Pub Date : 2025-03-05DOI: 10.1016/j.jfranklin.2025.107614
Shengjie Zhu , Xiaofeng Zong , Yuanyuan Zhang
This paper addresses constrained attitude control problems of flexible spacecraft on SO(3) subject to external disturbances and stochastic uncertainties without modal variable measurement. To handle the attitude constraints, an artificial potential function (APF) is constructed based on the rotation matrix. By combining the adaptive super-twisting control technique and the APF, an adaptive robust control law is proposed to achieve constrained attitude control of flexible spacecraft without prior information on the bound of the norm of flexible vibration and external disturbance. The results are then extended to the case that stochastic uncertainties exist and the adaptive robust control law is modified by designing a Lyapunov-function-based control parameter. Numerical simulations are presented to demonstrate the effectiveness of the proposed control laws.
{"title":"Constrained attitude control of flexible spacecraft with external disturbances and stochastic uncertainties on SO(3)","authors":"Shengjie Zhu , Xiaofeng Zong , Yuanyuan Zhang","doi":"10.1016/j.jfranklin.2025.107614","DOIUrl":"10.1016/j.jfranklin.2025.107614","url":null,"abstract":"<div><div>This paper addresses constrained attitude control problems of flexible spacecraft on SO(3) subject to external disturbances and stochastic uncertainties without modal variable measurement. To handle the attitude constraints, an artificial potential function (APF) is constructed based on the rotation matrix. By combining the adaptive super-twisting control technique and the APF, an adaptive robust control law is proposed to achieve constrained attitude control of flexible spacecraft without prior information on the bound of the norm of flexible vibration and external disturbance. The results are then extended to the case that stochastic uncertainties exist and the adaptive robust control law is modified by designing a Lyapunov-function-based control parameter. Numerical simulations are presented to demonstrate the effectiveness of the proposed control laws.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107614"},"PeriodicalIF":3.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a hybrid observer-based fixed-time tracking control for constrained nonlinear systems. Multiple factors constrain the considered nonlinear systems: internally by dynamic uncertainties and full-state constraints, and externally by external disturbances, actuator faults, and input saturation. A hybrid observer, combining the bias RBFNN (radial basis function neural network) with fixed-time sliding mode, is proposed. The bias RBFNN approximates dynamic uncertainties, while an extended state is designed to estimate the network approximation error, external disturbances, and actuator faults and feed them back to the controller within a fixed time. Meanwhile, the hybrid observer can acquire the velocity information simultaneously. To prevent system states from exceeding predefined boundaries, a barrier function-based state transformation method is implemented. An anti-windup compensator is designed to mitigate the adverse effects caused by input saturation. The semi-globally ultimately fixed-time boundedness (SGUFTB) of the closed-loop system is proven through Lyapunov theory. The effectiveness of the proposed control strategy is demonstrated through simulation and comparative results.
{"title":"Hybrid observer-based fixed-time tracking control for constrained nonlinear systems","authors":"Zihang Guo, Shuangsi Xue, Huan Li, Junkai Tan, Dapeng Yan, Hui Cao","doi":"10.1016/j.jfranklin.2025.107610","DOIUrl":"10.1016/j.jfranklin.2025.107610","url":null,"abstract":"<div><div>This paper introduces a hybrid observer-based fixed-time tracking control for constrained nonlinear systems. Multiple factors constrain the considered nonlinear systems: internally by dynamic uncertainties and full-state constraints, and externally by external disturbances, actuator faults, and input saturation. A hybrid observer, combining the bias RBFNN (radial basis function neural network) with fixed-time sliding mode, is proposed. The bias RBFNN approximates dynamic uncertainties, while an extended state is designed to estimate the network approximation error, external disturbances, and actuator faults and feed them back to the controller within a fixed time. Meanwhile, the hybrid observer can acquire the velocity information simultaneously. To prevent system states from exceeding predefined boundaries, a barrier function-based state transformation method is implemented. An anti-windup compensator is designed to mitigate the adverse effects caused by input saturation. The semi-globally ultimately fixed-time boundedness (SGUFTB) of the closed-loop system is proven through Lyapunov theory. The effectiveness of the proposed control strategy is demonstrated through simulation and comparative results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107610"},"PeriodicalIF":3.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article delves into the economic dispatch problem (EDP) within smart grids, specifically exploring it in time-varying directed networks. The objective is to allocate generation power efficiently among generators to fulfill load demands while minimizing the total generation cost, adhering to local capacity constraints. Each generator carries its unique local generation cost, and the total cost is calculated by summing these individual costs. To this aim, a novel algorithm (ADED-TVD) Accelerated Decentralized Economic Dispatch Algorithm is introduced, which is suitable for Time-Varying Directed networks well. ADED-TVD takes inspiration from the parameter momentum accelerated technique to improve the convergence with different parameters resulting in different momentum (Nesterov or heavy-ball) methods. In addition, ADED-TVD lies in time-varying directed communication networks, where theoretical evidence of linear convergence towards the optimal dispatch is offered. Also, explicit bounds for the step-size and momentum parameters are obtained. Finally, simulations that delve into various aspects of EDP in smart grids are presented.
