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Optimal Dispatch of Urban Distribution Networks Considering Virtual Power Plant Coordination under Extreme Scenarios
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作者 Yong Li Yuxuan Chen +4 位作者 Jiahui He Guowei He Chenxi Dai Jingjing Tong Wenting Lei 《Energy Engineering》 2026年第1期204-220,共17页
Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the... Ensuring reliable power supply in urban distribution networks is a complex and critical task.To address the increased demand during extreme scenarios,this paper proposes an optimal dispatch strategy that considers the coordination with virtual power plants(VPPs).The proposed strategy improves systemflexibility and responsiveness by optimizing the power adjustment of flexible resources.In the proposed strategy,theGaussian Process Regression(GPR)is firstly employed to determine the adjustable range of aggregated power within the VPP,facilitating an assessment of its potential contribution to power supply support.Then,an optimal dispatch model based on a leader-follower game is developed to maximize the benefits of the VPP and flexible resources while guaranteeing the power balance at the same time.To solve the proposed optimal dispatch model efficiently,the constraints of the problem are reformulated and resolved using the Karush-Kuhn-Tucker(KKT)optimality conditions and linear programming duality theorem.The effectiveness of the strategy is illustrated through a detailed case study. 展开更多
关键词 Urban distribution network virtual power plant power supply support leader-follower optimization game extreme weather scenarios
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Artificial Intelligence (AI)-Enabled Unmanned Aerial Vehicle (UAV) Systems for Optimizing User Connectivity in Sixth-Generation (6G) Ubiquitous Networks
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作者 Zeeshan Ali Haider Inam Ullah +2 位作者 Ahmad Abu Shareha Rashid Nasimov Sufyan Ali Memon 《Computers, Materials & Continua》 2026年第1期534-549,共16页
The advent of sixth-generation(6G)networks introduces unprecedented challenges in achieving seamless connectivity,ultra-low latency,and efficient resource management in highly dynamic environments.Although fifth-gener... The advent of sixth-generation(6G)networks introduces unprecedented challenges in achieving seamless connectivity,ultra-low latency,and efficient resource management in highly dynamic environments.Although fifth-generation(5G)networks transformed mobile broadband and machine-type communications at massive scales,their properties of scaling,interference management,and latency remain a limitation in dense high mobility settings.To overcome these limitations,artificial intelligence(AI)and unmanned aerial vehicles(UAVs)have emerged as potential solutions to develop versatile,dynamic,and energy-efficient communication systems.The study proposes an AI-based UAV architecture that utilizes cooperative reinforcement learning(CoRL)to manage an autonomous network.The UAVs collaborate by sharing local observations and real-time state exchanges to optimize user connectivity,movement directions,allocate power,and resource distribution.Unlike conventional centralized or autonomous methods,CoRL involves joint state sharing and conflict-sensitive reward shaping,which ensures fair coverage,less interference,and enhanced adaptability in a dynamic urban environment.Simulations conducted in smart city scenarios with 10 UAVs and 50 ground users demonstrate that the proposed CoRL-based UAV system increases user coverage by up to 10%,achieves convergence 40%faster,and reduces latency and energy consumption by 30%compared with centralized and decentralized baselines.Furthermore,the distributed nature of the algorithm ensures scalability and flexibility,making it well-suited for future large-scale 6G deployments.The results highlighted that AI-enabled UAV systems enhance connectivity,support ultra-reliable low-latency communications(URLLC),and improve 6G network efficiency.Future work will extend the framework with adaptive modulation,beamforming-aware positioning,and real-world testbed deployment. 展开更多
关键词 6G networks UAV-based communication cooperative reinforcement learning network optimization user connectivity energy efficiency
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Optimal Synchronization of Higher-Order Dynamical Networks 被引量:1
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作者 Guanrong CHEN 《Artificial Intelligence Science and Engineering》 2025年第1期31-36,共6页
This article briefly reviews the topic of complex network synchronization,with its graph-theoretic criterion,showing that the homogeneous and symmetrical network structures are essential for optimal synchronization.Fu... This article briefly reviews the topic of complex network synchronization,with its graph-theoretic criterion,showing that the homogeneous and symmetrical network structures are essential for optimal synchronization.Furthermore,it briefly reviews the notion of higher-order network topologies and shows their promising potential in application to evaluating the optimality of network synchronizability. 展开更多
关键词 complex network SYNCHRONIZATION optimal synchronizability SIMPLEX higher-order topology
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Optimal Control of Unknown Collective Spin Systems via a Neural Network Surrogate
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作者 Yaofeng Chen Li You 《Chinese Physics Letters》 2025年第10期117-128,共12页
Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this wor... Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations. 展开更多
关键词 neural network quantum optimal control surrogate model trained neural network nn assuming quantum optimal control qoc relies collective spin system optimal control captures system s dynamics
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Effects of information and policy regulation on green behavior propagation in multilayer networks: Modeling, analysis,and optimal allocation
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作者 Xian-Li Sun Ling-Hua Zhang 《Chinese Physics B》 2025年第6期635-646,共12页
