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

{"title":"Cyclic pursuit formation control for arbitrary desired shapes","authors":"Anna Fujioka ,&nbsp;Masaki Ogura ,&nbsp;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}

{"title":"Distributed aggregative optimization over directed networks with column-stochasticity","authors":"Qixing Zhou ,&nbsp;Keke Zhang ,&nbsp;Hao Zhou ,&nbsp;Qingguo Lü ,&nbsp;Xiaofeng Liao ,&nbsp;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}

{"title":"Edge-based time-dynamic event triggered consensus control for multi-agent systems with disconnected switching topologies","authors":"Yonghui Wu ,&nbsp;Huaqing Li ,&nbsp;Chuandong Li ,&nbsp;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}

{"title":"Neural network-based adaptive fault-tolerant control for strict-feedback nonlinear systems with input dead zone and saturation","authors":"Mohamed Kharrat ,&nbsp;Moez Krichen ,&nbsp;Hadil Alhazmi ,&nbsp;Paolo Mercorelli","doi":"10.1016/j.jfranklin.2024.107471","DOIUrl":"10.1016/j.jfranklin.2024.107471","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107471"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137846","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}

{"title":"Prescribed-time privacy-preserving bipartite consensus of multiagent systems via edge-event-triggered method","authors":"Lianghao Ji ,&nbsp;Fanghui Niu ,&nbsp;Xing Guo ,&nbsp;Yan Xie ,&nbsp;Huaqing Li","doi":"10.1016/j.jfranklin.2024.107423","DOIUrl":"10.1016/j.jfranklin.2024.107423","url":null,"abstract":"<div><div>This paper investigates the prescribed-time privacy-preserving bipartite consensus problem of multiagent systems (MASs). A novel edge-event-triggered prescribed-time privacy-preserving consensus protocol is proposed to achieve accurate bipartite consensus of MASs in a prescribed time while protecting the agents’ states from being obtained by curious agents. To mask the agents’ states, a new edge-based output mask function is designed. This function allows the agents to set different private parameters for different neighbors, effectively preventing the curious agents from accessing all the information used by the protected agent, thereby achieving a better privacy preservation effect. In addition, an edge-based dynamic event-triggered strategy (ETS) is designed to save communication resources while further reducing the risk of privacy leakage. Sufficient conditions that can guarantee accurate bipartite consensus of MASs in a prescribed time and prevent the agents’ states from being reconstructed by curious agents are obtained. Furthermore, the Zeno behavior is excluded throughout the period except for the prescribed time. Finally, numerical simulations validate the theoretical results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107423"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143168676","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}

{"title":"Robust attitude control for hypersonic reentry vehicle via composite fixed-time stable control method","authors":"Wei Wang ,&nbsp;Jing Yang ,&nbsp;Yuxiang Nan ,&nbsp;Shaoyong Hu ,&nbsp;Yuchen Wang","doi":"10.1016/j.jfranklin.2024.107426","DOIUrl":"10.1016/j.jfranklin.2024.107426","url":null,"abstract":"<div><div>A novel adaptive nonsingular fixed-time converged terminal sliding mode control method is proposed for a standard nonlinear system suffering from uncertainties and disturbance. The obtained results are applied to attitude maneuver controller design for hypersonic reentry vehicles (HRV). First, an adaptive disturbance observer with fixed-time stability is introduced to cope with the total disturbance consisting of uncertainties and disturbance. Considering the singularity issue inherent in classical fixed-time converged terminal sliding mode, an improved nonsingular fixed-time terminal sliding mode(NFxTSM) is designed by implementing the switching function, ensuring faster convergence and singularity-free. The adaptive technique is also incorporated with the controller design to enhance the robustness of the NFxTSM. Then, considering the inherent time-scale separation feature, the composite attitude maneuver controller is further designed for HRV based on the backstepping technique. The outer loop generates the desired angle rate command, and the inner loop is designed to track the outer loop command. Finally, the numerical simulations are established to verify the effectiveness of the proposed controller.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107426"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143168683","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}

{"title":"Fractional-order input-to-state stability and its converse Lyapunov theorem","authors":"Tong Guo ,&nbsp;Yiheng Wei ,&nbsp;Luyao Zhang ,&nbsp;Yao Mao ,&nbsp;Xi Zhou ,&nbsp;Jinde Cao","doi":"10.1016/j.jfranklin.2024.107414","DOIUrl":"10.1016/j.jfranklin.2024.107414","url":null,"abstract":"<div><div>This paper establishes input-to-state stability (ISS) for fractional-order nonlinear systems, providing a stability constraint framework for fractional-order systems affected by external inputs. The general fractional comparison principle aids in constructing Lyapunov functions, offering criteria for input-to-state stability of fractional-order nonlinear systems. The concept of weak robustness and the converse Lyapunov theorem for fractional-order nonlinear systems further enhance the completeness of input-to-state stability in these systems. By designing systems to maintain fractional-order input-to-state stability (FOISS), the system can remain robust against the effects of bounded external inputs. Serving as a foundational ”toolbox,” this work provides insights into the stability analysis of fractional-order nonlinear systems, benefiting researchers and practitioners in the field of control theory.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107414"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143168690","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}

