of nonholonomic mobile robots with connectivity maintenance and collision avoidance","authors":"Wanning Peng , Chen Chen , Zhengrong Xiang","doi":"10.1016/j.jfranklin.2026.108494","DOIUrl":"10.1016/j.jfranklin.2026.108494","url":null,"abstract":"<div><div>In this article, a practical prescribed-time (PPT) formation control strategy is proposed for multiple nonholonomic mobile robots (NMRs). Due to the limited communication range of devices and the physical size of robots, the connectivity maintenance and collision avoidance are considered. Firstly, a bounded and differentiable saturated prescribed-time adjustment (SPTA) function is introduced, allowing users to specify the settling time. Subsequently, a virtual multi-robot system is constructed by employing a potential function that incorporates both the communication range and the safe distance, which generates reference trajectories for the actual mobile robots. Additionally, fuzzy logic systems (FLSs) are employed to approximate the unknown dynamics of the NMR model. In particular, adaptive techniques are further introduced to compensate for the approximation errors, thus improving the accuracy of the approximation. The control scheme ensures that multiple NMRs achieve a desired formation pattern within a prescribed time while satisfying the connectivity and collision avoidance requirements. Finally, simulations are conducted to validate the effectiveness of the proposed control method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108494"},"PeriodicalIF":4.2,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172562","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 : 2026-02-09DOI: 10.1016/j.jfranklin.2026.108495
Haoli Gu , Bo Chen , Rusheng Wang
While state estimation plays a critical role in power system operation and control, it suffers from multi-rate problem caused by the different sampling frequency of multiple sensors. A multi-rate mechanism is proposed based on the non-common multiples assumption to deal with this problem. On this basis, an enhanced batch covariance intersection (CI) algorithm is used to solve the multi-sensor fusion problem. In addition, an anti-outlier unscented Kalman filter (AO-UKF) is developed in order to solve the problem of outliers, which caused by phenomena such as communication loss and transformer saturation. The proposed AO-UKF is able to estimate system instantaneous states in a more robust way than other traditional Kalman filtering methods thanks to a novel mixed outlier detection mechanism. This mechanism is designed by utilizing projection statistic and least square methods, which is inspired by the distribution characteristics of the innovation-based and the prediction-based sample points. Since two types of sample points are bivariate Gaussian distribution and linear distribution respectively, the designed mechanism has a wider applicability compared to a single detection mechanism. Finally, comparisons have been extensively conducted with other traditional Kalman filtering methods including UKF, and the results show that the proposed AO-UKF method can provide a better estimation accuracy when outliers are taken into account.
{"title":"Anti-outlier unscented kalman filter for power system state estimation","authors":"Haoli Gu , Bo Chen , Rusheng Wang","doi":"10.1016/j.jfranklin.2026.108495","DOIUrl":"10.1016/j.jfranklin.2026.108495","url":null,"abstract":"<div><div>While state estimation plays a critical role in power system operation and control, it suffers from multi-rate problem caused by the different sampling frequency of multiple sensors. A multi-rate mechanism is proposed based on the non-common multiples assumption to deal with this problem. On this basis, an enhanced batch covariance intersection (CI) algorithm is used to solve the multi-sensor fusion problem. In addition, an anti-outlier unscented Kalman filter (AO-UKF) is developed in order to solve the problem of outliers, which caused by phenomena such as communication loss and transformer saturation. The proposed AO-UKF is able to estimate system instantaneous states in a more robust way than other traditional Kalman filtering methods thanks to a novel mixed outlier detection mechanism. This mechanism is designed by utilizing projection statistic and least square methods, which is inspired by the distribution characteristics of the innovation-based and the prediction-based sample points. Since two types of sample points are bivariate Gaussian distribution and linear distribution respectively, the designed mechanism has a wider applicability compared to a single detection mechanism. Finally, comparisons have been extensively conducted with other traditional Kalman filtering methods including UKF, and the results show that the proposed AO-UKF method can provide a better estimation accuracy when outliers are taken into account.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108495"},"PeriodicalIF":4.2,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172568","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 : 2026-02-09DOI: 10.1016/j.jfranklin.2026.108499
Lingling Lv , Yulin Zhang , Yu Wu , Chongbin Xu , Zhongyang Li , Huaicheng Yan
In this paper, we address the problem of parameter identification for a Wiener nonlinear system with an autoregressive (AR) noise model. We propose two novel algorithms, namely the Wiener system generalized gradient iterative (WS-GGI) algorithm and the Wiener system zebra optimization (WS-ZO) algorithm. The WS-GGI algorithm is rooted in the gradient search principle, while the WS-ZO algorithm is a metaheuristic approach characterized by its robust parallel search capability. The core concept of the WS-ZO method is to identify the optimal solution by simulating the random movements of zebras within the search space and evaluating the objective function. The effectiveness of the proposed algorithms is demonstrated through experimental data and further compared with the recursive generalized least squares (RGLS) algorithm and the particle swarm optimization (PSO) algorithm. In conclusion, our findings indicate that these two new algorithms offer significant advantages in terms of accuracy and computational efficiency.
