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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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Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances 被引量:2
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作者 Maojiao Ye Danhu Li +1 位作者 Qing-Long Han Lei Ding 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第2期376-387,共12页
This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for ... This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB. 展开更多
关键词 Distributed networks disturbance rejection Nash equilibrium networked games
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Tracking Control of Multi-Agent Systems Using a Networked Predictive PID Tracking Scheme 被引量:1
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作者 Guo-Ping Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第1期216-225,共10页
With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper stu... With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper studies the tracking control problem of networked multi-agent systems with communication constraints,where each agent has no information on the dynamics of other agents except their outputs.A networked predictive proportional integral derivative(PPID)tracking scheme is proposed to achieve the desired tracking performance,compensate actively for communication delays,and simplify implementation in a distributed manner.This scheme combines the past,present and predictive information of neighbour agents to form a tracking error signal for each agent,and applies the proportional,integral,and derivative of the agent tracking error signal to control each individual agent.The criteria of the stability and output tracking consensus of multi-agent systems with the networked PPID tracking scheme are derived through detailed analysis on the closed-loop systems.The effectiveness of the networked PPID tracking scheme is illustrated via an example. 展开更多
关键词 Coordinative tracking control networked multiagent systems PID control predictive control
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Consensus of networked control multi-agent systems using a double-layer encryption scheme
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作者 Yamin Yan Zhiyong Chen Vijay Varadharajan 《Journal of Automation and Intelligence》 2023年第4期218-226,共9页
This paper addresses the decentralized consensus problem for a system of multiple dynamic agents with remote controllers via networking,known as a networked control multi-agent system(NCMAS).It presents a challenging ... This paper addresses the decentralized consensus problem for a system of multiple dynamic agents with remote controllers via networking,known as a networked control multi-agent system(NCMAS).It presents a challenging scenario where partial dynamic entities or remote control units are vulnerable to disclosure attacks,making them potentially malicious.To tackle this issue,we propose a secure decentralized control design approach employing a double-layer cryptographic strategy.This approach not only ensures that the input and output information of the benign entities remains protected from the malicious entities but also practically achieves consensus performance.The paper provides an explicit design,supported by theoretical proof and numerical verification,covering stability,steady-state error,and the prevention of computation overflow or underflow. 展开更多
关键词 Multi-agent systems networked control Cyberphysical security ENCRYPTION CONSENSUS
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A Looped Functional Method to Design State Feedback Controllers for Lurie Networked Control Systems
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作者 Wei Wang Hong-Bing Zeng 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第4期1093-1095,共3页
Dear Editor,This letter deals with the stabilization of Lurie networked control systems with network-induced delays(NID).By constructing a twosided looped Lyapunov functional,a sufficient condition is derived to ensur... Dear Editor,This letter deals with the stabilization of Lurie networked control systems with network-induced delays(NID).By constructing a twosided looped Lyapunov functional,a sufficient condition is derived to ensure the absolute stability of the resultant closed-loop system under a state feedback controller.Then,based on this condition,a cone complementary linearisation(CCL)iterative algorithm is presented to design state feedback controller.It is shown via a numerical example that the proposed method can deliver less conservative results as well as fewer iterations if compared with existing ones. 展开更多
关键词 NETWORK sided STABILIZATION
