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Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer 被引量:1
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作者 Chi Ma Dianbiao Dong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期1039-1050,共12页
This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eli... This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm. 展开更多
关键词 Finite-time control multi-agent systems neural network prescribed performance control time-varying formation control
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Quantization and Event-Triggered Policy Design for Encrypted Networked Control
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作者 Yongxia Shi Ehsan Nekouei 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期946-955,共10页
This paper proposes a novel event-driven encrypted control framework for linear networked control systems(NCSs),which relies on two modified uniform quantization policies,the Paillier cryptosystem,and an event-trigger... This paper proposes a novel event-driven encrypted control framework for linear networked control systems(NCSs),which relies on two modified uniform quantization policies,the Paillier cryptosystem,and an event-triggered strategy.Due to the fact that only integers can work in the Pailler cryptosystem,both the real-valued control gain and system state need to be first quantized before encryption.This is dramatically different from the existing quantized control methods,where only the quantization of a single value,e.g.,the control input or the system state,is considered.To handle this issue,static and dynamic quantization policies are presented,which achieve the desired integer conversions and guarantee asymptotic convergence of the quantized system state to the equilibrium.Then,the quantized system state is encrypted and sent to the controller when the triggering condition,specified by a state-based event-triggered strategy,is satisfied.By doing so,not only the security and confidentiality of data transmitted over the communication network are protected,but also the ciphertext expansion phenomenon can be relieved.Additionally,by tactfully designing the quantization sensitivities and triggering error,the proposed event-driven encrypted control framework ensures the asymptotic stability of the overall closedloop system.Finally,a simulation example of the secure motion control for an inverted pendulum cart system is presented to evaluate the effectiveness of the theoretical results. 展开更多
关键词 Cyber-security encrypted control event-triggered control(ETC) networked control systems(ncss) semi-homomorphic encryption
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Deep Learning Social Network Access Control Model Based on User Preferences
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作者 Fangfang Shan Fuyang Li +3 位作者 Zhenyu Wang Peiyu Ji Mengyi Wang Huifang Sun 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期1029-1044,共16页
A deep learning access controlmodel based on user preferences is proposed to address the issue of personal privacy leakage in social networks.Firstly,socialusers andsocialdata entities are extractedfromthe social netw... A deep learning access controlmodel based on user preferences is proposed to address the issue of personal privacy leakage in social networks.Firstly,socialusers andsocialdata entities are extractedfromthe social networkandused to construct homogeneous and heterogeneous graphs.Secondly,a graph neural networkmodel is designed based on user daily social behavior and daily social data to simulate the dissemination and changes of user social preferences and user personal preferences in the social network.Then,high-order neighbor nodes,hidden neighbor nodes,displayed neighbor nodes,and social data nodes are used to update user nodes to expand the depth and breadth of user preferences.Finally,a multi-layer attention network is used to classify user nodes in the homogeneous graph into two classes:allow access and deny access.The fine-grained access control problem in social networks is transformed into a node classification problem in a graph neural network.The model is validated using a dataset and compared with other methods without losing generality.The model improved accuracy by 2.18%compared to the baseline method GraphSAGE,and improved F1 score by 1.45%compared to the baseline method,verifying the effectiveness of the model. 展开更多
关键词 Graph neural networks user preferences access control social network
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H-infinity control for networked control systems (NCS) with time-varying delays 被引量:4
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作者 Hong ZHAO Min WU +1 位作者 Guoping LIU Jinhua SHE 《控制理论与应用(英文版)》 EI 2005年第2期157-162,共6页
This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the flee-weighing matrix method, a dehy-dependent stability criterion satisfying a prescribed H-... This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the flee-weighing matrix method, a dehy-dependent stability criterion satisfying a prescribed H-infinity norm bound is presented for an NCS with unknown, time-varying and bounded delays. And then, the criterion is transformed into sufficient conditions based on linear matrix inequalities for H-infinity control. The conditions thus obtained are also used to design an H-infinity state feedback controller. This design method is further extended to solve the design problem of robust H-infinity state feedback control. A numerical example demonstrates the validity of the method. 展开更多