{"title":"Fault detection observer design for interval type-2 T–S fuzzy systems based on locally optimized membership function-dependent H− performance","authors":"Guoqiang Cai,&nbsp;Jiuxiang Dong","doi":"10.1016/j.jfranklin.2024.107461","DOIUrl":"10.1016/j.jfranklin.2024.107461","url":null,"abstract":"<div><div>A fault detection observer design method for interval Type-2 Takagi–Sugeno fuzzy systems based on a newly defined locally optimized membership function dependent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance index is proposed in this paper. In the field of fault detection, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance index is a crucial measure of the sensitivity of residual signals to fault signals. Therefore, utilizing <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance for fault detection observer design is common, and enhancing this index is significant for improving the sensitivity and reducing the false alarm rate of observers. This paper introduces a novel <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance index, considering that Takagi–Sugeno fuzzy systems do not operate on all linear subsystems indefinitely. The focus is on enhancing the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance of subsystems operating for extended periods. Additionally, by partitioning the state space and fully utilizing upper and lower membership function information, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance of locally dominant subsystems with high membership on long-running linear subsystems is improved. A novel locally optimized membership function-dependent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance index is thus defined. Moreover, combining the line-integral fuzzy Lyapunov function and descriptor system method, the relaxation variable technique is provided and overcomes the requirement for time derivatives of membership functions. The newly defined <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>−</mo></mrow></msub></math></span> performance index introduces a novel approach to designing fault detection observers. By providing sufficient conditions for the existence of fault detection observers, this method offers promise for enhancing fault detection capabilities in systems. The simulation results further validate the effectiveness of this approach, indicating its potential for practical application.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107461"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137849","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}

{"title":"A recurrent neural network based on Taylor difference for solving discrete time-varying linear matrix problems and application in robot arms","authors":"Chenfu Yi,&nbsp;Xuan Li,&nbsp;Mingdong Zhu,&nbsp;Jianliang Ruan","doi":"10.1016/j.jfranklin.2024.107469","DOIUrl":"10.1016/j.jfranklin.2024.107469","url":null,"abstract":"<div><div>Discrete time-varying linear matrix problems (DTVLMP) play an important role in the field of artificial intelligence and control engineering. This article presents a direct solution to the DTVLMP based on Taylor difference discrete time-varying recurrent neural network (TD-DRNN) model. First of all, the TD-DRNN operates in a directly discrete time-varying framework, avoiding the need to build a theoretical foundation from a continuous time-varying recurrent neural network (RNN) model. Then, the theoretical properties of the TD-DRNN have been rigorously analyzed, demonstrating both its convergence and accuracy. These results show that the new TD-DRNN model has remarkable computational performance. Furthermore, the effectiveness and versatility of the TD-DRNN model have been substantiated through a numerical simulation and the application of two robotic trials.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107469"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137851","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}

{"title":"Adaptive quantized control for hypersonic flight vehicles subject to actuator faults and backlash nonlinearity","authors":"Zhihui Wang,&nbsp;Chenliang Wang,&nbsp;Linling Bai,&nbsp;Yu Wang,&nbsp;Jianzhong Qiao,&nbsp;Lei Guo","doi":"10.1016/j.jfranklin.2024.107500","DOIUrl":"10.1016/j.jfranklin.2024.107500","url":null,"abstract":"<div><div>In this paper, an adaptive quantized control scheme is proposed for a class of hypersonic flight vehicles with actuator faults and elevator backlash. An improved hysteretic quantizer is employed to reduce the communication burden and chattering phenomenon, whose parameters are allowed to be freely changed according to tracking performance and communication capability. By designing adaptive laws to estimate the bounds of time-varying uncertainties, the impacts of the actuator faults, the input quantization and the backlash nonlinearity are successfully compensated for and boundedness of all the closed-loop signals is ensured. Meanwhile, by introducing a double transformation technique, both the altitude and the velocity of the vehicle can track desired trajectories with prescribed transient and steady-state performance, which implies that the proposed adaptive quantized control scheme provides satisfactory tracking performance in addition to higher reliability. The effectiveness of the proposed scheme is demonstrated via simulation results.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 2","pages":"Article 107500"},"PeriodicalIF":3.7,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138507","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}