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

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Adaptive event-triggered secure control for IT2 fuzzy systems vulnerable to hybrid attacks and its application 易受混合攻击的 IT2 模糊系统的自适应事件触发安全控制及其应用
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-11-02 DOI: 10.1016/j.jfranklin.2024.107365
M. Mubeen Tajudeen , M. Syed Ali , R. Perumal , Tarek F. Ibrahim , Faizah D. Alanazi
{"title":"Adaptive event-triggered secure control for IT2 fuzzy systems vulnerable to hybrid attacks and its application","authors":"M. Mubeen Tajudeen ,&nbsp;M. Syed Ali ,&nbsp;R. Perumal ,&nbsp;Tarek F. Ibrahim ,&nbsp;Faizah D. Alanazi","doi":"10.1016/j.jfranklin.2024.107365","DOIUrl":"10.1016/j.jfranklin.2024.107365","url":null,"abstract":"<div><div>This work addresses the adaptive event-triggered control issue that interval type-2 (IT2) fuzzy systems are vulnerable to hybrid attacks. They were initially developed for fuzzy systems by thoroughly addressing the characteristics of hybrid attacks, which include deception attacks and replay attacks. Our main goal is to mitigate the effects of hybrid attacks and protect communication resources by developing an event-triggered controller for IT2 fuzzy systems with adjustable thresholds. The proposed hybrid attacks are described by a stochastic random variable that satisfies the Bernoulli distribution. Based on Lyapunov-Krasvoskii stability theory, the resulting closed-loop IT2 fuzzy system clearly satisfies sufficient criteria to ensure mean square stability. Also, the weight matrices of the trigger condition and controller gain matrices are obtained using LMI techniques. Lastly, a numerical example is provided to illustrate the effectiveness and applicability of the proposed control strategy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107365"},"PeriodicalIF":3.7,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662797","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
Distributed integral controllability for non-square processes: A comprehensive study and numerical analysis 非平方过程的分布式积分可控性:综合研究与数值分析
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-11-02 DOI: 10.1016/j.jfranklin.2024.107338
Steven Weidong Su , Zhihan Zhang , Branko Celler , Andrey Savkin
{"title":"Distributed integral controllability for non-square processes: A comprehensive study and numerical analysis","authors":"Steven Weidong Su ,&nbsp;Zhihan Zhang ,&nbsp;Branko Celler ,&nbsp;Andrey Savkin","doi":"10.1016/j.jfranklin.2024.107338","DOIUrl":"10.1016/j.jfranklin.2024.107338","url":null,"abstract":"<div><div>Distributed control systems offer significant benefits such as enhanced flexibility, improved failure tolerance, and simplified system design compared to centralized systems. While the controllability of linear square systems under decentralized structures incorporating integral action is well-explored, challenges arise when dealing with non-square processes, which are prevalent in various control and optimization scenarios. Traditionally, non-square systems are manipulated into square configurations by adjusting inputs and outputs to apply decentralized integral controllability (DIC) analysis, potentially affecting the system’s reliability and controller flexibility. To address this issue, we propose a direct application of decentralized integral controllability to non-square processes, termed DIC-NSQ. We approach this problem by representing the system through a state space description, transforming it into standard singular perturbation form, and subsequently establishing its necessary as well as sufficient conditions using singular perturbation analysis. Through numerical examples, we demonstrate that DIC-NSQ effectively maintains offset-free tracking and ensures robust performance, even in the presence of actuator failures. This contribution marks an advancement in the field of distributed control systems, particularly for applications involving non-square processes.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107338"},"PeriodicalIF":3.7,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593381","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
Truncated predictive control for delayed cyber–physical systems under deception attacks 欺骗攻击下延迟网络物理系统的截断预测控制
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-31 DOI: 10.1016/j.jfranklin.2024.107361
S. Anusuya , R. Sakthivel , A. Mohammadzadeh , O.M. Kwon
