Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107536
Xiaofan Ma, Haitao Li
This paper analyzes the cluster synchronization of Boolean networks (BNs) subject to deterministic function perturbation. Firstly, the perturbation injection matrix is constructed based on the structure matrix of original BNs and the information of function perturbation to determine whether the cluster synchronization is still maintained after one-bit function perturbation occurs. Secondly, based on the idea of robust cluster synchronization of BNs subject to one-bit function perturbation, we give a necessary and sufficient condition for robust cluster synchronization of BNs with multi-bit function perturbations. Finally, as an application, the robust feedback cluster synchronization is further studied for Boolean control networks subject to function perturbation.
{"title":"Robust cluster synchronization of Boolean networks with function perturbation","authors":"Xiaofan Ma, Haitao Li","doi":"10.1016/j.jfranklin.2025.107536","DOIUrl":"10.1016/j.jfranklin.2025.107536","url":null,"abstract":"<div><div>This paper analyzes the cluster synchronization of Boolean networks (BNs) subject to deterministic function perturbation. Firstly, the perturbation injection matrix is constructed based on the structure matrix of original BNs and the information of function perturbation to determine whether the cluster synchronization is still maintained after one-bit function perturbation occurs. Secondly, based on the idea of robust cluster synchronization of BNs subject to one-bit function perturbation, we give a necessary and sufficient condition for robust cluster synchronization of BNs with multi-bit function perturbations. Finally, as an application, the robust feedback cluster synchronization is further studied for Boolean control networks subject to function perturbation.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107536"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137143","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 : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107535
Deqiong Ding, Guixiang Huang, Yu Gao, Kai-Ning Wu
Parabolic partial differential equations (PPDEs) are essential in practical engineering applications, and interval estimation methods offer an effective framework for fault detection in these systems. However, research on fault detection for time-delayed PPDEs using interval estimation remains limited. In this paper, we propose a new fault detection strategy for time-delay PPDE with uncertainties. The detection thresholds are designed within the framework of a two-step interval estimation method. First, we estimate the bounds of the auxiliary function through descriptive approach and inequality techniques. Then, we derive the detection threshold through the bounds of the auxiliary function and peak-to-peak analysis techniques. Finally, an example of a shallow geothermal system demonstrates the effectiveness of the proposed method.
{"title":"Interval estimation-based fault detection for time-delay parabolic systems","authors":"Deqiong Ding, Guixiang Huang, Yu Gao, Kai-Ning Wu","doi":"10.1016/j.jfranklin.2025.107535","DOIUrl":"10.1016/j.jfranklin.2025.107535","url":null,"abstract":"<div><div>Parabolic partial differential equations (PPDEs) are essential in practical engineering applications, and interval estimation methods offer an effective framework for fault detection in these systems. However, research on fault detection for time-delayed PPDEs using interval estimation remains limited. In this paper, we propose a new fault detection strategy for time-delay PPDE with uncertainties. The detection thresholds are designed within the framework of a two-step interval estimation method. First, we estimate the bounds of the auxiliary function through descriptive approach and inequality techniques. Then, we derive the detection threshold through the bounds of the auxiliary function and peak-to-peak analysis techniques. Finally, an example of a shallow geothermal system demonstrates the effectiveness of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107535"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137196","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 : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107544
Xingyi Li , Xin Liu , Jiliang Zhang , Jun Wang , Shanghui Li , Zi Yuan , Gaofeng Pan
In this paper, physical-layer security performance for a multi-relaying based satellite-free-space optical network, which consists of a single-antenna satellite source (S), M (M ) relays (R) with each equipping with (L ) receiving antennas and a photo-aperture transmitter with N (N ) lasers, a single-aperture destination (D) and a single-aperture eavesdropper (E), is evaluated. Specifically, a relay, which first adopts a maximum ratio combining protocol to process the received signals from S and then transforms the decoded signal into an optical one before transmitting it to D with a transmit aperture selection scheme, is selected based on a general K-th best relay selection criteria to assist the information forwarding. Additionally, the probability density functions and cumulative distribution functions of the instantaneous signal-to-noise ratio at R and D are formatted, serving as the foundation for deriving both analytical and asymptotic expressions of the lower bound of secrecy outage probability. Finally, the accuracy of those derived expressions is validated through Monte-Carlo simulations.