{"title":"Parameter estimation of wiener nonlinear systems based on gradient iteration theory and zebra optimization algorithm","authors":"Lingling Lv , Yulin Zhang , Yu Wu , Chongbin Xu , Zhongyang Li , Huaicheng Yan","doi":"10.1016/j.jfranklin.2026.108499","DOIUrl":"10.1016/j.jfranklin.2026.108499","url":null,"abstract":"<div><div>In this paper, we address the problem of parameter identification for a Wiener nonlinear system with an autoregressive (AR) noise model. We propose two novel algorithms, namely the Wiener system generalized gradient iterative (WS-GGI) algorithm and the Wiener system zebra optimization (WS-ZO) algorithm. The WS-GGI algorithm is rooted in the gradient search principle, while the WS-ZO algorithm is a metaheuristic approach characterized by its robust parallel search capability. The core concept of the WS-ZO method is to identify the optimal solution by simulating the random movements of zebras within the search space and evaluating the objective function. The effectiveness of the proposed algorithms is demonstrated through experimental data and further compared with the recursive generalized least squares (RGLS) algorithm and the particle swarm optimization (PSO) algorithm. In conclusion, our findings indicate that these two new algorithms offer significant advantages in terms of accuracy and computational efficiency.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108499"},"PeriodicalIF":4.2,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172570","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 : 2026-02-09DOI: 10.1016/j.jfranklin.2026.108477
Hamada El Kabtane , Fatima Zohra Ennaji , Khaoula Elkabtane , Maryam Knouzi , Amal Ourdou
Enhancing e-learning systems through engagement monitoring is a critical priority. Adapting e-learning platforms to be responsive to learners’ emotional states is viewed as an innovative approach in this domain. However, a key challenge faced by researchers is determining how to effectively measure and assess student engagement based on their emotional cues and behaviors. Thus, several methods have been developed to evaluate student engagement in online learning environments. Yet, many of these existing methods have focused primarily on detecting the engagement level without adequately considering whether the student is actively engaged in the learning process itself. This paper presents a novel system for real-time engagement detection in online learning environments using facial emotion recognition based on a fine-tuned VGG-19. The proposed system utilizes a camera to capture learners’ facial expressions and classify them into seven emotional states: Angry, Disgust, Fear, Happy, Neutral, Sad, and Surprise. Additionally, the system detects four other states: No face detected, Not looking forward, Sleepiness, and None (devoid of human presence frame). Our experimental evaluations include two tests: the first without assigned weights for the learners’ emotional and states indicators, achieving an accuracy of 87.09%, while the second, with weighted coefficients, resulting in a significant improvement to 95.12%. The weighted approach enhances the system’s ability to prioritize emotional cues, demonstrating its effectiveness in accurately identifying engagement levels. The proposed system has potential applications in enhancing online learning experiences by providing real-time feedback to educators and improving learner engagement.