{"title":"Truncated predictive control for delayed cyber–physical systems under deception attacks","authors":"S. Anusuya ,&nbsp;R. Sakthivel ,&nbsp;A. Mohammadzadeh ,&nbsp;O.M. Kwon","doi":"10.1016/j.jfranklin.2024.107361","DOIUrl":"10.1016/j.jfranklin.2024.107361","url":null,"abstract":"<div><div>In this work, the state tracking, input delay prediction, uncertainty and disturbance rejection problems are studied for the delayed cyber–physical systems under uncertainties, nonlinearities and external disturbances in which the addressed model is described by the fuzzy technique. More specifically, such an input-delayed system is linearized through an interval type-2 fuzzy technique accompanied by a parallel distribution compensation method. Further, the presence of constant input delays in the examined system is proficiently compensated with the assistance of a truncated predictor feedback approach. In parallel, the impacts of external disturbances and uncertainties that are occurred in the system are estimated by means of uncertainty and disturbance estimator method in an efficacious way. With the help of this estimated information, an uncertainty and disturbance estimator-based truncated predictive tracking control protocol is formulated to acquire the state tracking results of the underlying system in the presence of external disturbances and uncertainties. Remarkably, in this study, the interval type-2 fuzzy is blended with the designed reference system. Furthermore, the secure tracking control law is designed for the considered system under the random deception attacks. To address the deception attacks, the Bernoulli stochastic distribution is considered in this study. Moreover, the constraints are expressed for computing the truncated predictive feedback control gain matrices. Conclusively, the numerical simulation analysis is carried out to demonstrate the usefulness of the devised approach.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107361"},"PeriodicalIF":3.7,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593910","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
Adaptive fault tolerant control of unmanned underwater glider with predefined-time stability 具有预定时间稳定性的无人水下滑翔机自适应容错控制
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-31 DOI: 10.1016/j.jfranklin.2024.107364
Jiarun Wang, Yimin Chen, Jian Gao, Boxu Min, Guang Pan
{"title":"Adaptive fault tolerant control of unmanned underwater glider with predefined-time stability","authors":"Jiarun Wang,&nbsp;Yimin Chen,&nbsp;Jian Gao,&nbsp;Boxu Min,&nbsp;Guang Pan","doi":"10.1016/j.jfranklin.2024.107364","DOIUrl":"10.1016/j.jfranklin.2024.107364","url":null,"abstract":"<div><div>Actuator faults of the underwater gliders (UGs) not only jeopardize the motion control performance but may also threaten the sailing safety. This paper proposes an adaptive sliding mode fault-tolerant controller with predefined-time stability for the UGs, considering the modeling uncertainties and the unknown disturbances. Three types of actuator faults are developed and incorporated in the fault model of the UGs, which are utilized for the fault tolerant controller design. Then, the adaptive terms are utilized to estimate the modeling uncertainties and the unknown disturbances. An adaptive sliding mode fault tolerant controller is thus designed with the theoretical proof that the global stability can be achieved within a predefined time. The hardware-in-the-loop simulations are conducted to verify the effectiveness of the proposed fault tolerant controller. The simulation results show that the UG can achieve the stability of the pitching attitude under three kinds of actuator fault conditions.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107364"},"PeriodicalIF":3.7,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662828","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
Resilient event-triggered H∞ control for autonomous vehicle under novel important-data-based DoS attack 基于重要数据的新型 DoS 攻击下自动驾驶汽车的弹性事件触发 H∞ 控制
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-30 DOI: 10.1016/j.jfranklin.2024.107358
Jing Wang , Engang Tian , Lei Li , Huwei Chen , Xinxian Xu
{"title":"Resilient event-triggered H∞ control for autonomous vehicle under novel important-data-based DoS attack","authors":"Jing Wang ,&nbsp;Engang Tian ,&nbsp;Lei Li ,&nbsp;Huwei Chen ,&nbsp;Xinxian Xu","doi":"10.1016/j.jfranklin.2024.107358","DOIUrl":"10.1016/j.jfranklin.2024.107358","url":null,"abstract":"<div><div>This paper presents the method of a resilient event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> controller for autonomous vehicles (AVs) to address the emerging threat of important-data-based (IDB) Denial-of-Service (DoS) attack. Specifically, a unique IDB DoS attack strategy from an adversarial perspective is proposed to enhance the attack’s destructiveness. Unlike many mature DoS attack methods, the proposed IDB DoS attack could discern the importance level for the data and selectively launch attacks on crucial information, resulting in more significant damage. Furthermore, a novel resilient event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> control technique is employed to mitigate the impact of the attack and counteract the negative effects produced by the IDB DoS attack. Utilizing the Lyapunov functional method, sufficient conditions are successfully derived to ensure the asymptotical stability of the resulted closed-loop system and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> interference suppression performance. Subsequently, simulation results demonstrate that: (1) the addressed IDB DoS attack method leads to a more severe system degradation, highlighting the potential risks associated with this novel attack approach; and (2) the proposed event-triggered <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> controller effectively mitigates the potential impact of the IDB DoS attack, showcasing its efficiency in preserving system performance under adversarial conditions.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107358"},"PeriodicalIF":3.7,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662791","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