{"title":"Performing accelerated convergence in decentralized economic dispatch over dynamic directed networks","authors":"Yunshan Lv , Hailing Xiong , Fuqing Zhang , Shengying Dong","doi":"10.1016/j.jfranklin.2025.107611","DOIUrl":"10.1016/j.jfranklin.2025.107611","url":null,"abstract":"<div><div>This article delves into the economic dispatch problem (EDP) within smart grids, specifically exploring it in time-varying directed networks. The objective is to allocate generation power efficiently among generators to fulfill load demands while minimizing the total generation cost, adhering to local capacity constraints. Each generator carries its unique local generation cost, and the total cost is calculated by summing these individual costs. To this aim, a novel algorithm (ADED-TVD) <u>A</u>ccelerated <u>D</u>ecentralized <u>E</u>conomic <u>D</u>ispatch Algorithm is introduced, which is suitable for <u>T</u>ime-<u>V</u>arying <u>D</u>irected networks well. ADED-TVD takes inspiration from the parameter momentum accelerated technique to improve the convergence with different parameters resulting in different momentum (Nesterov or heavy-ball) methods. In addition, ADED-TVD lies in time-varying directed communication networks, where theoretical evidence of linear convergence towards the optimal dispatch is offered. Also, explicit bounds for the step-size and momentum parameters are obtained. Finally, simulations that delve into various aspects of EDP in smart grids are presented.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107611"},"PeriodicalIF":3.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563693","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 : 2025-03-01DOI: 10.1016/j.jfranklin.2025.107626
{"title":"2026 Bower Call","authors":"","doi":"10.1016/j.jfranklin.2025.107626","DOIUrl":"10.1016/j.jfranklin.2025.107626","url":null,"abstract":"","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 5","pages":"Article 107626"},"PeriodicalIF":3.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549347","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, the state estimation issue for the two-time-scale semi-Markov jump coupled neural networks is addressed, in which the information of the system is transmitted through analog fading channels. A singular perturbation parameter is introduced to indicate the two-time-scale characteristics of semi-Markov jump coupled neural networks. Different from the existing Markov processes, this work uses the semi-Markov processes to model the jumping behavior, and further eliminates the restriction of the sojourn time probability distribution. Then, the Lyapunov function is considered to be related to singular perturbation parameters, sojourn times and system modes. Meanwhile, the mean square index stability criterion is introduced. Based on the criterion, the systems are mean square exponentially stable with the given mixed and passivity performance index by using the designed state estimation law. Finally, an illustrative example is used to show the design state estimation law is effective.