As the economy grows, environmental issues are becoming increasingly severe, making the promotion of green behavior more urgent. Information dissemination and policy regulation play crucial roles in influencing and am... As the economy grows, environmental issues are becoming increasingly severe, making the promotion of green behavior more urgent. Information dissemination and policy regulation play crucial roles in influencing and amplifying the spread of green behavior across society. To this end, a novel three-layer model in multilayer networks is proposed. In the novel model, the information layer describes green information spreading, the physical contact layer depicts green behavior propagation, and policy regulation is symbolized by an isolated node beneath the two layers. Then, we deduce the green behavior threshold for the three-layer model using the microscopic Markov chain approach. Moreover, subject to some individuals who are more likely to influence others or become green nodes and the limitations of the capacity of policy regulation, an optimal scheme is given that could optimize policy interventions to most effectively prompt green behavior.Subsequently, simulations are performed to validate the preciseness and theoretical results of the new model. It reveals that policy regulation can prompt the prevalence and outbreak of green behavior. Then, the green behavior is more likely to spread and be prevalent in the SF network than in the ER network. Additionally, optimal allocation is highly successful in facilitating the dissemination of green behavior. In practice, the optimal allocation strategy could prioritize interventions at critical nodes or regions, such as highly connected urban areas, where the impact of green behavior promotion would be most significant. 展开更多
关键词 green behavior propagation multilayer networks information dissemination optimal allocation
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Global dynamics and optimal control of SEIQR epidemic model on heterogeneous complex networks
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作者 Xiongding Liu Xiaodan Zhao +1 位作者 Xiaojing Zhong Wu Wei 《Chinese Physics B》 2025年第6期262-274,共13页
This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading d... This paper investigates a new SEIQR(susceptible–exposed–infected–quarantined–recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh–Hurwitz criterion, Lyapunov method and La Salle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate(γ1, γ2), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19. 展开更多
关键词 epidemic spreading SEIQR model stability and sensitivity analysis heterogeneous complex networks optimal control
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Optimal Secure Control of Networked Control Systems Under False Data Injection Attacks:A Multi-Stage Attack-Defense Game Approach
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作者 Dajun Du Yi Zhang +1 位作者 Baoyue Xu Minrui Fei 《IEEE/CAA Journal of Automatica Sinica》 2025年第4期821-823,共3页
Dear Editor,The attacker is always going to intrude covertly networked control systems(NCSs)by dynamically changing false data injection attacks(FDIAs)strategy,while the defender try their best to resist attacks by de... Dear Editor,The attacker is always going to intrude covertly networked control systems(NCSs)by dynamically changing false data injection attacks(FDIAs)strategy,while the defender try their best to resist attacks by designing defense strategy on the basis of identifying attack strategy,maintaining stable operation of NCSs.To solve this attack-defense game problem,this letter investigates optimal secure control of NCSs under FDIAs.First,for the alterations of energy caused by false data,a novel attack-defense game model is constructed,which considers the changes of energy caused by the actions of the defender and attacker in the forward and feedback channels. 展开更多
关键词 designing defense strategy networked control systems ncss alterations energy networked control systems false data injection attacks fdias strategywhile false data injection attacks optimal secure control identifying attack strategymaintaining
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Robust Predefined-Time Control for Optimal Formation of Networked Mobile Vehicle Systems
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作者 Jing-Zhe Xu Zhi-Wei Liu +2 位作者 Dingxin He Ming-Feng Ge Ming Chi 《IEEE/CAA Journal of Automatica Sinica》 2025年第4期824-826,共3页
Dear Editor,This letter addresses the robust predefined-time control challenge for leaderless optimal formation in networked mobile vehicle(NMV)systems.The aim is to minimize a composite global cost function derived f... Dear Editor,This letter addresses the robust predefined-time control challenge for leaderless optimal formation in networked mobile vehicle(NMV)systems.The aim is to minimize a composite global cost function derived from individual strongly convex functions of each agent,considering both input disturbances and network communication constraints.A novel predefined-time optimal formation control(PTOFC)algorithm is presented,ensuring agent state convergence to optimal formation positions within an adjustable settling time.Through the integration of an integral sliding mode technique,disturbances are effectively countered.A representative numerical example highlights the effectiveness and robustness of the developed approach. 展开更多
关键词 minimize composite global cost function integral sliding mode technique agent state convergence optimal formation networked mobile vehicle systems robust predefined time control strongly convex functions disturbances
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Optimal path finding algorithms based on SLSD road network model 被引量:3
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作者 张小国 王庆 龚福祥 《Journal of Southeast University(English Edition)》 EI CAS 2010年第4期558-562,共5页
