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

{"title":"Optimal consensus control of nonlinear multi-agent systems by data-driven optimistic policy iteration","authors":"Gang Chen ,&nbsp;Ziyi Li,&nbsp;Lei Wang","doi":"10.1016/j.jfranklin.2025.107764","DOIUrl":"10.1016/j.jfranklin.2025.107764","url":null,"abstract":"<div><div>This paper investigates the optimal consensus control of nonlinear multi-agent systems with completely unknown dynamics. To overcome the difficulties in solving the coupled Hamilton–Jacobi–Bellman equations for the optimal control, a data-driven optimistic policy iteration algorithm is proposed based on adaptive dynamic programming techniques, which generalizes the classical value and policy iteration algorithms. By approximating the performance function and control policy through critic and actor networks and considering the inevitable neural network approximation errors, we give the rigorous optimal consensus convergence analyses. The efficacy of our method is validated through two simulation examples, highlighting its superior convergence performance over the typical value iteration algorithm.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107764"},"PeriodicalIF":3.7,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291054","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":"Reliable truncation parameter selection and model order estimation for stochastic subspace identification","authors":"Khashayar Bayati,&nbsp;Karthikeyan Umapathy,&nbsp;Soosan Beheshti","doi":"10.1016/j.jfranklin.2025.107766","DOIUrl":"10.1016/j.jfranklin.2025.107766","url":null,"abstract":"<div><div>Stochastic subspace identification (SSID) is a fundamental technique for the analysis and prediction of dynamic systems influenced by stochastic processes. This paper addresses critical challenges in SSID, focusing on two steps of SSID, the estimation of truncation hyperparameters and the model order selection, which are pivotal for accurate and robust system parameter estimation. While the existing approaches for truncation hyperparameter estimation mostly rely on arbitrary choices in practice, a new fully automated approach, denoted as Multivariate Reconstruction Error Modelling (MREM), is introduced that is based on a solid theory of measurement errors. Similarly, the existing order selection approaches utilize different penalty terms. However, in application, the optimum approach is chosen by trial and error, and as the data length increases, the methods seem to perform worse, which alarms the issue of consistency. A new method for model order estimation, called Advanced Mean Square Eigenvalue Error (AMSEE) Minimization, is proposed in this work, which is not only consistent as the data length grows but also shows superiority over these existing methods. Instead of a penalty term, the method focuses on the mean square error of the singular value decomposition (SVD) and provides a method that, unlike existing ones, is robust to noise variation. The combination of MREM and AMSEE collectively denoted as MRSEE, achieves rapid convergence to the true model order, maintaining accuracy even as the data length increases. Simulation results consistently confirm these properties and the superiority of MRSEE over the existing approaches, exhibiting better accuracy and robustness against overfitting and underfitting in varying measurement noise conditions. In experiments with synthesized electroencephalogram (EEG) data, MRSEE reduces estimation and true error rates up to 43.44% and 41.16%, respectively, compared to the state-of-the-art approaches. These results highlight MRSEE’s capability to provide robust and reliable solutions for SSID applications, particularly in scenarios with relatively shorter data lengths and lower signal-to-noise ratio (SNR).</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107766"},"PeriodicalIF":3.7,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280845","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":"Nonlinear distributed filtering for time-varying saturated stochastic systems with cyber-attack via FlexRay regulation mechanism","authors":"Jiaxing Li ,&nbsp;Jun Hu ,&nbsp;Junhua Du ,&nbsp;Mingqing Zhu ,&nbsp;Ruixue Zhang","doi":"10.1016/j.jfranklin.2025.107762","DOIUrl":"10.1016/j.jfranklin.2025.107762","url":null,"abstract":"<div><div>In this paper, the distributed recursive filtering (DRF) issue is addressed for time-varying saturated stochastic systems, where the communications between sensors and filters undergo the FlexRay regulation protocol (FRRP) and false data injection attack. For the sake of mitigating undesirable data congestion, the FRRP is implemented in the communication channel to regulate data transmission. The false data injection attack might occur in the transmission process owing to open yet vulnerable networked environments. The focus of this paper is to develop a novel resource-saving DRF scheme and performance evaluation criterion under the framework of variance constraint. Specifically, an upper bound on the filtering error covariance (UBFEC) is firstly derived and then such a UBFEC is minimized via selecting a proper filter gain. Moreover, the boundedness of UBFEC is examined according to the matrix theory and the theoretical proof is presented. Finally, a comparative simulation experiment with practical application in mass–spring system is exploited to verify the validity of the newly designed DRF strategy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107762"},"PeriodicalIF":3.