{"title":"Mixed H∞ and passivity state estimation for two-time-scale semi-Markov jump coupled neural networks under analog fading channels","authors":"Yongqian Wang, Zhenghao Ni, Jing Wang, Feng Li, Hao Shen","doi":"10.1016/j.jfranklin.2025.107575","DOIUrl":"10.1016/j.jfranklin.2025.107575","url":null,"abstract":"<div><div>In this work, the state estimation issue for the two-time-scale semi-Markov jump coupled neural networks is addressed, in which the information of the system is transmitted through analog fading channels. A singular perturbation parameter is introduced to indicate the two-time-scale characteristics of semi-Markov jump coupled neural networks. Different from the existing Markov processes, this work uses the semi-Markov processes to model the jumping behavior, and further eliminates the restriction of the sojourn time probability distribution. Then, the Lyapunov function is considered to be related to singular perturbation parameters, sojourn times and system modes. Meanwhile, the mean square index stability criterion is introduced. Based on the criterion, the systems are mean square exponentially stable with the given mixed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> and passivity performance index by using the designed state estimation law. Finally, an illustrative example is used to show the design state estimation law is effective.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107575"},"PeriodicalIF":3.7,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552023","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 : 2025-02-27DOI: 10.1016/j.jfranklin.2025.107597
Cheng Han , Zhengguang Xu , Nan Deng
Non-Newtonian mechanical systems, as a specific type of system governed by statistical laws, are commonly found in industrial production processes involving solid–liquid transitions. The challenge of describing the statistical characteristics of such systems using deterministic variables (such as state or output variables) often leads existing control methods to either ignore these systems or treat them as systems with disturbances. This approach, however, frequently results in high energy consumption within the control system. To address the system’s inherent statistical characteristics, this paper introduced a statistical variable called the pattern category variable, which replaces traditional deterministic variables in describing system motion. Additionally, a dynamic description and control framework based on probability density evolution was proposed. The conditional probability density was used as a measure for the pattern category variables, and its evolution law was derived using the principles of probability conservation and non-parametric dynamic linearization theory. Building on this, the probability density evolution of the tracking error was further determined, leading to the formulation of a minimum entropy control law based on pattern movement, accompanied by a parameter estimation algorithm. This approach transformed the control problem of non-Newtonian mechanical systems into reducing the randomness of the system’s tracking errors. Finally, the convergence and stability of both the parameter estimation algorithm and the control algorithm were validated through theoretical analysis. The effectiveness of the proposed method was demonstrated through numerical simulations.
{"title":"Minimum entropy control for non-Newtonian mechanical systems based on pattern moving probability density evolution","authors":"Cheng Han , Zhengguang Xu , Nan Deng","doi":"10.1016/j.jfranklin.2025.107597","DOIUrl":"10.1016/j.jfranklin.2025.107597","url":null,"abstract":"<div><div>Non-Newtonian mechanical systems, as a specific type of system governed by statistical laws, are commonly found in industrial production processes involving solid–liquid transitions. The challenge of describing the statistical characteristics of such systems using deterministic variables (such as state or output variables) often leads existing control methods to either ignore these systems or treat them as systems with disturbances. This approach, however, frequently results in high energy consumption within the control system. To address the system’s inherent statistical characteristics, this paper introduced a statistical variable called the pattern category variable, which replaces traditional deterministic variables in describing system motion. Additionally, a dynamic description and control framework based on probability density evolution was proposed. The conditional probability density was used as a measure for the pattern category variables, and its evolution law was derived using the principles of probability conservation and non-parametric dynamic linearization theory. Building on this, the probability density evolution of the tracking error was further determined, leading to the formulation of a minimum entropy control law based on pattern movement, accompanied by a parameter estimation algorithm. This approach transformed the control problem of non-Newtonian mechanical systems into reducing the randomness of the system’s tracking errors. Finally, the convergence and stability of both the parameter estimation algorithm and the control algorithm were validated through theoretical analysis. The effectiveness of the proposed method was demonstrated through numerical simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107597"},"PeriodicalIF":3.7,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521147","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 : 2025-02-27DOI: 10.1016/j.jfranklin.2025.107596
Manlu Ban , Jianjun Li , Hongyong Deng , Yanhong Wang , Jun Cheng
This paper investigates the leader–follower mean-square consensus problem for nonlinear stochastic multi-agent systems with semi-Markov switching topologies. We address the scenario where the partial communication topology has a directed spanning tree, thus eliminating the special condition that each communication topology must have a directed spanning tree. Given the finite system resources, to minimize unnecessary waste, an improved dynamic event-triggered protocol is designed. To tackle the modal mismatch between the system and the controller, an asynchronous controller with non-homogeneous hidden semi-Markov chains is introduced. Subsequently, by constructing a suitable Lyapunov function, we derive sufficient conditions for the system to achieve leader–follower mean-square consensus and meet the performance index . Thereafter, the obtained results are applied to address the leader–follower mean-square consensus of stochastic multi-agent systems under network attacks. Finally, numerical simulations are employed to validate the effectiveness of the theoretical results.