{"title":"Secrecy performance for a multi-relaying SIMO-satellite/MISO-FSO network","authors":"Xingyi Li , Xin Liu , Jiliang Zhang , Jun Wang , Shanghui Li , Zi Yuan , Gaofeng Pan","doi":"10.1016/j.jfranklin.2025.107544","DOIUrl":"10.1016/j.jfranklin.2025.107544","url":null,"abstract":"<div><div>In this paper, physical-layer security performance for a multi-relaying based satellite-free-space optical network, which consists of a single-antenna satellite source (S), <em>M</em> (<em>M</em> <span><math><mrow><mo>≥</mo><mn>1</mn></mrow></math></span>) relays (R) with each equipping with <span><math><mi>L</mi></math></span> (<em>L</em> <span><math><mrow><mo>≥</mo><mn>1</mn></mrow></math></span>) receiving antennas and a photo-aperture transmitter with <em>N</em> (<em>N</em> <span><math><mrow><mo>≥</mo><mn>1</mn></mrow></math></span>) lasers, a single-aperture destination (D) and a single-aperture eavesdropper (E), is evaluated. Specifically, a relay, which first adopts a maximum ratio combining protocol to process the received signals from S and then transforms the decoded signal into an optical one before transmitting it to D with a transmit aperture selection scheme, is selected based on a general <em>K</em>-th best relay selection criteria to assist the information forwarding. Additionally, the probability density functions and cumulative distribution functions of the instantaneous signal-to-noise ratio at R and D are formatted, serving as the foundation for deriving both analytical and asymptotic expressions of the lower bound of secrecy outage probability. Finally, the accuracy of those derived expressions is validated through Monte-Carlo simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107544"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137197","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 : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107527
Jiewen Pang , Junxing Zhang , Menghan Li , Shaoyang Li
This paper improves the design methodology of the permanent magnet synchronous motor (PMSM) controller by using different approaches. First, it introduces bounded time-varying filter gains. It integrates time-varying command filters into the controller design of PMSMs for the first time to optimize the system's filtering capability. Second, this paper presents a fixed-time asymmetric prescribed performance control (PPC) strategy to limit the output response of the PMSM to a specific asymmetric district and uses a prescribed time convergence function to raise the convergence speed. Finally, introducing disturbance observer (DOB) and Lyapunov-Krasovskii functions to compensate for external load disturbances and time delays improves the system's robustness. In summary, the novelties of this paper are to utilize these improvements to PMSM control, making the proposed time-varying command filters-based neural adaptive control (CFNAC) method closer to the practical situation.
{"title":"Time-varying command filters-based neural adaptive control with fixed-time prescribed performance for the PMSM with external disturbance and time delays","authors":"Jiewen Pang , Junxing Zhang , Menghan Li , Shaoyang Li","doi":"10.1016/j.jfranklin.2025.107527","DOIUrl":"10.1016/j.jfranklin.2025.107527","url":null,"abstract":"<div><div>This paper improves the design methodology of the permanent magnet synchronous motor (PMSM) controller by using different approaches. First, it introduces bounded time-varying filter gains. It integrates time-varying command filters into the controller design of PMSMs for the first time to optimize the system's filtering capability. Second, this paper presents a fixed-time asymmetric prescribed performance control (PPC) strategy to limit the output response of the PMSM to a specific asymmetric district and uses a prescribed time convergence function to raise the convergence speed. Finally, introducing disturbance observer (DOB) and Lyapunov-Krasovskii functions to compensate for external load disturbances and time delays improves the system's robustness. In summary, the novelties of this paper are to utilize these improvements to PMSM control, making the proposed time-varying command filters-based neural adaptive control (CFNAC) method closer to the practical situation.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107527"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145436","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 studies disturbance-observer-based dynamic sliding mode controller design for trajectory tracking control of ball screw drive systems with matched and mismatched disturbances. Specifically, a unified observer is constructed to estimate the state and disturbance of the ball screw drive system simultaneously. Then, a novel sliding surface is constructed based on the tracking error, the disturbance observer, and the reference trajectory, where the tracking error is defined according to state observer and reference trajectory, and the disturbance observer and reference trajectory are, respectively, introduced for disturbance attenuation and tracking error reduction. Further, a dynamic sliding mode controller is synthesized to drive the tracking error, i.e., the linear trajectory error and rotational trajectory error, onto the sliding surface in a finite time. It is shown that the proposed dynamic sliding mode control suppresses not only matched but also mismatched disturbances. Finally, the effectiveness of the presented control strategy is verified through experimental studies.