关键词 H-infinity control networked control system (ncs Time-varying delay State feedback Linear matrix inequality(LMI) Robust control
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Optimal bandwidth scheduling of networked control systems (NCSs) in accordance with jitter 被引量:3
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作者 白涛 吴智铭 杨根科 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第6期535-542,共8页
Network-induced delay and jitter are key factors causing performance degradation and instability of NCSs (networked control systems). The relationships between the sampling periods of the control loops, network-induce... Network-induced delay and jitter are key factors causing performance degradation and instability of NCSs (networked control systems). The relationships between the sampling periods of the control loops, network-induced delay and jitter were studied aimed at token-type networks. A jitter-dependent optimal bandwidth scheduling algorithm for NCSs is proposed, which tries to achieve a tradeoff between bandwidth occupancy and system performance. Simulation tests proved the effectiveness of this optimal scheduling algorithm. 展开更多
关键词 ncss (networked control systems) network-induced delay JITTER DEADLINE Loop delay
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ADAPTIVE PREDICTIVE CONTROL OF NEAR-SPACE VEHICLE USING FUNCTIONAL LINK NETWORK 被引量:3
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作者 都延丽 吴庆宪 姜长生 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2010年第2期148-154,共7页
A novel nonlinear adaptive control method is presented for a near-space hypersonic vehicle (NHV) in the presence of strong uncertainties and disturbances. The control law consists of the optimal generalized predicti... A novel nonlinear adaptive control method is presented for a near-space hypersonic vehicle (NHV) in the presence of strong uncertainties and disturbances. The control law consists of the optimal generalized predictive controller (OGPC) and the functional link network (FLN) direct adaptive law. OGPC is a continuous-time nonlinear predictive control law. The FLN adaptive law is used to offset the unknown uncertainties and disturbances in a flight through the online learning. The learning process does not need any offline training phase. The stability analyses of the NHV close-loop system are provided and it is proved that the system error and the weight learning error are uniformly ultimately hounded. Simulation results show the satisfactory performance of the con- troller for the attitude tracking. 展开更多
关键词 predictive control systems adaptive control systems UncERTAINTY functional link network near-space vehicle
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Adaptive and distance-driven power control scheme in mobile ad hoc networks
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作者 陶军 刘莹 +2 位作者 肖鹏 朱利旻 陈文强 《Journal of Southeast University(English Edition)》 EI CAS 2013年第3期252-258,共7页
In order to save the energy and reduce the latency of the end-to-end transmission in mobile ad hoc networks an adaptive and distance-driven power control ADPC scheme is proposed by means of distance research in random... In order to save the energy and reduce the latency of the end-to-end transmission in mobile ad hoc networks an adaptive and distance-driven power control ADPC scheme is proposed by means of distance research in random geometrics. Through mathematical proof the optimal number of relay nodes and the optimal location of each node for data transmission can be obtained when a distance is given.In the ADPC first the source node computes the optimal number and the sites of the relay nodes between the source and the destination nodes.Then it searches feasible relay nodes around the optimal virtual relay-sites and selects one link with the minimal total transmission energy consumption for data transmission.Simulation results show that the ADPC can reduce both the energy dissipation and the end-to-end latency of the transmission. 展开更多
关键词 power control mobile ad hoc networks energyefficient route optimal virtual relay-site
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Time-stamped predictive functional control for networked control systems with random delays
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作者 张奇智 张卫东 《Journal of Southeast University(English Edition)》 EI CAS 2005年第2期149-152,共4页
The random delays in a networked control system (NCS) degrade control performance and can even destabilize the control system.To deal with this problem,the time-stamped predictive functional control (PFC) algorithm is... The random delays in a networked control system (NCS) degrade control performance and can even destabilize the control system.To deal with this problem,the time-stamped predictive functional control (PFC) algorithm is proposed,which generalizes the standard PFC algorithm to networked control systems with random delays.The algorithm uses the time-stamp method to estimate the control delay,predicts the future outputs based on a discrete time delay state space model,and drives the control law that applies to an NCS from the idea of a PFC algorithm.A networked control system was constructed based on TrueTime simulator,with which the time-stamped PFC algorithm was compared with the standard PFC algorithm.The response curves show that the proposed algorithm has better control performance. 展开更多