{"title":"Dynamic event-triggered H∞ leader-following consensus for nonlinear stochastic multi-agent systems with semi-Markov switching topologies and application","authors":"Manlu Ban , Jianjun Li , Hongyong Deng , Yanhong Wang , Jun Cheng","doi":"10.1016/j.jfranklin.2025.107596","DOIUrl":"10.1016/j.jfranklin.2025.107596","url":null,"abstract":"<div><div>This paper investigates the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> leader–follower mean-square consensus problem for nonlinear stochastic multi-agent systems with semi-Markov switching topologies. We address the scenario where the partial communication topology has a directed spanning tree, thus eliminating the special condition that each communication topology must have a directed spanning tree. Given the finite system resources, to minimize unnecessary waste, an improved dynamic event-triggered protocol is designed. To tackle the modal mismatch between the system and the controller, an asynchronous controller with non-homogeneous hidden semi-Markov chains is introduced. Subsequently, by constructing a suitable Lyapunov function, we derive sufficient conditions for the system to achieve leader–follower <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> mean-square consensus and meet the performance index <span><math><mi>γ</mi></math></span>. Thereafter, the obtained results are applied to address the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> leader–follower mean-square consensus of stochastic multi-agent systems under network attacks. Finally, numerical simulations are employed to validate the effectiveness of the theoretical results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107596"},"PeriodicalIF":3.7,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526665","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 : 2025-02-26DOI: 10.1016/j.jfranklin.2025.107590
Weiwu Yan , Peng Wang , Renchao Xu , Rui Han , Enze Chen , Yongqiang Han , Xi Zhang
This paper proposes an innovative end-to-end time-series decomposition-forecasting framework based on recurrent neural networks called DF-RNN for electricity price. The framework combines an RNN-based decomposition model and an RNN-based forecasting model to perform mid- and long-term time-series forecasting tasks effectively. A hierarchical RNN-based time-series decomposition model is introduced to decompose time series data into trend, seasonal, and residual components. The RNN-based forecasting models generate forecasts for each component series, aggregated to produce the time-series forecast. The DF-RNN model simultaneously optimizes the objective functions of both the time-series decomposition model and the forecasting model, resulting in an optimal time-series forecasting model. The DF-RNN model has a flexible network structure and clear interpretability, making it easy to analyze and understand the results. The effectiveness of the proposed framework is evaluated in a real-world electricity-price forecasting in the European Power Exchange France. The experimental results demonstrate that DF-RNN is a promising and effective mid- and long-term time-series forecasting model.
{"title":"A novel mid- and long-term time-series forecasting framework for electricity price based on hierarchical recurrent neural networks","authors":"Weiwu Yan , Peng Wang , Renchao Xu , Rui Han , Enze Chen , Yongqiang Han , Xi Zhang","doi":"10.1016/j.jfranklin.2025.107590","DOIUrl":"10.1016/j.jfranklin.2025.107590","url":null,"abstract":"<div><div>This paper proposes an innovative end-to-end time-series decomposition-forecasting framework based on recurrent neural networks called DF-RNN for electricity price. The framework combines an RNN-based decomposition model and an RNN-based forecasting model to perform mid- and long-term time-series forecasting tasks effectively. A hierarchical RNN-based time-series decomposition model is introduced to decompose time series data into trend, seasonal, and residual components. The RNN-based forecasting models generate forecasts for each component series, aggregated to produce the time-series forecast. The DF-RNN model simultaneously optimizes the objective functions of both the time-series decomposition model and the forecasting model, resulting in an optimal time-series forecasting model. The DF-RNN model has a flexible network structure and clear interpretability, making it easy to analyze and understand the results. The effectiveness of the proposed framework is evaluated in a real-world electricity-price forecasting in the European Power Exchange France. The experimental results demonstrate that DF-RNN is a promising and effective mid- and long-term time-series forecasting model.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107590"},"PeriodicalIF":3.7,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552022","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 : 2025-02-25DOI: 10.1016/j.jfranklin.2025.107592
Bentelhoda Zali, Saeed Karimi
In this paper, we present an iterative method for solving tensor equations, specifically multilinear systems of the form with one of the constraints , , and , where and are reflexive tensors. The proposed method is grounded in the generalized least squares method with the Einstein product. To address the constrained tensor equation using the global least squares method, we introduce a multilinear operator and its adjoint. For a more detailed survey, we compare the proposed method for solving the constrained tensor equation with one of the matrix format methods for the associated matrix equation. We also use the new method to solve the image restoration problem with a symmetrical structure, as a special case of constrained tensor equation. Finally, we give some examples to illustrate the effectiveness of the proposed method.