{"title":"Dynamic sliding mode control for ball screw drive systems under a disturbance observer scheme","authors":"Yanling Wei , Shuo Zhang , Yufan Chen , Hamid Reza Karimi","doi":"10.1016/j.jfranklin.2025.107517","DOIUrl":"10.1016/j.jfranklin.2025.107517","url":null,"abstract":"<div><div>This paper studies disturbance-observer-based dynamic sliding mode controller design for trajectory tracking control of ball screw drive systems with matched and mismatched disturbances. Specifically, a unified observer is constructed to estimate the state and disturbance of the ball screw drive system simultaneously. Then, a novel sliding surface is constructed based on the tracking error, the disturbance observer, and the reference trajectory, where the tracking error is defined according to state observer and reference trajectory, and the disturbance observer and reference trajectory are, respectively, introduced for disturbance attenuation and tracking error reduction. Further, a dynamic sliding mode controller is synthesized to drive the tracking error, i.e., the linear trajectory error and rotational trajectory error, onto the sliding surface in a finite time. It is shown that the proposed dynamic sliding mode control suppresses not only matched but also mismatched disturbances. Finally, the effectiveness of the presented control strategy is verified through experimental studies.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107517"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145984","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 addresses the problem of cooperative output regulation for uncertain linear multi-agent systems under asynchronous intermittent measurements. The relevant theory for the solution of the robust output regulation problem with asynchronous intermittent reference transmission for a single agent is first developed, extending the classical assumptions and the invariance condition given by the Francis equations and the internal model principle of the continuous output regulation problem to the hybrid framework. The results obtained for a single agent are then applied to multi-agent systems by developing a novel hybrid distributed observer and control law, despite the communication constraints between agents, which are assumed to share their outputs at asynchronous instants. The controller design is based on a leader–follower scheme with a virtual leader, modeled as an exosystem, and a set of followers, modeled as heterogeneous linear systems with uncertainties. The communication structure is described by a directed graph, which only needs to be available at least once between two time bounds, solving the frequent problems of switching topologies and Zeno-like behaviors. The stability and regulation conditions of the multi-agent system are proven and guaranteed by the existence of a solution to a finite set of linear matrix inequalities. The effectiveness of the contribution is compared with previous results in numerical examples and demonstrated through simulation in a particular example of a multi-agent system.
{"title":"Robust cooperative output regulation for linear multi-agent systems under intermittent measurements","authors":"Horacio García-Vázquez , Ulises Larios-Navarro , Bernardino Castillo-Toledo , Stefano Di Gennaro","doi":"10.1016/j.jfranklin.2024.107473","DOIUrl":"10.1016/j.jfranklin.2024.107473","url":null,"abstract":"<div><div>This paper addresses the problem of cooperative output regulation for uncertain linear multi-agent systems under asynchronous intermittent measurements. The relevant theory for the solution of the robust output regulation problem with asynchronous intermittent reference transmission for a single agent is first developed, extending the classical assumptions and the invariance condition given by the Francis equations and the internal model principle of the continuous output regulation problem to the hybrid framework. The results obtained for a single agent are then applied to multi-agent systems by developing a novel hybrid distributed observer and control law, despite the communication constraints between agents, which are assumed to share their outputs at asynchronous instants. The controller design is based on a leader–follower scheme with a virtual leader, modeled as an exosystem, and a set of followers, modeled as heterogeneous linear systems with uncertainties. The communication structure is described by a directed graph, which only needs to be available at least once between two time bounds, solving the frequent problems of switching topologies and Zeno-like behaviors. The stability and regulation conditions of the multi-agent system are proven and guaranteed by the existence of a solution to a finite set of linear matrix inequalities. The effectiveness of the contribution is compared with previous results in numerical examples and demonstrated through simulation in a particular example of a multi-agent system.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107473"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01DOI: 10.1016/j.jfranklin.2024.107443
Anouar Ben-Loghfyry
This study introduces a novel PDE-constrained optimization approach tailored to determine the optimal fractional-time order in diffusion PDEs for image denoising. By incorporating a time-fractional derivative, our framework effectively enhances image clarity and reduces virtual artifacts. The Accelerated Primal–Dual algorithm is utilized to improve the efficiency of the model. We conduct a comprehensive evaluation of the denoising performance of this PDE-constrained method through various numerical experiments, considering different images and noise levels across a wide range of noise intensities. Furthermore, the robustness of the model is tested under high noise conditions, and a detailed analysis of the behavior of the fractional-time derivative is provided. The experimental results demonstrate the model’s effectiveness and resilience in noise reduction, supported by both visual inspections and quantitative metrics. Compared to several state-of-the-art techniques, our approach delivers superior image denoising, producing images that are significantly cleaner, exhibit a natural appearance, and show a marked reduction in undesirable artifacts.