A novel ultra-local model-based finite time synergetic robustness control for uncertain robotic manipulator 基于超局部模型的不确定机器人机械手有限时间协同鲁棒性控制新方法
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-30 DOI: 10.1016/j.jfranklin.2024.107362
Peng Zhang, Hongmei Li, Bin Chen, Jinwei Wang, Hengguo Zhang
{"title":"A novel ultra-local model-based finite time synergetic robustness control for uncertain robotic manipulator","authors":"Peng Zhang,&nbsp;Hongmei Li,&nbsp;Bin Chen,&nbsp;Jinwei Wang,&nbsp;Hengguo Zhang","doi":"10.1016/j.jfranklin.2024.107362","DOIUrl":"10.1016/j.jfranklin.2024.107362","url":null,"abstract":"<div><div>A novel ultra-local model-based finite time synergetic robustness control (FSRC) is developed to ensure the tracking accuracy and strong robustness of trajectory tracking for uncertain robotic manipulator. The ultra-local model is first established for the uncertain robotic manipulator, with algebraic method which is used to estimate the uncertain part in real time. Then the manifold with finite time convergence and finite time dynamic evolution equation (DEE) are proposed to achieve the FSRC controller of uncertain robotic manipulator. Moreover, the Lyapunov functions are designed and used to verify that the proposed control can achieve the stable operation of uncertain robotic manipulator, furthermore, the explicit expression of the convergence time of uncertain robotic manipulator trajectory tracking control is derived. Finally, it was demonstrated through physical simulation experiments that the proposed control can achieve the fast and accurate robust control of trajectory tracking for uncertain robotic manipulator.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"361 18","pages":"Article 107362"},"PeriodicalIF":3.7,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587362","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
Adaptive active disturbance rejection control for velocity tracking trajectory tasks 速度跟踪轨迹任务的自适应主动干扰抑制控制
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-30 DOI: 10.1016/j.jfranklin.2024.107344
Luis Luna , Erick Asiain , Rubén Garrido
{"title":"Adaptive active disturbance rejection control for velocity tracking trajectory tasks","authors":"Luis Luna ,&nbsp;Erick Asiain ,&nbsp;Rubén Garrido","doi":"10.1016/j.jfranklin.2024.107344","DOIUrl":"10.1016/j.jfranklin.2024.107344","url":null,"abstract":"<div><div>This work reports a Proportional plus Adaptive Desired Disturbance Observer (P+ADDOB) controller for a perturbed servo system aimed to track time-varying references. The controller is composed of three parts. The first part is an adaptive feedforward term, the second part corresponds to a proportional action, and a term aimed to compensate the disturbances affecting the closed-loop system corresponds to the third part. The structure of the ADDOB is inspired in the Ohnishi Disturbance Observer, however, instead resorting on measurements of the velocity and acceleration, the ADDOB employs their desired values thus reducing the impact of measurement noise in the closed loop system. The ADDOB is computed using the servo system parameter estimates obtained by means of a gradient algorithm endowed with a parameter projection mechanism. A stability analysis allows concluding boundedness of all the closed-loop signals. Real-time experiments assess the effectiveness of the proposed controller.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"361 18","pages":"Article 107344"},"PeriodicalIF":3.7,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593272","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
Covert attack detection and secure control based on signal generator 基于信号发生器的隐蔽攻击检测和安全控制
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-29 DOI: 10.1016/j.jfranklin.2024.107323
Xianghua Wang , Ali Zolghadri , Changqing Wang
