Pub Date : 2025-12-22DOI: 10.1016/j.jfranklin.2025.108283
Xiaoming Liu , Fuchun Wu , Yunshan Deng , Ming Wang , Yuanqing Xia
This paper addresses the trajectory planning problem for unmanned vehicles with free terminal time in constrained environments with obstacles. A variable substitution method is employed to handle the free terminal time, transforming the nonconvex cost function and constraints into convex forms while maintaining feasibility. For obstacle avoidance, we propose a Chebyshev-node based discretization method that focuses on the vertices of vehicles and obstacles modeled as convex polygons, along with a convexification approach for volumetric obstacle avoidance. The optimization problem is solved within a sequential convex programming framework by converting it into a series of second-order cone programming subproblems, enhancing real-time performance. The effectiveness and computational efficiency of the proposed method are validated through numerical simulations and comparisons with other methods.
{"title":"Collision-free trajectory planning for unmanned vehicles using sequential second-order cone programming","authors":"Xiaoming Liu , Fuchun Wu , Yunshan Deng , Ming Wang , Yuanqing Xia","doi":"10.1016/j.jfranklin.2025.108283","DOIUrl":"10.1016/j.jfranklin.2025.108283","url":null,"abstract":"<div><div>This paper addresses the trajectory planning problem for unmanned vehicles with free terminal time in constrained environments with obstacles. A variable substitution method is employed to handle the free terminal time, transforming the nonconvex cost function and constraints into convex forms while maintaining feasibility. For obstacle avoidance, we propose a Chebyshev-node based discretization method that focuses on the vertices of vehicles and obstacles modeled as convex polygons, along with a convexification approach for volumetric obstacle avoidance. The optimization problem is solved within a sequential convex programming framework by converting it into a series of second-order cone programming subproblems, enhancing real-time performance. The effectiveness and computational efficiency of the proposed method are validated through numerical simulations and comparisons with other methods.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108283"},"PeriodicalIF":4.2,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881154","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 : 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":"2025-12-21","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 : 2025-12-21DOI: 10.1016/j.jfranklin.2025.108323
Xiaonan Liu , Wenrui Li , Jian Sun , Yonggui Kao
This paper develops a chattering-free sliding mode control framework for uncertain stochastic systems subject to hybrid dynamics, including time-varying delays and impulsive perturbations. A novel integral sliding surface is designed to incorporate time-varying delays, parametric uncertainties, and impulsive perturbations, thereby unifying the analysis of continuous and discrete dynamics. Furthermore, the proposed adaptive scheme with the hyperbolic tangent function ensures chattering suppression while maintaining finite-time convergence from the initial moment. Additionally, sufficient conditions for the stability of the stochastic system are derived on the specified sliding surface for all admissible uncertainties, based on the Lyapunov function and the average impulsive interval. Finally, a numerical example is presented to illustrate the proposed method.
{"title":"Chattering-free adaptive sliding mode control for uncertain delayed stochastic systems with impulsive dynamics","authors":"Xiaonan Liu , Wenrui Li , Jian Sun , Yonggui Kao","doi":"10.1016/j.jfranklin.2025.108323","DOIUrl":"10.1016/j.jfranklin.2025.108323","url":null,"abstract":"<div><div>This paper develops a chattering-free sliding mode control framework for uncertain stochastic systems subject to hybrid dynamics, including time-varying delays and impulsive perturbations. A novel integral sliding surface is designed to incorporate time-varying delays, parametric uncertainties, and impulsive perturbations, thereby unifying the analysis of continuous and discrete dynamics. Furthermore, the proposed adaptive scheme with the hyperbolic tangent function ensures chattering suppression while maintaining finite-time convergence from the initial moment. Additionally, sufficient conditions for the stability of the stochastic system are derived on the specified sliding surface for all admissible uncertainties, based on the Lyapunov function and the average impulsive interval. Finally, a numerical example is presented to illustrate the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108323"},"PeriodicalIF":4.2,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837947","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 : 2025-12-21DOI: 10.1016/j.jfranklin.2025.108360
Mohammad Motaharifar, Mohammad Ataei
This paper explores the challenges of synchronizing Euler-Lagrange networks that include a dynamic leader, utilizing a disturbance observer method. In this network, each agent is characterized by Euler-Lagrange equations of motion with dynamics that are not fully known. Unlike most existing approaches for handling uncertainties in Euler-Lagrange networks, the structure of the dynamic equations is assumed to be unavailable, making existing adaptive control schemes inapplicable. Therefore, a new formulation is proposed for Euler-Lagrange networks to lump the uncertain dynamical terms, estimate them, and suppress their effects accordingly. The closed-loop stability of the overall system is analyzed using the Lyapunov stability theorem. Simulation results show that the proposed approach outperforms two existing benchmark control methods.