关键词 networked control systems random delays predictive functional control industrial Ethernet
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Study on the network delay of periodic information in the NCS based on EPA
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作者 刘宁 《High Technology Letters》 EI CAS 2009年第4期349-355,共7页
The network delay of the periodic messages transmission in the network control system (NCS) based on Ethemet for plant automation (EPA) is analyzed from the theoretical and experimental perspective in this paper. ... The network delay of the periodic messages transmission in the network control system (NCS) based on Ethemet for plant automation (EPA) is analyzed from the theoretical and experimental perspective in this paper. The composition and the characteristics of the network delay of EPA periodic messages transmission in a subnet is studied through analyzing the information transmission regularity and EPA deterministic scheduling mechanism. On this basis, the queuing delay at communication schedule management entity (EPA _ CSME) that is the most important component of network delay is analyzed, during which the formulas for the queuing delay of periodic messages and other real time parameters are proposed. Furthermore, an experiment is developed to test each component of network delay of periodic messages transmission in a EPA subnet. According to the experimental and the theoretical analysis, the conclusion is drawn that the delay during which the periodic messages wait for the periodic messages transmission time slice is the main factor that causes considerable network delay, and improvement method is presented. 展开更多
关键词 Ethernet for plant automation (EPA) network control system (ncs periodic rues- sages network delay
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混合整数非线性规划的WNCS鲁棒调度算法
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作者 郑洲 《机械设计与制造》 北大核心 2024年第12期95-103,共9页
为了提升对丢包拓扑和传感器需求变化的鲁棒性,提出了一种基于混合整数非线性规划的无线网络控制系统鲁棒调度算法。首先将仅支持有限传输速率集的离散速率传输模型的调度、功率控制和速率自适应的联合优化问题描述为一个混合整数非线... 为了提升对丢包拓扑和传感器需求变化的鲁棒性,提出了一种基于混合整数非线性规划的无线网络控制系统鲁棒调度算法。首先将仅支持有限传输速率集的离散速率传输模型的调度、功率控制和速率自适应的联合优化问题描述为一个混合整数非线性规划问题,并证明了该问题是NP难的。然后提出一个最佳多项式时间功率控制与速率适配演算法,以最小化节点子集的传输时间。进一步设计了一种多项式时间启发式调度算法从而均匀分布时间节点子集。最后通过仿真证明在满足已知的周期性数据生成传输延迟的前提下,提出方法能够满足能耗要求,并且能够对拓扑和信道变化提供最大的鲁棒性以及传感器节点可靠性。 展开更多
关键词 无线网络控制系统 调度算法 非线性规划 鲁棒性
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Recent Progress in Reinforcement Learning and Adaptive Dynamic Programming for Advanced Control Applications 被引量:4
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作者 Ding Wang Ning Gao +2 位作者 Derong Liu Jinna Li Frank L.Lewis 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第1期18-36,共19页
Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and ... Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence. 展开更多
关键词 Adaptive dynamic programming(ADP) advanced control complex environment data-driven control event-triggered design intelligent control neural networks nonlinear systems optimal control reinforcement learning(RL)
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Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer 被引量:1
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作者 Wenxue Chen Yudong Hu +1 位作者 Changsheng Gao Ruoming An 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第2期412-429,共18页
This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance system... This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots. 展开更多
关键词 BP network neural Integral sliding mode control(ISMC) Missile defense Prescribed performance function(PPF) State observer Tracking guidance system
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D-stability and disturbance attenuation properties fornetworked control systems: switched system approach 被引量:2
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作者 Qiuxia Chen Andong Liu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第5期1108-1114,共7页
Both D-stability and finite L2-gain properties are studiedfor a class of uncertain discrete-time systems with timevaryingnetwork-induced delays. By using coordinate transformand delay partition, the D-stability and H... Both D-stability and finite L2-gain properties are studiedfor a class of uncertain discrete-time systems with timevaryingnetwork-induced delays. By using coordinate transformand delay partition, the D-stability and H∞ performance problemsfor such networked control systems (NCSs) are equivalentlytransferred into the corresponding problems for switching systemswith arbitrary switching. Then, a sufficient condition for the existenceof the robust D-stabilizing controllers is derived in termsof linear matrix inequality (LMI), and the design method is alsopresented for the state feedback controllers which guarantee thatall the closed-loop poles remain inside the specified disk D(α,r)and the desired disturbance attenuation level. Finally, an illustrativeexample is given to demonstrate the effectiveness of the proposedresults. 展开更多
关键词 D-STABILITY networked control system (ncs H∞performance switching system.