{"title":"Toward emotionally intelligent e-learning: Real-time engagement detection through fine-tuned deep facial emotion recognition","authors":"Hamada El Kabtane , Fatima Zohra Ennaji , Khaoula Elkabtane , Maryam Knouzi , Amal Ourdou","doi":"10.1016/j.jfranklin.2026.108477","DOIUrl":"10.1016/j.jfranklin.2026.108477","url":null,"abstract":"<div><div>Enhancing e-learning systems through engagement monitoring is a critical priority. Adapting e-learning platforms to be responsive to learners’ emotional states is viewed as an innovative approach in this domain. However, a key challenge faced by researchers is determining how to effectively measure and assess student engagement based on their emotional cues and behaviors. Thus, several methods have been developed to evaluate student engagement in online learning environments. Yet, many of these existing methods have focused primarily on detecting the engagement level without adequately considering whether the student is actively engaged in the learning process itself. This paper presents a novel system for real-time engagement detection in online learning environments using facial emotion recognition based on a fine-tuned VGG-19. The proposed system utilizes a camera to capture learners’ facial expressions and classify them into seven emotional states: Angry, Disgust, Fear, Happy, Neutral, Sad, and Surprise. Additionally, the system detects four other states: No face detected, Not looking forward, Sleepiness, and None (devoid of human presence frame). Our experimental evaluations include two tests: the first without assigned weights for the learners’ emotional and states indicators, achieving an accuracy of 87.09%, while the second, with weighted coefficients, resulting in a significant improvement to 95.12%. The weighted approach enhances the system’s ability to prioritize emotional cues, demonstrating its effectiveness in accurately identifying engagement levels. The proposed system has potential applications in enhancing online learning experiences by providing real-time feedback to educators and improving learner engagement.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108477"},"PeriodicalIF":4.2,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172569","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 : 2026-02-09DOI: 10.1016/j.jfranklin.2026.108507
Taotao Hu , Miaomiao Shi , Kaibo Shi , Xianya Wuliu
This article concentrates on the event-triggered consensus control for short memory fractional-order multiagent systems with input delay. First, considering the limitation of network communication resources, an event-triggered consensus strategy with input delay is designed, which only depend on the sampled state information of neighboring agents. It is shown that the proposed event-triggered control strategy is able to effectively adjust the frequency of the information transfer between neighboring agents. Utilizing the fractional Lyapunov stability theory and some inequality techniques, the delay-dependent consensus criteria for fractional-order multiagent systems are established. Meanwhile, analyzing the existence of the lower bound of the triggering time interval for any two continuous events, Zeno behavior is excluded. Finally, some simulations results are given to confirm the correctness of the proposed consensus approach, which show that the designed event-triggered consensus strategy can effectively reduce the communication frequency between neighboring agents compared with the known works.
{"title":"Event-triggered consensus control for short memory fractional-order multiagent systems with input delay","authors":"Taotao Hu , Miaomiao Shi , Kaibo Shi , Xianya Wuliu","doi":"10.1016/j.jfranklin.2026.108507","DOIUrl":"10.1016/j.jfranklin.2026.108507","url":null,"abstract":"<div><div>This article concentrates on the event-triggered consensus control for short memory fractional-order multiagent systems with input delay. First, considering the limitation of network communication resources, an event-triggered consensus strategy with input delay is designed, which only depend on the sampled state information of neighboring agents. It is shown that the proposed event-triggered control strategy is able to effectively adjust the frequency of the information transfer between neighboring agents. Utilizing the fractional Lyapunov stability theory and some inequality techniques, the delay-dependent consensus criteria for fractional-order multiagent systems are established. Meanwhile, analyzing the existence of the lower bound of the triggering time interval for any two continuous events, Zeno behavior is excluded. Finally, some simulations results are given to confirm the correctness of the proposed consensus approach, which show that the designed event-triggered consensus strategy can effectively reduce the communication frequency between neighboring agents compared with the known works.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108507"},"PeriodicalIF":4.2,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172566","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 : 2026-02-09DOI: 10.1016/j.jfranklin.2026.108497
Qing-Hao Zhang , Xiao-Chuang Jin , Jun-Guo Lu , Zhen Zhu
Complex Industrial Internet systems are often challenged by communication delays, posing significant threats to the stability of the systems. This paper conducts an in-depth investigation into the stability problems of a representative model, fractional-order time-delay systems, in Industrial Internet. The paper aims to provide theoretical support for enhancing the stability in interconnected industrial systems. To conclude this goal, the stability problem of fractional-order time-delay systems is transformed to the robust stability problem of delay-free interconnected uncertain systems. By applying the small gain theorem and fractional-order bounded real lemma, a delay-dependent stability condition is derived. Then, different covering sets and well-designed filters that capture the phase and gain information of the uncertainties are utilized to further reduce the conservatism of the proposed stability condition. The results are formulated as linear/bilinear matrix inequalities (LMIs/BMIs), and the proposed LMI/BMI criteria yield enlarged delay margins compared with previously reported conditions in the literature. Finally, two examples are analyzed and the results indicate that the new proposed conditions are effective and have less conservatism than other existing criteria.