{"title":"An iterative method for solving the constrained tensor equations with the Einstein product","authors":"Bentelhoda Zali, Saeed Karimi","doi":"10.1016/j.jfranklin.2025.107592","DOIUrl":"10.1016/j.jfranklin.2025.107592","url":null,"abstract":"<div><div>In this paper, we present an iterative method for solving tensor equations, specifically multilinear systems of the form <span><math><mrow><mi>A</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>B</mi><mo>+</mo><mi>C</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>D</mi><mo>=</mo><mi>E</mi></mrow></math></span> with one of the constraints <span><math><mrow><mi>X</mi><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>T</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mi>X</mi><mo>=</mo><mi>P</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>Q</mi></mrow></math></span>, <span><math><mrow><mi>X</mi><mo>=</mo><mo>−</mo><mi>P</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>Q</mi></mrow></math></span> and <span><math><mrow><mi>X</mi><mo>=</mo><mi>P</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>X</mi><msub><mrow><mo>∗</mo></mrow><mrow><mi>N</mi></mrow></msub><mi>P</mi></mrow></math></span>, where <span><math><mi>P</mi></math></span> and <span><math><mi>Q</mi></math></span> are reflexive tensors. The proposed method is grounded in the generalized least squares method with the Einstein product. To address the constrained tensor equation using the global least squares method, we introduce a multilinear operator and its adjoint. For a more detailed survey, we compare the proposed method for solving the constrained tensor equation with one of the matrix format methods for the associated matrix equation. We also use the new method to solve the image restoration problem with a symmetrical structure, as a special case of constrained tensor equation. Finally, we give some examples to illustrate the effectiveness of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107592"},"PeriodicalIF":3.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511009","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 : 2025-02-25DOI: 10.1016/j.jfranklin.2025.107589
Nam-Jin Park , Seong-Ho Kwon , Yoo-Bin Bae , Byeong-Yeon Kim , Kevin L. Moore , Hyo-Sung Ahn
This paper explores the conditions for strong structural controllability in structured networks determined by the zero/non-zero patterns of edges. For undirected networks, starting with the fundamental unit for controllability, the path graph, we investigate the strong structural controllability of larger components such as cycles, trees, and ultimately, a pactus (a generalization of the well-known cactus graph) through the merging rules. In this process, we introduce the notion of a component input node, which functions identically to an external input node, providing a new perspective on how internal nodes can facilitate controllability. Furthermore, we offer an intuitive interpretation by decomposing complex graph structures into simpler path graphs and applying merging rules to understand how disjoint controllable components can merge to maintain overall controllability. Finally, we present an algorithm to solve the minimum input problem in a pactus, which leverages the concept of component input nodes to optimize the number of external inputs for strong structural controllability.
{"title":"Merging rules for strong structural controllability and minimum input problem in undirected networks","authors":"Nam-Jin Park , Seong-Ho Kwon , Yoo-Bin Bae , Byeong-Yeon Kim , Kevin L. Moore , Hyo-Sung Ahn","doi":"10.1016/j.jfranklin.2025.107589","DOIUrl":"10.1016/j.jfranklin.2025.107589","url":null,"abstract":"<div><div>This paper explores the conditions for strong structural controllability in structured networks determined by the zero/non-zero patterns of edges. For undirected networks, starting with the fundamental unit for controllability, the path graph, we investigate the strong structural controllability of larger components such as cycles, trees, and ultimately, a pactus (a generalization of the well-known cactus graph) through the merging rules. In this process, we introduce the notion of a component input node, which functions identically to an external input node, providing a new perspective on how internal nodes can facilitate controllability. Furthermore, we offer an intuitive interpretation by decomposing complex graph structures into simpler path graphs and applying merging rules to understand how disjoint controllable components can merge to maintain overall controllability. Finally, we present an algorithm to solve the minimum input problem in a pactus, which leverages the concept of component input nodes to optimize the number of external inputs for strong structural controllability.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 6","pages":"Article 107589"},"PeriodicalIF":3.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526616","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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