{"title":"A disturbance observer-based synchronization control architecture for Euler-Lagrange networks with a dynamic leader","authors":"Mohammad Motaharifar, Mohammad Ataei","doi":"10.1016/j.jfranklin.2025.108360","DOIUrl":"10.1016/j.jfranklin.2025.108360","url":null,"abstract":"<div><div>This paper explores the challenges of synchronizing Euler-Lagrange networks that include a dynamic leader, utilizing a disturbance observer method. In this network, each agent is characterized by Euler-Lagrange equations of motion with dynamics that are not fully known. Unlike most existing approaches for handling uncertainties in Euler-Lagrange networks, the structure of the dynamic equations is assumed to be unavailable, making existing adaptive control schemes inapplicable. Therefore, a new formulation is proposed for Euler-Lagrange networks to lump the uncertain dynamical terms, estimate them, and suppress their effects accordingly. The closed-loop stability of the overall system is analyzed using the Lyapunov stability theorem. Simulation results show that the proposed approach outperforms two existing benchmark control methods.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108360"},"PeriodicalIF":4.2,"publicationDate":"2025-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881061","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 : 2025-12-20DOI: 10.1016/j.jfranklin.2025.108366
Lei Fu , Shang Cui , Huilan Liu
This paper presents a novel event-triggered mechanism (ETM) with adaptive triggering thresholds and develops a distributed cooperative load frequency control (LFC) framework for cyber-physical power systems (CPPS) subject to hybrid attacks. By integrating uncertain saturated nonlinearities inherent in turbine and governor dynamics of the CPPS, this paper establishes a Takagi-Sugeno (T-S) fuzzy system framework to characterize nonlinear features and devises a fuzzy distributed cooperative proportional-integral (PI) controller that explicitly accounts for actuator faults. Through the construction of a two-sided closed-loop Lyapunov-Krasovskii functional (LKF) incorporating delay-dependent matrices, an asymptotic stability criterion with enhanced H∞ performance is rigorously derived. Illustrative examples involving a one-area and a three-area CPPS validate the effectiveness of the methodology in improving dynamic performance and cyber-resilience.
{"title":"Event-triggered control for T-S fuzzy multi-area cyber-physical power system under hybrid attacks","authors":"Lei Fu , Shang Cui , Huilan Liu","doi":"10.1016/j.jfranklin.2025.108366","DOIUrl":"10.1016/j.jfranklin.2025.108366","url":null,"abstract":"<div><div>This paper presents a novel event-triggered mechanism (ETM) with adaptive triggering thresholds and develops a distributed cooperative load frequency control (LFC) framework for cyber-physical power systems (CPPS) subject to hybrid attacks. By integrating uncertain saturated nonlinearities inherent in turbine and governor dynamics of the CPPS, this paper establishes a Takagi-Sugeno (T-S) fuzzy system framework to characterize nonlinear features and devises a fuzzy distributed cooperative proportional-integral (PI) controller that explicitly accounts for actuator faults. Through the construction of a two-sided closed-loop Lyapunov-Krasovskii functional (LKF) incorporating delay-dependent matrices, an asymptotic stability criterion with enhanced <em>H</em><sub>∞</sub> performance is rigorously derived. Illustrative examples involving a one-area and a three-area CPPS validate the effectiveness of the methodology in improving dynamic performance and cyber-resilience.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108366"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-20DOI: 10.1016/j.jfranklin.2025.108349
Qian Zhang, Ximei Liu
This paper investigates computationally efficient identification methods for multivariable autoregressive output-error autoregressive moving-average systems. To tackle high-dimensional parameter estimation challenges, the multivariable system is decomposed into several subsystems. Furthermore, each subsystem identification model is decomposed into two small-scale sub-identification models to reduce the computational burden. Based on the hierarchical identification principle, a two-stage auxiliary model maximum likelihood least squares-based iterative algorithm is proposed. The analysis of floating point operations shows that the proposed algorithm achieves higher computational efficiency than the existing auxiliary model maximum likelihood least squares-based iterative algorithm. Simulation results demonstrate that the proposed algorithm is effective and achieves high parameter estimation accuracy.