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Book Review:The Socially Networked Classroom:Teaching in the New Media Age 被引量:1
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作者 唐艳花 《海外英语》 2011年第4X期132-133,共2页
This book is greatly appreciated for its collection of various innovative activities which could be applied in different levels of technology-savvy classrooms.It is regarded as guidance to show paths for language educ... This book is greatly appreciated for its collection of various innovative activities which could be applied in different levels of technology-savvy classrooms.It is regarded as guidance to show paths for language educators to teach in digital age,although most of the teachers today are digital immigrants who "have become fascinated by and adopted many,or most aspects of the new technology are,and always will be compared to them"(Prensky,2001).They have to attempt to equip themselves with the knowledge of new media,which aims to provide the current students with their needs to become fully literate in this digital age.However,when the Internet began to arrive in schools,it was embraced by educators already seasoned in the challenges of change. 展开更多
关键词 BOOK review TEACHING socially networked CLASSROOM
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A Dual-Channel Secure Transmission Scheme for Internet-Based Networked Control Systems
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作者 田德振 戴亚平 +1 位作者 胡敬炉 平泽宏太郎 《Journal of Beijing Institute of Technology》 EI CAS 2010年第2期183-190,共8页
Two significant issues in Internet-based networked control systems (INCSs),transport performance of different protocols and security breach from Internet side,are investigated. First,for improving the performance of d... Two significant issues in Internet-based networked control systems (INCSs),transport performance of different protocols and security breach from Internet side,are investigated. First,for improving the performance of data transmission,user datagram protocol (UDP) is adopted as the main stand for controllers and plants using INCSs. Second,a dual-channel secure transmission scheme (DCSTS)based on data transmission characteristics of INCSs is proposed,in which a raw UDP channel and a secure TCP (transmission control protocol) connection making use of SSL/TLS (secure sockets layer/transport layer security) are included. Further,a networked control protocol (NCP) at application layer for supporting DCSTS between the controllers and plants in INCSs is designed,and it also aims at providing a universal communication mechanism for interoperability of devices among the networked control laboratories in Beijing Institute of Technology of China,Central South University of China and Tokyo University of Technology of Japan. By means of a networked single-degree-of-freedom robot arm,an INCS under the new protocol and security environment is created. Compared with systems such as IPSec or SSL/TLS,which may cause more than 91% network throughput deduction,the new DCSTS protocol may yield results ten times better,being just 5.67%. 展开更多
关键词 Internet-based networked control system (INCS) networked control protocol(NCP) dual-channel secure transmission scheme(DCSTS)
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Modeling Delay and Packet Drop in Networked Control Systems Using Network Simulator NS2 被引量:9
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作者 Mohammad Shahidul Hasan Christopher Harding Alison Griffiths 《International Journal of Automation and computing》 EI 2005年第2期187-194,共8页
Wireless Networked Control Systems (WNCS) are used to implement a control mechanism over a wireless network that is capable of carrying real-time traffic. This field has drawn enormous attention from current researche... Wireless Networked Control Systems (WNCS) are used to implement a control mechanism over a wireless network that is capable of carrying real-time traffic. This field has drawn enormous attention from current researchers because of its flexibility and robustness. However, designing efficient WNCS over Mobile Ad Hoc Networks (MANET) is still a challenging topic because of its less-predictable aspects, such as inconsistent delay, packet drop probability, and dynamic topology. This paper presents design guidelines for WNCS over MANET using the Network Simulator version 2, NS2 software. It investigates the impact of packet delay and packet drop under the AODV and DSR routing protocols. The simulation results have been compared to MATLAB results for validation. 展开更多
关键词 ADHOC ON-DEMAND Distance Vector (AODV) ROUTING Dynamic Source ROUTING (DSR) Mobile ADHOC Networks (MANET) Wireless networked Control Systems (WNCS).
