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.2025.108353
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}
Pub Date : 2025-12-20DOI: 10.1016/j.jfranklin.2025.108339
Jiarui Liu , Jinhai Liu , Zhenning Wu , Anjun Tan , Yanhong Luo
Reliable path planning is crucial for the autonomy of inspection robots operating in complex constrained environments. Sampling-based methods are widely used in robot path planning due to their computational efficiency. However, they still face three key challenges in practice: poor real-time performance in narrow passages, an inherent trade-off between search efficiency and path quality, and node redundancy caused by incomplete pruning. To overcome these challenges, we propose an efficient path planner, Bidirectional Ring Guide-RRT* (BRG-RRT*). First, a bidirectional ring guide (BRG) mechanism is proposed, which dynamically adjusts obstacle-boundary sample density and introduces orientation guidance, significantly enhancing the planner’s real-time performance in narrow passages. Second, a foresighted path generation method is proposed to refine the balance between search efficiency and path quality. It accelerates the path search while effectively reducing the zigzags and local optima within the path. Third, we propose a hybrid path pruning method leveraging both local and global collision feedback. This allows the planner to solve node redundancy in a single operation, improving overall path robustness. Finally, a spline parameterization method is used to ensure the smooth operation of the robot. Simulations and real-world experiments demonstrate significant improvements in planning time cost, path quality, node redundancy, task efficiency, and navigation success rate.
{"title":"A heuristic sampling-based planner towards optimal path planning in narrow passage","authors":"Jiarui Liu , Jinhai Liu , Zhenning Wu , Anjun Tan , Yanhong Luo","doi":"10.1016/j.jfranklin.2025.108339","DOIUrl":"10.1016/j.jfranklin.2025.108339","url":null,"abstract":"<div><div>Reliable path planning is crucial for the autonomy of inspection robots operating in complex constrained environments. Sampling-based methods are widely used in robot path planning due to their computational efficiency. However, they still face three key challenges in practice: poor real-time performance in narrow passages, an inherent trade-off between search efficiency and path quality, and node redundancy caused by incomplete pruning. To overcome these challenges, we propose an efficient path planner, Bidirectional Ring Guide-RRT* (BRG-RRT*). First, a bidirectional ring guide (BRG) mechanism is proposed, which dynamically adjusts obstacle-boundary sample density and introduces orientation guidance, significantly enhancing the planner’s real-time performance in narrow passages. Second, a foresighted path generation method is proposed to refine the balance between search efficiency and path quality. It accelerates the path search while effectively reducing the zigzags and local optima within the path. Third, we propose a hybrid path pruning method leveraging both local and global collision feedback. This allows the planner to solve node redundancy in a single operation, improving overall path robustness. Finally, a spline parameterization method is used to ensure the smooth operation of the robot. Simulations and real-world experiments demonstrate significant improvements in planning time cost, path quality, node redundancy, task efficiency, and navigation success rate.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108339"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837889","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}
In this work, we propose an innovative approach to shadow removal in images by enhancing the space-variant anisotropic Partial Differential Equation (PDE) framework. This enhancement involves redefining existing osmosis models to incorporate tensor-based characteristics inspired by Weickert-type operators. The model leverages spatially distant pixel similarities, using a specified window size to improve image restoration. The numerical solution is obtained through the Split Bregman Iterative method (SBI). To thoroughly evaluate the model’s performance, we conduct a series of tests, including both perceptual and quantitative assessments. The results demonstrate that our approach outperforms state-of-the-art methods in shadow removal.
{"title":"Enhanced shadow removal using space-variant anisotropic PDEs and tensor-based osmosis models","authors":"Fakhr-Eddine Limami , Aissam Hadri , Amine Laghrib , Lekbir Afraites","doi":"10.1016/j.jfranklin.2025.108315","DOIUrl":"10.1016/j.jfranklin.2025.108315","url":null,"abstract":"<div><div>In this work, we propose an innovative approach to shadow removal in images by enhancing the space-variant anisotropic Partial Differential Equation (PDE) framework. This enhancement involves redefining existing osmosis models to incorporate tensor-based characteristics inspired by Weickert-type operators. The model leverages spatially distant pixel similarities, using a specified window size to improve image restoration. The numerical solution is obtained through the Split Bregman Iterative method (SBI). To thoroughly evaluate the model’s performance, we conduct a series of tests, including both perceptual and quantitative assessments. The results demonstrate that our approach outperforms state-of-the-art methods in shadow removal.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108315"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981007","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.2025.108317
Yanhua Song , Hanbo Wang , Fei Han , Yuxuan Shen , Hongli Dong , Shikun Shao
This paper deals with the scalable distributed filtering problem with binary measurements for a class of discrete time-varying uncertain Markovian jump linear systems. The system and the original measurement are subject to random noise with known means and variances. A Markov chain is introduced to formulate the switching of system parameters, the uncertainties of which are characterized by the norm-bounded constraint. The useful information for estimation purpose is extracted via the crossings between the original binary measurements and the desirable binary measurements. By using the information from neighboring nodes, sufficient conditions are established for every node to guarantee the existence of the distributed filter such that the filtering error satisfies the exponential boundedness in the mean square. The filter gains are calculated on each node by means of recursive linear matrix inequalities, which achieve the desirable scalability of distributed filtering owing to such a manner. Finally, a simulation example demonstrates the applicability of the distributed filtering scheme proposed in this paper.