{"title":"Two-stage auxiliary model maximum likelihood least squares-based iterative estimation method for general stochastic multivariable systems","authors":"Qian Zhang, Ximei Liu","doi":"10.1016/j.jfranklin.2025.108349","DOIUrl":"10.1016/j.jfranklin.2025.108349","url":null,"abstract":"<div><div>This paper investigates computationally efficient identification methods for multivariable autoregressive output-error autoregressive moving-average systems. To tackle high-dimensional parameter estimation challenges, the multivariable system is decomposed into several subsystems. Furthermore, each subsystem identification model is decomposed into two small-scale sub-identification models to reduce the computational burden. Based on the hierarchical identification principle, a two-stage auxiliary model maximum likelihood least squares-based iterative algorithm is proposed. The analysis of floating point operations shows that the proposed algorithm achieves higher computational efficiency than the existing auxiliary model maximum likelihood least squares-based iterative algorithm. Simulation results demonstrate that the proposed algorithm is effective and achieves high parameter estimation accuracy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108349"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 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":"2025-12-20","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 : 2025-12-20DOI: 10.1016/j.jfranklin.2025.108357
Fanyueyang Zhang , Jun-e Feng , Yuanhua Wang
The finite multi-objective potential game (FMOPG) with different objective sets is proposed in this paper. Leveraging the semi-tensor product of matrices, two necessary and sufficient conditions for verifying FMOPGs have been presented, which provide the theoretical foundation for the research on potential-based multi-objective distributed optimization. In addition, the Pareto equilibrium in this class of games is examined by establishing two equivalent verification criteria. Significantly, the relationship between Pareto equilibrium and potential functions is further characterized, which demonstrates that this model can exhibit richer equilibrium behaviors and model more complex interaction patterns compared to FMOPGs with a common objective set for all players. Finally, taking multi-objective facility-based systems as an example, the applicability of the results is validated.
{"title":"Multi-objective potential games: model, equilibrium, and applications","authors":"Fanyueyang Zhang , Jun-e Feng , Yuanhua Wang","doi":"10.1016/j.jfranklin.2025.108357","DOIUrl":"10.1016/j.jfranklin.2025.108357","url":null,"abstract":"<div><div>The finite multi-objective potential game (FMOPG) with different objective sets is proposed in this paper. Leveraging the semi-tensor product of matrices, two necessary and sufficient conditions for verifying FMOPGs have been presented, which provide the theoretical foundation for the research on potential-based multi-objective distributed optimization. In addition, the Pareto equilibrium in this class of games is examined by establishing two equivalent verification criteria. Significantly, the relationship between Pareto equilibrium and potential functions is further characterized, which demonstrates that this model can exhibit richer equilibrium behaviors and model more complex interaction patterns compared to FMOPGs with a common objective set for all players. Finally, taking multi-objective facility-based systems as an example, the applicability of the results is validated.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108357"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838022","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 : 2025-12-20DOI: 10.1016/j.jfranklin.2025.108340
Guoqing Qi, Ruochen Kong, Yinya Li, Andong Sheng
This paper presents a critical node identification algorithm for the non-cooperative group targets, such as unmanned aerial vehicle(UAV) swarm, with unknown communication topology. First, by simulating the information transmission among targets within the group, a minimum connected network topology is constructed using an adjacency matrix-based graph model. Second, by analyzing the structural similarity and effective communication distance(SSECD) between nodes, a secondary aggregation of neighbor information is formed, which combines with the initial information of node to generate the final information for ranking nodes importance. Then, the algorithm’s effectiveness is validated through tests on public datasets and a simulated UAV group data. The experimental results demonstrate that the proposed SSECD algorithm yields nodes ranking more consistent with that of the epidemiological SIR model, achieving higher average Kendall correlation coefficients than other algorithms. The proposed approach offers theoretical guidance for countermeasures against UAV group targets and demonstrate significant engineering application value.