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Fault-Tolerant Control Research for Networked Control System under Communication Constraints 被引量:11
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作者 HUO Zhi-Hong FANG Hua-Jing 《自动化学报》 EI CSCD 北大核心 2006年第5期659-666,共8页
Implementing a control system over a communication network induces inevitable time delays that may degrade performance and even cause instability. One of the most effective ways to reduce the negative effect of delays... Implementing a control system over a communication network induces inevitable time delays that may degrade performance and even cause instability. One of the most effective ways to reduce the negative effect of delays on the performance of networked control system (NCS) is to reduce network traffic. In this paper, adjustable deadbands are explored as a solution to reduce network traffic in NCS. A method of fault-tolerant control of networked control system is presented, which takes into account system response as well as network traffic. The integrity design for a kind of NCS with sensor failures and actuator failures is analyzed based on robust fault-tolerant control theory and information scheduling. After detailed theoretical analysis, the paper also provides the simulation results, which further validate the proposed scheme. 展开更多
关键词 networked control system (NCS) deadbands fault-tolerant control (FTC) integrity design time delay
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Networked Control Systems:A Survey of Trends and Techniques 被引量:25
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作者 Xian-Ming Zhang Qing-Long Han +4 位作者 Xiaohua Ge Derui Ding Lei Ding Dong Yue Chen Peng 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2020年第1期1-17,共17页
Networked control systems are spatially distributed systems in which the communication between sensors, actuators,and controllers occurs through a shared band-limited digital communication network. Several advantages ... Networked control systems are spatially distributed systems in which the communication between sensors, actuators,and controllers occurs through a shared band-limited digital communication network. Several advantages of the network architectures include reduced system wiring, plug and play devices,increased system agility, and ease of system diagnosis and maintenance. Consequently, networked control is the current trend for industrial automation and has ever-increasing applications in a wide range of areas, such as smart grids, manufacturing systems,process control, automobiles, automated highway systems, and unmanned aerial vehicles. The modelling, analysis, and control of networked control systems have received considerable attention in the last two decades. The ‘control over networks’ is one of the key research directions for networked control systems. This paper aims at presenting a survey of trends and techniques in networked control systems from the perspective of ‘control over networks’, providing a snapshot of five control issues: sampled-data control, quantization control, networked control, event-triggered control, and security control. Some challenging issues are suggested to direct the future research. 展开更多
关键词 Index Terms—Event-triggered control networked control systems quantization control sampled-data control security control
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Feedback Scheduling of Model-based Networked Control Systems with Flexible Workload 被引量:4
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作者 Xian-Ming Tang~* Jin-Shou Yu Research Institute of Automation, East China University of Science and Technology, Shanghai 200237, PRC 《International Journal of Automation and computing》 EI 2008年第4期389-394,共6页
In this paper, a novel control structure called feedback scheduling of model-based networked control systems is proposed to cope with a flexible network load and resource constraints. The state update time is adjusted... In this paper, a novel control structure called feedback scheduling of model-based networked control systems is proposed to cope with a flexible network load and resource constraints. The state update time is adjusted according to the real-time network congestion situation. State observer is used under the situation where the state of the controlled plant could not be acquired. The stability criterion of the proposed structure is proved with time-varying state update time. On the basis of the stability of the novel system structure, the compromise between the control performance and the network utilization is realized by using feedback scheduler.Examples are provided to show the advantage of the proposed control structure. 展开更多
关键词 MODEL-BASED networked control system state UPDATE time stability CRITERION FEEDBACK scheduling.
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A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays 被引量:7
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作者 Guodong Zhao Yuzhen Wang Haitao Li 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第4期818-826,共9页
Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic ex... Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results. 展开更多
关键词 Fictitious play process Nash equilibrium networked evolutionary games(NEGs) semi-tensor product of matrices
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Fault detection for networked systems subject to access constraints and packet dropouts 被引量:3
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作者 Xiongbo Wan Huajing Fang Sheng Fu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第1期127-134,共8页
This paper addresses the problem of fault detection(FD) for networked systems with access constraints and packet dropouts.Two independent Markov chains are used to describe the sequences of channels which are availabl... This paper addresses the problem of fault detection(FD) for networked systems with access constraints and packet dropouts.Two independent Markov chains are used to describe the sequences of channels which are available for communication at an instant and the packet dropout process,respectively.Performance indexes H∞ and H_ are introduced to describe the robustness of residual against external disturbances and sensitivity of residual to faults,respectively.By using a mode-dependent fault detection filter(FDF) as residual generator,the addressed FD problem is converted into an auxiliary filter design problem with the above index constraints.A sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities(LMIs).When these LMIs are feasible,the explicit expression of the desired FDF can also be characterized.A numerical example is exploited to show the usefulness of the proposed results. 展开更多
关键词 fault detection(FD) networked control system(NCS) access constraints packet dropouts linear matrix inequality(LMI).