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263601","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 novel event-triggered mechanism-based optimal safe control for nonlinear multi-player systems using adaptive dynamic programming","authors":"Shihui Liu ,&nbsp;Ben Niu ,&nbsp;Ning Zhao ,&nbsp;Guangdeng Zong ,&nbsp;Xudong Zhao ,&nbsp;Lun Li","doi":"10.1016/j.jfranklin.2025.107761","DOIUrl":"10.1016/j.jfranklin.2025.107761","url":null,"abstract":"<div><div>In this paper, an approximate optimal safe control method is proposed for nonlinear multi-player systems under a novel event-triggered mechanism (ETM). First, a control barrier function is introduced into the performance index function for ensuring the safety of the system. Then, the coupled Hamilton–Jacobi equations (HJEs) are obtained for multi-player nonzero-sum games. By utilizing a novel event-triggered adaptive dynamic programming algorithm, the Nash equilibrium solutions of HJEs are approximated under a critic architecture. Under the developed novel ETM, signals between sensors, controllers, and actuators are updated aperiodically, significantly saving communication resources. Meanwhile, the approximate optimal controllers are completely discretized, which provides conditions for wireless communications. Based on the Lyapunov theory, state- and weight-dependent triggering conditions are designed to guarantee the stability of the closed-loop system. Finally, a simulation example is presented to exemplify the effectiveness of the proposed control scheme.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107761"},"PeriodicalIF":3.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280844","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":"Unified prescribed-time performance control for HONSs with input saturation","authors":"Peng Chen ,&nbsp;Jieqing Tan ,&nbsp;Yangang Yao ,&nbsp;Yan Xing ,&nbsp;Yan Yao","doi":"10.1016/j.jfranklin.2025.107760","DOIUrl":"10.1016/j.jfranklin.2025.107760","url":null,"abstract":"<div><div>This article is concerned with the issue of unified prescribed-time performance control(UPTPC) for high-order nonlinear systems(HONSs) subject to input saturation. The “unified performance” means that multiple performance of output tracking error can be achieved by choosing different arguments, such as global performance, asymmetric performance and semi-global performance(Case 1-3 in Remark 4), which makes the control algorithm more flexible and the control application easier. A class of prescribed-time performance functions(PTPFs) is constructed to guarantee the unified performance, and the error transformation is introduced to convert the issue of ensuring the unified performance into the stability problem of the error variable. Furthermore, the proposed UPTPC algorithm can ensure that the output tracking error converges to a prescribed steady-state accuracy within a prescribed time, and the settling time is irrelevant to the initial states and system parameters. Meanwhile, the singularity problem can be avoided by the proposed algorithm when the tracking error approaches performance boundaries. Additionally, due to the consideration of input saturation and HONSs, it is difficult to isolate the control input as an independent quantity, which increases the difficulty of control design. To solve this problem, a novel Lyapunov function(LF) is constructed in the final step of the backstepping technique, incorporating the properties of hyperbolic tangent function and the mean value theorem, not only the effect of input saturation is eliminated, but also the closed-loop system is stable. Simulations confirm the validity of the developed control.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107760"},"PeriodicalIF":3.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144255017","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":"Strictly (Q,S,R)-dissipativity and exponential stability for switched systems with a dynamic event-triggered mechanism","authors":"Wenqin Wang ,&nbsp;Wenhui Jia ,&nbsp;Jun Cheng ,&nbsp;Kaibo Shi ,&nbsp;Feng Liu","doi":"10.1016/j.jfranklin.2025.107758","DOIUrl":"10.1016/j.jfranklin.2025.107758","url":null,"abstract":"<div><div>In order to enhance system efficiency and adaptability, this study investigates switched nonlinear systems with time-varying delay via a novel dynamic event-triggering mechanism incorporating a state-dependent threshold. With the goal to achieve strictly <span><math><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></math></span>-dissipativity and exponential stability, a minimum LKF switching rule and a combination of multiple Lyapunov function approaches are adopted. The LKF contains not only the information of states and their derivatives, but also the related single integral and double integral information. Besides, to decouple coupling terms in the controller gain matrix, a more simple method is employed by introduced an additional external matrix, rather than the left–right multiplication approach used in the traditional way. Lastly, the numerical examples verify the efficacy of the suggested approaches.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107758"},"PeriodicalIF":3.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270492","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":"Control and maximum power extraction of a switched reluctance generator with low resolution pulse-based position estimation","authors":"Zeineb Touati ,&nbsp;Giacomo Moretti ,&nbsp;Adel Khedher ,&nbsp;Luca Zaccarian","doi":"10.1016/j.jfranklin.2025.107757","DOIUrl":"10.1016/j.jfranklin.2025.107757","url":null,"abstract":"<div><div>This paper presents a control approach for switched reluctance generators (SRGs), based on single-pulse-per-revolution position sensors (e.g., Hall-effect sensors or single pulse encoders, as opposed to high-resolution encoders). The framework comprises a multi-level control architecture, based on the assumption of a single-pulse SRG control mode, which adjusts the generator firing angles to pursue control of the average speed (measured once per cycle) and maximization of the power yield via an extremum seeking approach.</div><div>To consistently formulate the control law in terms of the cyclic average speed, we use a recasting of the SRG dynamic equations via the hybrid dynamical formalism. We then assess the performance of the proposed control scheme in simulation, using a traditional four-phase 8/6 SRG as a target for the investigation. The simulation results demonstrate the effectiveness of the proposed control approach, even in complex scenarios in which the SRG is coupled with a small-scale wind turbine operating in realistic wind conditions.