{"title":"A critical node identification method for group targets based on structural similarity and effective communication distance","authors":"Guoqing Qi, Ruochen Kong, Yinya Li, Andong Sheng","doi":"10.1016/j.jfranklin.2025.108340","DOIUrl":"10.1016/j.jfranklin.2025.108340","url":null,"abstract":"<div><div>This paper presents a critical node identification algorithm for the non-cooperative group targets, such as unmanned aerial vehicle(UAV) swarm, with unknown communication topology. First, by simulating the information transmission among targets within the group, a minimum connected network topology is constructed using an adjacency matrix-based graph model. Second, by analyzing the structural similarity and effective communication distance(SSECD) between nodes, a secondary aggregation of neighbor information is formed, which combines with the initial information of node to generate the final information for ranking nodes importance. Then, the algorithm’s effectiveness is validated through tests on public datasets and a simulated UAV group data. The experimental results demonstrate that the proposed SSECD algorithm yields nodes ranking more consistent with that of the epidemiological SIR model, achieving higher average Kendall correlation coefficients than other algorithms. The proposed approach offers theoretical guidance for countermeasures against UAV group targets and demonstrate significant engineering application value.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108340"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838017","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 : 2025-12-20DOI: 10.1016/j.jfranklin.2025.108352
Meng Tao , Yiheng Wei , Jinde Cao , Hanen Karamti , Mahmoud Abdel-Aty
This paper investigates the design and robustness of distributed Proportional-Integral-Derivative (PID) continuous-time algorithms in the context of unbalanced directed network topologies. To address the challenge of unbalancedness affecting convergence accuracy, we introduce a novel approach using prescribed-time estimates of the left eigenvectors, ensuring the system converges to the true solution without the usual distortions caused by unbalanced topologies. Through a Lyapunov-based stability analysis, we rigorously prove the exponential convergence of the proposed algorithm. Furthermore, we extend the algorithm to handle systems with bounded disturbances by presenting a robust PID variant, demonstrating that it can return to disturbance-free behavior within a specified time frame. Experimental simulations validate the algorithm’s effectiveness in both disturbance-free and disturbance-affected scenarios, showcasing its applicability and efficiency in practical distributed control environments.
{"title":"Enhancing distributed optimization: A PID-Based approach for unbalanced graphs with bounded disturbances","authors":"Meng Tao , Yiheng Wei , Jinde Cao , Hanen Karamti , Mahmoud Abdel-Aty","doi":"10.1016/j.jfranklin.2025.108352","DOIUrl":"10.1016/j.jfranklin.2025.108352","url":null,"abstract":"<div><div>This paper investigates the design and robustness of distributed Proportional-Integral-Derivative (PID) continuous-time algorithms in the context of unbalanced directed network topologies. To address the challenge of unbalancedness affecting convergence accuracy, we introduce a novel approach using prescribed-time estimates of the left eigenvectors, ensuring the system converges to the true solution without the usual distortions caused by unbalanced topologies. Through a Lyapunov-based stability analysis, we rigorously prove the exponential convergence of the proposed algorithm. Furthermore, we extend the algorithm to handle systems with bounded disturbances by presenting a robust PID variant, demonstrating that it can return to disturbance-free behavior within a specified time frame. Experimental simulations validate the algorithm’s effectiveness in both disturbance-free and disturbance-affected scenarios, showcasing its applicability and efficiency in practical distributed control environments.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108352"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838020","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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