{"title":"A fractional-time PDE-constrained parameter identification for inverse image noise removal problem","authors":"Anouar Ben-Loghfyry","doi":"10.1016/j.jfranklin.2024.107443","DOIUrl":"10.1016/j.jfranklin.2024.107443","url":null,"abstract":"<div><div>This study introduces a novel PDE-constrained optimization approach tailored to determine the optimal fractional-time order <span><math><mi>α</mi></math></span> in diffusion PDEs for image denoising. By incorporating a time-fractional derivative, our framework effectively enhances image clarity and reduces virtual artifacts. The Accelerated Primal–Dual algorithm is utilized to improve the efficiency of the model. We conduct a comprehensive evaluation of the denoising performance of this PDE-constrained method through various numerical experiments, considering different images and noise levels across a wide range of noise intensities. Furthermore, the robustness of the model is tested under high noise conditions, and a detailed analysis of the behavior of the fractional-time derivative is provided. The experimental results demonstrate the model’s effectiveness and resilience in noise reduction, supported by both visual inspections and quantitative metrics. Compared to several state-of-the-art techniques, our approach delivers superior image denoising, producing images that are significantly cleaner, exhibit a natural appearance, and show a marked reduction in undesirable artifacts.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107443"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137853","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 : 2025-01-01DOI: 10.1016/j.jfranklin.2024.107460
Tingting Shi , Cheng Hu , Juan Yu , Shiping Wen
In the age of digitization and networking, as a significant interactive information mode, quantitative communication effectively alleviates communication pressure and improves transmission efficiency. Besides, boundary control has significant advantages over traditional full-domain control in reducing control cost and improving controller implementation. In view this, this article is concerned about fixed-time synchronization of spatiotemporal networks with Robin boundary condition and output-based quantization communication. Firstly, based on output information, a type of quantization communication mechanism is introduced into the network model. Subsequently, an output-based quantization controller is developed, which is distributed on the Robin boundary. As a result, several flexible fixed-time output and state synchronization criteria are obtained based on Lyapunov-like method and an artful matrix analytical technique, and the upper bound of the synchronization time is explicitly estimated. The derived results are further extended to spatiotemporal networks with Neumann and mixed boundary conditions. Note that there is no strict requirement on the output matrix compared with the previous semi-positive, non-singular or column full rank form. An urban public traffic network is presented at last to confirm the developed controllers and criteria.
{"title":"Fixed-time quantized synchronization of spatiotemporal networks with output-based quantization communication via boundary control","authors":"Tingting Shi , Cheng Hu , Juan Yu , Shiping Wen","doi":"10.1016/j.jfranklin.2024.107460","DOIUrl":"10.1016/j.jfranklin.2024.107460","url":null,"abstract":"<div><div>In the age of digitization and networking, as a significant interactive information mode, quantitative communication effectively alleviates communication pressure and improves transmission efficiency. Besides, boundary control has significant advantages over traditional full-domain control in reducing control cost and improving controller implementation. In view this, this article is concerned about fixed-time synchronization of spatiotemporal networks with Robin boundary condition and output-based quantization communication. Firstly, based on output information, a type of quantization communication mechanism is introduced into the network model. Subsequently, an output-based quantization controller is developed, which is distributed on the Robin boundary. As a result, several flexible fixed-time output and state synchronization criteria are obtained based on Lyapunov-like method and an artful matrix analytical technique, and the upper bound of the synchronization time is explicitly estimated. The derived results are further extended to spatiotemporal networks with Neumann and mixed boundary conditions. Note that there is no strict requirement on the output matrix compared with the previous semi-positive, non-singular or column full rank form. An urban public traffic network is presented at last to confirm the developed controllers and criteria.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107460"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137854","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 : 2025-01-01DOI: 10.1016/j.jfranklin.2024.107467
Anna Fujioka , Masaki Ogura , Naoki Wakamiya
A multi-agent system (MAS) comprises numerous agents that autonomously make decisions to collectively accomplish tasks, drawing significant attention due to their wide range of applications. Within this context, formation control has emerged as a prominent task, wherein agents collaboratively shape and maneuver while preserving formation integrity. This study focuses on cyclic pursuit, a method that facilitates the formation of circles, ellipses, and figure eights under the assumption that agents can only perceive the relative positions of those preceding them. However, the scope of this method has been restricted to these specific shapes, rendering the feasibility of forming other shapes uncertain. To overcome this limitation, we propose a novel method based on cyclic pursuit that is capable of forming a broader array of shapes, enabling agents to individually form the desired shape while pursuing preceding agents, thereby extending the repertoire of achievable formations. We develop two scenarios concerning the information available to the agents and devise formation control methods tailored to each scenario. Through extensive simulations, we demonstrate the efficacy of the proposed method in forming multiple shapes, including those represented as a Fourier series, thereby underscoring the versatility and effectiveness of the proposed approach.