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Backstepping sliding mode control for uncertain strict-feedback nonlinear systems using neural-network-based adaptive gain scheduling 被引量:12
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作者 YANG Yueneng YAN Ye 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第3期580-586,共7页
A neural-network-based adaptive gain scheduling backstepping sliding mode control(NNAGS-BSMC) approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain st... A neural-network-based adaptive gain scheduling backstepping sliding mode control(NNAGS-BSMC) approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control(SMC) law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network(RBFNN) is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network(NN), with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC. 展开更多
关键词 backstepping control sliding mode control(SMC) neural network(NN) strict-feedback system chattering decrease
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Adaptive Control Based on Neural Networks for an Uncertain 2-DOF Helicopter System With Input Deadzone and Output Constraints 被引量:15
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作者 Yuncheng Ouyang Lu Dong +1 位作者 Lei Xue Changyin Sun 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第3期807-815,共9页
In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertaintie... In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter. 展开更多
关键词 2-degree of FREEDOM (DOF) helicopter adaptive control INPUT DEADZONE integral barrier Lyapunov function neural networks output constraints
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Analysis of PROFIBUS-DP Network Delay and Its Influence on the Performance of Control Systems 被引量:5
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作者 TAO Jun WANG Zhan-lin 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第5期877-882,共6页
This paper analyzes PROFIBUS-DP network delay in detail and presents the calculational formula of its maximum time-delay, which is significant to the research of PROFIBUS-DP. At the same time, the paper puts forward a... This paper analyzes PROFIBUS-DP network delay in detail and presents the calculational formula of its maximum time-delay, which is significant to the research of PROFIBUS-DP. At the same time, the paper puts forward a method of simplifying the network induced time-varying indeterminate system according to the features of the network. Through the analysis of a pump-control-motor system which is composed of PROFIBUS-DP network, it illustrates the network's influence on the performance of control systems. This method helps to design and analyze the network's influence on the performance of control systems, which is of considerable practical value in a time when network control systern is widely used. 展开更多
关键词 network delay analysis network control system deterministic control
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Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions 被引量:5
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作者 邹艳丽 陈关荣 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第8期3337-3346,共10页
This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the contro... This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N+1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value. 展开更多
关键词 SYncHRONIZATION pinning control complex network synchronized region
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Application of neural networks for permanent magnet synchronous motor direct torque control 被引量:6
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作者 Zhang Chunmei Liu Heping +1 位作者 Chen Shujin Wang Fangjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第3期555-561,共7页
Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training a... Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. The application of neural networks to control interior permanent magnet synchronous motor using direct torque control (DTC) is discussed. A neural network is used to emulate the state selector of the DTC. The neural networks used are the back-propagation and radial basis function. To reduce the training patterns and increase the execution speed of the training process, the inputs of switching table are converted to digital signals, i.e., one bit represent the flux error, one bit the torque error, and three bits the region of stator flux. Computer simulations of the motor and neural-network system using the two approaches are presented and compared. Discussions about the back-propagation and radial basis function as the most promising training techniques are presented, giving its advantages and disadvantages. The system using back-propagation and radial basis function networks controller has quick parallel speed and high torque response. 展开更多
关键词 interior permanent magnet synchronous motor radial basis function neural network torque control direct torque control.
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Controlled synchronization of complex network with different kinds of nodes 被引量:4
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作者 Zhengquan YANG Zhongxin LIU Zengqiang CHEN Zhuzhi YUAN 《控制理论与应用(英文版)》 EI 2008年第1期11-15,共5页
In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a ... In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis. 展开更多
关键词 Complex network SYncHRONIZATION Pinning control CHAOS Exponential stable
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Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology 被引量:9
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作者 LIU Qiang FANG Jin-Qing LI Yong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第4期752-758,共7页
The synchronous conditions of two kinds of the small-world (SW) network are studied. The small world topology can affect on dynamical behaviors of the beam transport network (BTN) largely, if the BTN is constructe... The synchronous conditions of two kinds of the small-world (SW) network are studied. The small world topology can affect on dynamical behaviors of the beam transport network (BTN) largely, if the BTN is constructed with the SW topology, the global linear coupling and special linear feedback can realize the synchronization control of beam halo-chaos as well as periodic state in the BTN with the SW topology, respectively. This important result can provide an effective way for the experimental study and the engineering design of the BTN in the high-current accelerator driven radioactive clean nuclear power systems, and may have potential use in prospective applications for halo-chaos secure communication. 展开更多
关键词 beam halo-chaos synchronization control small-world network beam transport network global linear coupling special linear feedback
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