{"title":"Covert attack detection and secure control based on signal generator","authors":"Xianghua Wang ,&nbsp;Ali Zolghadri ,&nbsp;Changqing Wang","doi":"10.1016/j.jfranklin.2024.107323","DOIUrl":"10.1016/j.jfranklin.2024.107323","url":null,"abstract":"<div><div>The problem addressed in this paper is the monitoring and secure control in cyber–physical-systems subject to covert attacks. To reveal the covert attacks, an attack detection scheme by constructing signal generators in both cyber-layer and physical-layer is proposed. Different from the watermarking scheme, the dynamics of proposed signal generators are linear time invariant; also different from the moving target-based method, the proposed scheme does not need to rapidly alter the system dynamics. Moreover, the design parameter of signal generators can be chosen appropriately to guarantee the output tracking performance after the occurrence of attacks and before their detection. After the attack has been detected, the nominal output feedback controller is switched into a secure controller based on adaptive observer to ensure an output tracking performance level. Finally, numerical simulations are provided to show the effectiveness of the proposed scheme.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"361 18","pages":"Article 107323"},"PeriodicalIF":3.7,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573495","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
Prescribed-time formation-containment control and collision avoidance for second-order multi-agent systems 二阶多代理系统的规定时间编队控制和避免碰撞
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-29 DOI: 10.1016/j.jfranklin.2024.107354
Chengmei Tang , Lianghao Ji , Xiaofeng Qu , Huaqing Li
{"title":"Prescribed-time formation-containment control and collision avoidance for second-order multi-agent systems","authors":"Chengmei Tang ,&nbsp;Lianghao Ji ,&nbsp;Xiaofeng Qu ,&nbsp;Huaqing Li","doi":"10.1016/j.jfranklin.2024.107354","DOIUrl":"10.1016/j.jfranklin.2024.107354","url":null,"abstract":"<div><div>This paper studies prescribed-time formation-containment control (FCC) of a second-order multi-agent systems (MASs) in an environment with obstacles. When there is no continuous communication between leaders or followers, the new segmented triggering conditions are designed based on prescribed-time and a novel event-triggered protocol is raised. Meanwhile, a theoretical exploration using Lyapunov’s theorem is carried out to verify that proposed control protocol can achieve prescribed-time FCC convergence within the range of parameter allowable values. Through further theoretical analysis, Zeno behavior is excluded throughout the time span except <span><math><mi>T</mi></math></span>. Furthermore, to avoid unknown and moving obstacles in environment, a fresh collision avoidance controller is constructed based on the smooth potential function and speed factor. Finally, effectiveness and feasibility of presented protocol and controller are verified through simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"361 18","pages":"Article 107354"},"PeriodicalIF":3.7,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552974","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
Online adaptive critic designs with tensor product B-splines and incremental model techniques 利用张量积 B-样条和增量模型技术进行在线自适应批判者设计
IF 3.7 3区 计算机科学
Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-29 DOI: 10.1016/j.jfranklin.2024.107357
Yiting Feng , Ye Zhou , Hann Woei Ho , Hongyang Dong , Xiaowei Zhao
{"title":"Online adaptive critic designs with tensor product B-splines and incremental model techniques","authors":"Yiting Feng ,&nbsp;Ye Zhou ,&nbsp;Hann Woei Ho ,&nbsp;Hongyang Dong ,&nbsp;Xiaowei Zhao","doi":"10.1016/j.jfranklin.2024.107357","DOIUrl":"10.1016/j.jfranklin.2024.107357","url":null,"abstract":"<div><div>As an effective optimal control scheme in the field of reinforcement learning, adaptive dynamic programming (ADP) has attracted extensive attention in recent decades. Neural networks (NNs) are commonly employed in ADP algorithms to realize nonlinear function approximation. However, the learning process with NN approximation typically requires a substantial amount of training data and places a heavy computational burden. To improve learning efficiency and alleviate computational load, this paper develops a novel model-free ADP approach based on multivariate splines and incremental control techniques, aimed at achieving online learning of nonlinear control. By utilizing input and output data, an incremental linear approximation model is identified online without any prior knowledge of system dynamics. To improve nonlinear approximation capabilities and lessen computational demands, tensor product B-splines, instead of NNs, are integrated into the critic module to approximate the value function, and the recursive least squares temporal difference (RLS-TD) algorithm is employed to update the weights of spline bases. Convergence analysis of the proposed control scheme is conducted based on the dual-timescale stochastic approximation theory. To illustrate the effectiveness and feasibility of the proposed control scheme, numerical simulations are performed in solving the online nonlinear control problem within the context of the inverted pendulum system.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"361 18","pages":"Article 107357"},"PeriodicalIF":3.7,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573496","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
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