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An Optimal Hybrid Learning Approach for Attack Detection in Linear Networked Control Systems 被引量:2
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作者 Haifeng Niu Avimanyu Sahoo +1 位作者 Chandreyee Bhowmick S·Jagannathan 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第6期1404-1416,共13页
A novel learning-based attack detection and estimation scheme is proposed for linear networked control systems(NCS),wherein the attacks on the communication network in the feedback loop are expected to increase networ... A novel learning-based attack detection and estimation scheme is proposed for linear networked control systems(NCS),wherein the attacks on the communication network in the feedback loop are expected to increase network induced delays and packet losses,thus changing the physical system dynamics.First,the network traffic flow is modeled as a linear system with uncertain state matrix and an optimal Q-learning based control scheme over finite-horizon is utilized to stabilize the flow.Next,an adaptive observer is proposed to generate the detection residual,which is subsequently used to determine the onset of an attack when it exceeds a predefined threshold,followed by an estimation scheme for the signal injected by the attacker.A stochastic linear system after incorporating network-induced random delays and packet losses is considered as the uncertain physical system dynamics.The attack detection scheme at the physical system uses the magnitude of the state vector to detect attacks both on the sensor and the actuator.The maximum tolerable delay that the physical system can tolerate due to networked induced delays and packet losses is also derived.Simulations have been performed to demonstrate the effectiveness of the proposed schemes. 展开更多
关键词 ATTACK detection ATTACK estimation event-triggered CONTROL Lyapunov stability networked CONTROL system(NCS) OPTIMAL CONTROL Q-LEARNING
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Programmable Adaptive Security Scanning for Networked Microgrids 被引量:2
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作者 Zimin Jiang Zefan Tang +1 位作者 Peng Zhang Yanyuan Qin 《Engineering》 SCIE EI 2021年第8期1087-1100,共14页
Communication-dependent and software-based distributed energy resources(DERs)are extensively integrated into modern microgrids,providing extensive benefits such as increased distributed controllability,scalability,and... Communication-dependent and software-based distributed energy resources(DERs)are extensively integrated into modern microgrids,providing extensive benefits such as increased distributed controllability,scalability,and observability.However,malicious cyber-attackers can exploit various potential vulnerabilities.In this study,a programmable adaptive security scanning(PASS)approach is presented to protect DER inverters against various power-bot attacks.Specifically,three different types of attacks,namely controller manipulation,replay,and injection attacks,are considered.This approach employs both software-defined networking technique and a novel coordinated detection method capable of enabling programmable and scalable networked microgrids(NMs)in an ultra-resilient,time-saving,and autonomous manner.The coordinated detection method efficiently identifies the location and type of power-bot attacks without disrupting normal NM operations.Extensive simulation results validate the efficacy and practicality of the PASS for securing NMs. 展开更多
关键词 networked microgrids Programmable adaptive security scanning Coordinated detection Software defined networking
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Scheduling and control co-design for Networked Wind Energy Conversion Systems 被引量:3
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作者 Zhihong Huo Zhixue Zhang 《Global Energy Interconnection》 2019年第4期328-335,共8页
Fieldbus, industrial Ethernet that is simple, reliable, economical, and practical, is widely used in Wind Energy Conversion Systems(WECSs). These techniques belong to the field of networked control systems. Network em... Fieldbus, industrial Ethernet that is simple, reliable, economical, and practical, is widely used in Wind Energy Conversion Systems(WECSs). These techniques belong to the field of networked control systems. Network embedding to Wind Energy Conversion Systems brings many new challenges. Implementing a control system over a communication network causes inevitable time delays that may degrade performance and can even cause instability. This work addresses challenges related to the reliable control of wind energy conversion systems, based on the theoretical framework of networked control systems. A type of WECS with network-induced delay and packet dropout is modeled and adjustable deadbands are explored as a solution to reduce network traffic in WECSs. A method to study the reliable control of WECSs is presented, which takes into account system response as well as the network environment. After detailed theoretical analysis, simulation results are provided, which further demonstrate the feasibility of the proposed scheme. 展开更多
关键词 Wind Energy Conversion System(WECS) networked Control System(NCS) TIME-DELAY Deadband Package-dropout
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Robust H∞ output tracking control of uncertain networked control systems 被引量:2
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作者 刘义才 Liu Bin 《High Technology Letters》 EI CAS 2019年第3期316-325,共10页