{"title":"Cyclic pursuit formation control for arbitrary desired shapes","authors":"Anna Fujioka , Masaki Ogura , Naoki Wakamiya","doi":"10.1016/j.jfranklin.2024.107467","DOIUrl":"10.1016/j.jfranklin.2024.107467","url":null,"abstract":"<div><div>A multi-agent system (MAS) comprises numerous agents that autonomously make decisions to collectively accomplish tasks, drawing significant attention due to their wide range of applications. Within this context, formation control has emerged as a prominent task, wherein agents collaboratively shape and maneuver while preserving formation integrity. This study focuses on cyclic pursuit, a method that facilitates the formation of circles, ellipses, and figure eights under the assumption that agents can only perceive the relative positions of those preceding them. However, the scope of this method has been restricted to these specific shapes, rendering the feasibility of forming other shapes uncertain. To overcome this limitation, we propose a novel method based on cyclic pursuit that is capable of forming a broader array of shapes, enabling agents to individually form the desired shape while pursuing preceding agents, thereby extending the repertoire of achievable formations. We develop two scenarios concerning the information available to the agents and devise formation control methods tailored to each scenario. Through extensive simulations, we demonstrate the efficacy of the proposed method in forming multiple shapes, including those represented as a Fourier series, thereby underscoring the versatility and effectiveness of the proposed approach.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107467"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a distributed optimization algorithm for distributed aggregative optimization (DAO) problems on directed networks with column-stochastic matrices, referred to as the DACS algorithm. DAO problems, where each agent’s local cost function relies on the aggregation of other agents’ decisions as well as its own, pose significant challenges due to potential imbalances in the underlying interaction network. The DACS algorithm leverages an advanced push-sum protocol to facilitate efficient information aggregation and consensus formation. The algorithm’s convergence is guaranteed by the Lipschitz continuity of the gradient and the strong convexity of the cost functions. Additionally, the utilization of the heavy ball method significantly accelerates the convergence speed of DACS. Numerical simulations across various scenarios, including multi-robot surveillance, optimal placement, and Nash–Cournot games in power systems, demonstrate the algorithm’s convergence and efficiency. Furthermore, testing the algorithm under network disruptions shows that it maintains convergence in both fixed and time-varying networks, proving that as long as connectivity assumptions hold, our algorithm exhibits robustness across a wide range of real-world network environments.
{"title":"Distributed aggregative optimization over directed networks with column-stochasticity","authors":"Qixing Zhou , Keke Zhang , Hao Zhou , Qingguo Lü , Xiaofeng Liao , Huaqing Li","doi":"10.1016/j.jfranklin.2024.107492","DOIUrl":"10.1016/j.jfranklin.2024.107492","url":null,"abstract":"<div><div>This paper introduces a distributed optimization algorithm for distributed aggregative optimization (DAO) problems on directed networks with column-stochastic matrices, referred to as the DACS algorithm. DAO problems, where each agent’s local cost function relies on the aggregation of other agents’ decisions as well as its own, pose significant challenges due to potential imbalances in the underlying interaction network. The DACS algorithm leverages an advanced push-sum protocol to facilitate efficient information aggregation and consensus formation. The algorithm’s convergence is guaranteed by the Lipschitz continuity of the gradient and the strong convexity of the cost functions. Additionally, the utilization of the heavy ball method significantly accelerates the convergence speed of DACS. Numerical simulations across various scenarios, including multi-robot surveillance, optimal placement, and Nash–Cournot games in power systems, demonstrate the algorithm’s convergence and efficiency. Furthermore, testing the algorithm under network disruptions shows that it maintains convergence in both fixed and time-varying networks, proving that as long as connectivity assumptions hold, our algorithm exhibits robustness across a wide range of real-world network environments.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107492"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138502","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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