{"title":"Distributed filtering for uncertain time-varying Markovian jump linear systems over binary sensor network","authors":"Yanhua Song , Hanbo Wang , Fei Han , Yuxuan Shen , Hongli Dong , Shikun Shao","doi":"10.1016/j.jfranklin.2025.108317","DOIUrl":"10.1016/j.jfranklin.2025.108317","url":null,"abstract":"<div><div>This paper deals with the scalable distributed filtering problem with binary measurements for a class of discrete time-varying uncertain Markovian jump linear systems. The system and the original measurement are subject to random noise with known means and variances. A Markov chain is introduced to formulate the switching of system parameters, the uncertainties of which are characterized by the norm-bounded constraint. The useful information for estimation purpose is extracted via the crossings between the original binary measurements and the desirable binary measurements. By using the information from neighboring nodes, sufficient conditions are established for every node to guarantee the existence of the distributed filter such that the filtering error satisfies the exponential boundedness in the mean square. The filter gains are calculated on each node by means of recursive linear matrix inequalities, which achieve the desirable scalability of distributed filtering owing to such a manner. Finally, a simulation example demonstrates the applicability of the distributed filtering scheme proposed in this paper.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108317"},"PeriodicalIF":4.2,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881151","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 : 2025-12-19DOI: 10.1016/j.jfranklin.2025.108325
Qiliang Zhang , Ze Wang , Jianfang Jiao , Yongyuan Yu
This paper develops a robust optimal control method to study the finite-time set stabilization (FTSS) of probabilistic Boolean control networks (PBCNs). First, an efficient algorithm is proposed to determine the solvability of the FTSS of PBCNs by constructing index vectors. Then, a pre-step cost function is introduced, which is based on the largest control invariant subset of PBCNs. By applying the dynamic programming theory, an algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state. Compared with existing results, the proposed robust optimal control method transforms the FTSS of PBCNs into an optimization problem and significantly reduces the time complexity from O(γN3M) to O(γN2M). Finally, an illustrative example involving a biological system validates the effectiveness of the proposed approach, demonstrating significant improvements in computational efficiency.
{"title":"Finite-time set stabilization of probabilistic boolean control networks: A robust optimal control approach","authors":"Qiliang Zhang , Ze Wang , Jianfang Jiao , Yongyuan Yu","doi":"10.1016/j.jfranklin.2025.108325","DOIUrl":"10.1016/j.jfranklin.2025.108325","url":null,"abstract":"<div><div>This paper develops a robust optimal control method to study the finite-time set stabilization (FTSS) of probabilistic Boolean control networks (PBCNs). First, an efficient algorithm is proposed to determine the solvability of the FTSS of PBCNs by constructing index vectors. Then, a pre-step cost function is introduced, which is based on the largest control invariant subset of PBCNs. By applying the dynamic programming theory, an algorithm is presented to calculate the optimal feedback gain matrix and the optimal value for each state. Compared with existing results, the proposed robust optimal control method transforms the FTSS of PBCNs into an optimization problem and significantly reduces the time complexity from <em>O</em>(<em>γN</em><sup>3</sup><em>M</em>) to <em>O</em>(<em>γN</em><sup>2</sup><em>M</em>). Finally, an illustrative example involving a biological system validates the effectiveness of the proposed approach, demonstrating significant improvements in computational efficiency.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108325"},"PeriodicalIF":4.2,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.jfranklin.2025.108350
Chaolin Liang , Meng Yuan , Yuman Li , Sen Wang , Hong Lin , Peng Shi
This paper studies the state estimation for cyber-physical systems under hybrid Denial of Service (DoS) attacks and false data injection (FDI) attacks, where the attack parameters are unknown. Under such hybrid attacks, it is challenging to design a computationally efficient and stable estimator, since the traditional optimal estimator cannot be implemented in practice. This paper aims at addressing these issues, and the contributions are twofold: (i) Design of an detector, identifiers, and an estimator:A modified detector is designed to detect the occurrence of DoS attacks. Then, two detector-based identifiers ar designed to identify DoS-attack parameters and the FDI-attack parameters, respectively. Based on these, an attack-detection-and-identification-based (ADI-based) estimator is proposed. (ii) Theoretical analysis on performance and stability: The mean squared detection errors converge to zero, and the identified parameters converge with probability 1 to the real ones. For the proposed ADI-based estimator, it is proved that it is stable when the DoS attack rate is less than a threshold. Finally, a numerical simulation and a real experiment are given to verify the effectiveness of the proposed method.
{"title":"State estimation for systems subject to hybrid DoS and FDI attacks with unknown attack parameters","authors":"Chaolin Liang , Meng Yuan , Yuman Li , Sen Wang , Hong Lin , Peng Shi","doi":"10.1016/j.jfranklin.2025.108350","DOIUrl":"10.1016/j.jfranklin.2025.108350","url":null,"abstract":"<div><div>This paper studies the state estimation for cyber-physical systems under hybrid Denial of Service (DoS) attacks and false data injection (FDI) attacks, where the attack parameters are unknown. Under such hybrid attacks, it is challenging to design a computationally efficient and stable estimator, since the traditional optimal estimator cannot be implemented in practice. This paper aims at addressing these issues, and the contributions are twofold: <strong>(i) Design of an detector, identifiers, and an estimator:</strong>A modified <span><math><msup><mi>X</mi><mn>2</mn></msup></math></span> detector is designed to detect the occurrence of DoS attacks. Then, two detector-based identifiers ar designed to identify DoS-attack parameters and the FDI-attack parameters, respectively. Based on these, an attack-detection-and-identification-based (ADI-based) estimator is proposed. <strong>(ii) Theoretical analysis on performance and stability:</strong> The mean squared detection errors converge to zero, and the identified parameters converge with probability 1 to the real ones. For the proposed ADI-based estimator, it is proved that it is stable when the DoS attack rate is less than a threshold. Finally, a numerical simulation and a real experiment are given to verify the effectiveness of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108350"},"PeriodicalIF":4.2,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837946","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号