This paper investigates a problem of robust output tracking control of networked control systems(NCSs) with network-induced delays, packet dropouts, parameter uncertainties and external disturbances. Firstly, an augme... This paper investigates a problem of robust output tracking control of networked control systems(NCSs) with network-induced delays, packet dropouts, parameter uncertainties and external disturbances. Firstly, an augmented model of time-delay system is proposed for networked tracking control systems. Then, considering the piecewise differentiable characteristic of time-delay, the criterion to output tracking performance analysis and controller design are derived by using an approach of free weighting matrix, reciprocally convex and cone complementarity linearization(CCL). Finally, simulation results of numerical examples show the effectiveness of the proposed approach, and illustrate the advantages of the proposed criteria which outperform previous criteria in the literature. 展开更多
关键词 networked CONTROL systems(NCSs) H∞ output tracking CONTROL TIME-DELAY SYSTEMS cone complementarity LINEARIZATION
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LESO-based Position Synchronization Control for Networked Multi-Axis Servo Systems With Time-Varying Delay 被引量:2
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作者 Qi Wu Li Yu +1 位作者 Yao-Wei Wang Wen-An Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第4期1116-1123,共8页
The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the s... The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays, modeling uncertainties, and external disturbances are first modeled as a lumped disturbance. Then, a linear extended state observer(LESO) is devised to estimate the system state and the lumped disturbance, and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that, a cross-coupled control approach is used to further improve synchronization performance. The bounded-input-bounded-output(BIBO) stability of the closedloop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method. 展开更多
关键词 Active-disturbance rejection controller extended state observer networked motion control system(NMCS) timevarying delays
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Test and Experiment Study on Synchronous Cooperative Design System Over Networked Manufacturing Platform 被引量:1
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作者 LUO Yabo~1 ZHENG Li~2 ZOU Shiwei~1 ZHAO Liang~1 1.School of Mechanical and Electrical Engineering,Wuhan University of Technology,Wuhan 430070,China 2.Department of Biology and Light Industry,Changsha University of Science and Technology,Changsha 410076,China 《武汉理工大学学报》 CAS CSCD 北大核心 2006年第S2期656-658,共3页
Based on the analysis on the previous research in virtual manufacturing and virtual enterprises,this paper pro- vides a novel architecture of networked manufacturing system around the cooperative design.The key techno... Based on the analysis on the previous research in virtual manufacturing and virtual enterprises,this paper pro- vides a novel architecture of networked manufacturing system around the cooperative design.The key technologies for synchronous cooperative design in networked manufacturing platform,such as the cooperative mechanism,cooperative rules,control authority conveyed,cooperative efficiency,are detailed,with which a synchronous cooperative design system is developed.Due to the cooper- ative efficiency is the major bottleneck of the synchronous cooperative design over Internet,this research details the test and experi- ment to demonstrate the practicality of the system.Finally the advantages of the system are illustrated compared with current soft- ware tools. 展开更多
关键词 networked manufacturing SYNCHRONOUS COOPERATIVE design RESOURCE SHARING
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On Dynamics and Nash Equilibriums of Networked Games 被引量:1
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作者 Daizhan Cheng Tingting Xu +1 位作者 Fenghua He Hongsheng Qi 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2014年第1期10-18,共9页
Networked noncooperative games are investigated,where each player(or agent) plays with all other players in its neighborhood. Assume the evolution is based on the fact that each player uses its neighbors current infor... Networked noncooperative games are investigated,where each player(or agent) plays with all other players in its neighborhood. Assume the evolution is based on the fact that each player uses its neighbors current information to decide its next strategy. By using sub-neighborhood, the dynamics of the evolution is obtained. Then a method for calculating Nash equilibriums from mixed strategies of multi-players is proposed.The relationship between local Nash equilibriums based on individual neighborhoods and global Nash equilibriums of overall network is revealed. Then a technique is proposed to construct Nash equilibriums of an evolutionary game from its one step static Nash equilibriums. The basic tool of this approach is the semi-tensor product of matrices, which converts strategies into logical matrices and payoffs into pseudo-Boolean functions, then networked evolutionary games become discrete time dynamic systems. 展开更多
关键词 networked NON-COOPERATIVE game local infor-mation sub-neighborhood fundamental EVOLUTIONARY equation NASH equilibrium
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