{"title":"Less conservative stability conditions of fractional-order time-delay systems using covering sets and filters","authors":"Qing-Hao Zhang , Xiao-Chuang Jin , Jun-Guo Lu , Zhen Zhu","doi":"10.1016/j.jfranklin.2026.108497","DOIUrl":"10.1016/j.jfranklin.2026.108497","url":null,"abstract":"<div><div>Complex Industrial Internet systems are often challenged by communication delays, posing significant threats to the stability of the systems. This paper conducts an in-depth investigation into the stability problems of a representative model, fractional-order time-delay systems, in Industrial Internet. The paper aims to provide theoretical support for enhancing the stability in interconnected industrial systems. To conclude this goal, the stability problem of fractional-order time-delay systems is transformed to the robust stability problem of delay-free interconnected uncertain systems. By applying the small gain theorem and fractional-order bounded real lemma, a delay-dependent stability condition is derived. Then, different covering sets and well-designed filters that capture the phase and gain information of the uncertainties are utilized to further reduce the conservatism of the proposed stability condition. The results are formulated as linear/bilinear matrix inequalities (LMIs/BMIs), and the proposed LMI/BMI criteria yield enlarged delay margins compared with previously reported conditions in the literature. Finally, two examples are analyzed and the results indicate that the new proposed conditions are effective and have less conservatism than other existing criteria.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108497"},"PeriodicalIF":4.2,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172564","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 : 2026-02-09DOI: 10.1016/j.jfranklin.2026.108483
Jiaxu Liu , Pengkai Wang , Song Chen , Shengze Cai , Chao Xu
This paper addresses distributed optimization problems with equality constraints within the framework of cooperation-competition network. Motivated by the exceptional performance of proportional-integral-derivative (PID) controllers, we propose an accelerated distributed optimization algorithm to decompose the distributed optimization problem on the cooperation-competition network into two cooperative subnetworks and address them. By leveraging the Lyapunov stability theorem, we establish the exponential convergence of our algorithm over undirected connected and structurally balanced cooperation-competition graphs when the parameters (e.g., kp, ki, kd) are selected within certain ranges, assuming that the local objective functions are smooth and strongly convex. Additionally, we provide guidelines for selecting appropriate parameter values (e.g., kp, ki, kd). Furthermore, we show that the D-PID-CCN has great potential for nonconvex distributed optimization over the cooperation-competition network. Finally, we present the effectiveness and superiority of our proposed algorithms on several numerical simulations.
本文研究了合作-竞争网络框架下具有平等约束的分布式优化问题。基于比例-积分-导数（PID）控制器的优异性能，提出了一种加速分布式优化算法，将合作-竞争网络上的分布式优化问题分解为两个合作子网络，并对其进行求解。利用Lyapunov稳定性定理，在局部目标函数光滑且强凸的条件下，当参数（如kp， ki, kd）在一定范围内选择时，我们建立了算法在无向连接且结构平衡的合作竞争图上的指数收敛性。此外，我们还提供了选择适当参数值（例如，kp, ki, kd）的指南。此外，我们还证明了D-PID-CCN在合作-竞争网络上具有很大的非凸分布优化潜力。最后，在几个数值模拟中证明了所提算法的有效性和优越性。
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