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107757"},"PeriodicalIF":3.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280843","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":"Generalized negative imaginary synthesis for attitude stabilization of flexible satellites with negative imaginary uncertainty","authors":"Zhining Cheng ,&nbsp;Fanwei Meng ,&nbsp;Zhen He ,&nbsp;Jiaxiang Xie","doi":"10.1016/j.jfranklin.2025.107759","DOIUrl":"10.1016/j.jfranklin.2025.107759","url":null,"abstract":"<div><div>This paper studies the attitude control of a class of flexible satellites with negative imaginary (NI) uncertainty and proposes a new NI synthesis method for linear time invariant (LTI) system with two poles at the origin. Firstly, a dynamic parallel feedforward compensator is added to the controlled plant, which ensures that the augmented system exhibits negative imaginary property. Furthermore, a set of linear matrix inequalities (LMIs) conditions are derived, leading to easy application of this scheme. Secondly, a nonlinear numerical optimization method is adopted to design a set of strictly negative imaginary (SNI) controllers. An integral resonant controller is designed with internal stability and the worst-case <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> norm of the closed-loop system minimized. Finally, a two-body flexible satellite simulation experiment is carried out to verify the effectiveness of the proposed method. The results show that the robust stability of the scheme is significantly better than that of the traditional robust control scheme in the case of parameter perturbation or unmodeled dynamics.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107759"},"PeriodicalIF":3.7,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144243147","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 novel quaternion optimization model for imagined speech classification","authors":"Xiao-Ben Zheng ,&nbsp;Bingo Wing-Kuen Ling ,&nbsp;Nuo Xu ,&nbsp;Jian-Rong Chen ,&nbsp;Song-Yi Zheng","doi":"10.1016/j.jfranklin.2025.107789","DOIUrl":"10.1016/j.jfranklin.2025.107789","url":null,"abstract":"<div><div>Imagined speech, characterized by its extensive vocabulary and diverse applications, is a highly promising paradigm in BCI. Multi-channel EEGs are utilized for imagined speech classification. While low rank and sparse representation (LRSR) models have proven useful for EEG processing, they overlook the inter-channel correlations, leading to potential information loss. To address this issue, this paper proposes a quaternion valued LRSR (QLRSR) model for processing the EEGs. Quaternion algebra is a hypercomplex number system extending complex numbers with one real component and three orthogonal imaginary units(i,j,k). Since quaternion can excavate the potential connection of multi-dimensional signals, it is adopted in our QLRSR algorithm for processing muti-channel EEGs. The proposed QLRSR model for imagined speech classification involves two key steps. First, it models sampling points in four-channel EEGs as quaternion-valued numbers, exploiting cross-channel correlations during quaternion operations. Second, the model formulates the QLRSR problem as a quaternion-valued optimization problem. To validate the model's effectiveness, two public datasets are used: Track 3 of the BCI Competition 2020 and the Kara One dataset. By finding the solution of the quaternion valued optimization problem, it is found that the average classification accuracies of our proposed QLRSR model are 64.05 % and 75.46 %, which is higher than the existing models including low rank, sparse, LRSR-based model. Also, the required computational time for performing the classification of the imagined speech via our proposed QLRSR model is 5.12-17.33 % lower than of the aforementioned models. Since QLRSR integrates quaternion algebra into the LRSR-based method, which is more suitable for processing muti-channel signal than LRSR-based method. Hence, our proposed QLRSR model is efficient. Our work in the QLRSR is helpful for the researchers who work on finding a mathematical solution of the quaternion optimization problem. Furthermore, our proposed QLRSR model provides new directions and ideas for BCI and medical rehabilitation field.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107789"},"PeriodicalIF":3.7,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263603","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":"Response performance and stability analysis of fixed-wing airplane by improved control technique","authors":"Bowen Su ,&nbsp;Xiaoping Chen ,&nbsp;Yuehong Dai","doi":"10.1016/j.jfranklin.2025.107756","DOIUrl":"10.1016/j.jfranklin.2025.107756","url":null,"abstract":"<div><div>This paper researches response performance increment of a nonlinear fixed-wing airplane(FWA) system by refining stability, fastness and accuracy of state trajectory. Firstly, the airplane models are established in horizontal and longitudinal directions, with the corresponding linearization model proposed to accommodate control design. To increase stability and reduce input cost, Riccati equation based optimal control algorithm is proposed, which seeks the optimal parameters recursively by minimizing the objective function, and Lyapunov function is employed in the stability discussion to show the optimality. Then based on linear matrix inequalities(LMI) technique and eigenvalues assignment, the minimum eigenvalue problem to regulate damping ratio and natural frequency of the system is established, which improves the fastness in system evolving. Furthermore, augmented control system is applied and proven to increment steady accuracy, associated with potential overshoot and divergence in high-order perturbations. Finally, the designed control laws are tested in nonlinear model system by simulation.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 11","pages":"Article 107756"},"PeriodicalIF":3.7,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263604","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}