Journal of The Franklin Institute-engineering and Applied Mathematics最新文献

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Frequency analysis of two subsystems coupled by a spring-inerter-damper device and its application to continuous system for vibration control

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.jfranklin.2025.107567

Jun Wu , Brano Titurus

Two continuous subsystems interconnected by a spring-inerter-damper device are common engineering configurations for vibration control. To address the problem of designing device parameters for optimal vibration control, comprehensive and systematic mathematical analyses are carried out for the minimum 2-degrees-of-freedom (DOF) system which includes two subsystems interconnected by a spring-inerter-damper device. Then, the equivalence between the 2DOF system and the full-scale continuous system is established, which allows the results of the 2DOF system to be directly transferrable to the original full-scale system. Results show that there is an optimal tuning condition in which two roots coalesce and both damping ratios reach equally high value at the first bifurcation. The device parameters at this point are derived mathematically, and used for optimal vibration control. The subcritical and supercritical conditions are also defined and the associated properties are derived. When applied to a continuous rotating beam-tendon system as a case study, the device parameters derived based on the equivalent 2DOF system are shown to be close to the optimal parameters with errors less than 6 %, and the performance of the resulting full-scale continuous system is almost identical to the optimal performance.

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引用次数: 0

Existence of optimal control and time optimality of a stochastic age-space structured tuberculosis model

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-15 DOI: 10.1016/j.jfranklin.2025.107516

Dongchen Shangguan, Jing Hu, Xining Li, Qimin Zhang

In this paper, considering the influences of stochastic noise and age structure on the spread of tuberculosis, a stochastic age-space structured tuberculosis model that integrates both prevention and treatment control strategies is formulated. To be specific, the positivity and uniqueness of the mild solution of model are acquired. After that, from a cost-benefit perspective, an optimal control problem of tuberculosis is formulated to minimize the number of infected population and control cost by virtue of Gronwall’s inequality and Mazur’s lemma. The time optimal control is further discussed. Based on this analysis, some concrete examples are given for verify theoretical results.

引用次数: 0

Online algebraic disturbance estimation method for linear systems with noisy state measurements

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.jfranklin.2024.107442

Yan-Qiao Wei , Da-Yan Liu , Chang-Chun Hua , Cong Zhang

This paper aims to design an online algebraic disturbance estimation method for linear systems with noisy state measurements. The motivation is to provide a fast-convergent and robust online disturbance estimation method for active anti-disturbance control systems. By constructing a modulating functions vector, a state-based algebraic integral formula is derived for the disturbance of the studied system. Within a discrete noisy environment, the proposed formula can be numerically executed online with respect to a sliding integration window. Meanwhile, the analysis of error effects is also given based on the proposed formula. Finally, simulation examples are provided to illustrate the efficiency of the proposed method for an open-loop system and a closed-loop system, respectively.

引用次数: 0

Robust cooperative output regulation for linear multi-agent systems under intermittent measurements

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.jfranklin.2024.107473

Horacio García-Vázquez , Ulises Larios-Navarro , Bernardino Castillo-Toledo , Stefano Di Gennaro

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.

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引用次数: 0

A fractional-time PDE-constrained parameter identification for inverse image noise removal problem

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 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

α

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.

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引用次数: 0

Fixed-time quantized synchronization of spatiotemporal networks with output-based quantization communication via boundary control

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 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}

引用次数: 0

Cyclic pursuit formation control for arbitrary desired shapes

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 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.

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引用次数: 0

Distributed aggregative optimization over directed networks with column-stochasticity

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.jfranklin.2024.107492

Qixing Zhou , Keke Zhang , Hao Zhou , Qingguo Lü , Xiaofeng Liao , Huaqing Li

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}

引用次数: 0

Edge-based time-dynamic event triggered consensus control for multi-agent systems with disconnected switching topologies

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.jfranklin.2024.107495

Yonghui Wu , Huaqing Li , Chuandong Li , Qingguo Lü

The consensus problem of multi-agent systems under switching topologies with both connected and unconnected communication subgraphs is investigated in this study. To save resources and avoid the utilization of the global coordinate frame, an edge-based time-dynamic event triggered mechanism is developed to regulate the transmission of relative information for each edge in the network, where the time triggered mechanism is to ensure an explicit lower bound of triggering sequences and the dynamic event-triggered mechanism to enlarge the average time interval of triggering sequences. It is demonstrated that, under the planned distributed algorithm, the consensus could be reached exponentially if the ratio of the total activation time of connected subgraphs to that of unconnected subgraphs satisfies a given condition. Furthermore, under commonly verifiable assumptions, the procedure is presented to choose parameters and the existence of solutions to these parameters is also strictly proved. Finally, simulations are conducted to verify the proposed algorithm.

{"title":"Edge-based time-dynamic event triggered consensus control for multi-agent systems with disconnected switching topologies","authors":"Yonghui Wu , Huaqing Li , Chuandong Li , Qingguo Lü","doi":"10.1016/j.jfranklin.2024.107495","DOIUrl":"10.1016/j.jfranklin.2024.107495","url":null,"abstract":"<div><div>The consensus problem of multi-agent systems under switching topologies with both connected and unconnected communication subgraphs is investigated in this study. To save resources and avoid the utilization of the global coordinate frame, an edge-based time-dynamic event triggered mechanism is developed to regulate the transmission of relative information for each edge in the network, where the time triggered mechanism is to ensure an explicit lower bound of triggering sequences and the dynamic event-triggered mechanism to enlarge the average time interval of triggering sequences. It is demonstrated that, under the planned distributed algorithm, the consensus could be reached exponentially if the ratio of the total activation time of connected subgraphs to that of unconnected subgraphs satisfies a given condition. Furthermore, under commonly verifiable assumptions, the procedure is presented to choose parameters and the existence of solutions to these parameters is also strictly proved. Finally, simulations are conducted to verify the proposed algorithm.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107495"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137839","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}

引用次数: 0

Neural network-based adaptive fault-tolerant control for strict-feedback nonlinear systems with input dead zone and saturation

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics

Pub Date : 2025-01-01 DOI: 10.1016/j.jfranklin.2024.107471

Mohamed Kharrat , Moez Krichen , Hadil Alhazmi , Paolo Mercorelli

This study investigates the issue of adaptive fault-tolerant neural control in strict-feedback nonlinear systems. The system is subjected to actuator faults, dead-zone and saturation. To model the unknown functions, radial basis function neural networks (RBFNN) are employed. The proposed approach utilizes a backstepping technique to formulate an adaptive fault-tolerant controller, drawing upon the Lyapunov stability theory and the approximation capabilities of RBFNN. The resultant controller guarantees the boundedness of all signals in the closed-loop system, ensuring precise tracking of the reference signal by the system output with a small, bounded error. Finally, simulation results are provided to illustrate the efficacy of the proposed strategy in addressing actuator faults, dead-zone, and saturation.

引用次数: 0

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