A solution to compute the optimal path based on a single-line-single-directional(SLSD)road network model is proposed.Unlike the traditional road network model,in the SLSD conceptual model,being single-directional an... A solution to compute the optimal path based on a single-line-single-directional(SLSD)road network model is proposed.Unlike the traditional road network model,in the SLSD conceptual model,being single-directional and single-line style,a road is no longer a linkage of road nodes but abstracted as a network node.Similarly,a road node is abstracted as the linkage of two ordered single-directional roads.This model can describe turn restrictions,circular roads,and other real scenarios usually described using a super-graph.Then a computing framework for optimal path finding(OPF)is presented.It is proved that classical Dijkstra and A algorithms can be directly used for OPF computing of any real-world road networks by transferring a super-graph to an SLSD network.Finally,using Singapore road network data,the proposed conceptual model and its corresponding optimal path finding algorithms are validated using a two-step optimal path finding algorithm with a pre-computing strategy based on the SLSD road network. 展开更多
关键词 optimal path finding road network model conceptual model digital map vehicle navigation system A algorithm Dijkstra algorithm
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Optimal dispatching method of traffic incident rescue resource for freeway network 被引量:1
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作者 柴干 冉旭 夏井新 《Journal of Southeast University(English Edition)》 EI CAS 2013年第3期336-341,共6页
An optimal resource dispatching method is proposed to solve the multiple-response problem under the conditions of potential incidents on freeway networks.Travel time of the response vehicle is selected instead of rout... An optimal resource dispatching method is proposed to solve the multiple-response problem under the conditions of potential incidents on freeway networks.Travel time of the response vehicle is selected instead of route distance as the weight to reflect the impact of traffic conditions on the decisions of rescue resources.According to the characteristics of different types of rescue vehicles the dispatching decision-making time is revised to show the heterogeneity among different rescue vehicle dispatching modes. The genetic algorithm is used to obtain the solutions to the rescue resources dispatching model. A case study shows that the proposed method can accurately reveal the impact of potential incidents on the costs of rescues according to the variations in the types and quantities of rescue resources and the optimal dispatching plan with respect to potential incidents can be obtained.The proposed method is applicable in real world scenarios. 展开更多
关键词 optimal dispatching potential incident GENETICALGORITHM rescue resource freeway network
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STUDY ON OPTIMAL CONTROL OF MUNICIPAL WATER DISTRIBUTION NETWORK 被引量:1
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作者 张宏伟 杨芳 庄健 《Transactions of Tianjin University》 EI CAS 2001年第3期167-171,共5页
A systematic investigation is made on the problems which are related to the optimal control of the municipal water distribution network.A mathematical model of forecasting the water short term demand is proposed using... A systematic investigation is made on the problems which are related to the optimal control of the municipal water distribution network.A mathematical model of forecasting the water short term demand is proposed using the time series trigonometric function analysis method;the service discharge based macroscopic model of network performance is established using the network structuring method;a relatively satisfactory mathematical model for the optimal control of water distribution network is put forward in view of security and economy,and solved by the constrained mixed discrete variable complex arithmetic.The model is applied in many examples and the results are satisfactory. 展开更多
关键词 water distribution network water demand forecast macroscopic model optimal control
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Optimal Energy-Efficient Transmission for Hybrid Spectrum Sharing in Cooperative Cognitive Radio Networks 被引量:9
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作者 Linna Hu Rui Shi +3 位作者 Minghe Mao Zhiyu Chen Hongxi Zhou Weiliang Li 《China Communications》 SCIE CSCD 2019年第6期150-161,共12页
In order to improve the energy efficiency(EE)in cognitive radio(CR),this paper investigates the joint design of cooperative spectrum sensing time and the power control optimization problem for the secondary user syste... In order to improve the energy efficiency(EE)in cognitive radio(CR),this paper investigates the joint design of cooperative spectrum sensing time and the power control optimization problem for the secondary user systems to achieve the maximum energy efficiency in a cognitive network based on hybrid spectrum sharing,meanwhile considering the maximum transmit power,user quality of service(QoS)requirements,interference limitations,and primary user protection.The optimization of energy efficient sensing time and power allocation is formulated as a non-convex optimization problem.The Dinkelbach’s method is adopted to solve this problem and to transform the non-convex optimization problem in fractional form into an equivalent optimization problem in the form of subtraction.Then,an iterative power allocation algorithm is proposed to solve the optimization problem.The simulation results show the effectiveness of the proposed algorithms for energy-efficient resource allocation in the cognitive network. 展开更多
关键词 cognitive radio networks COOPERATIVE SPECTRUM SENSING ENERGY-EFFICIENCY HYBRID SPECTRUM sharing power control SENSING time optimization
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Application of the optimal Latin hypercube design and radial basis function network to collaborative optimization 被引量:16
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作者 ZHAO Min CUI Wei-cheng 《Journal of Marine Science and Application》 2007年第3期24-32,共9页
Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization (MDO) is a more promising approach. For this reason, Collabora... Improving the efficiency of ship optimization is crucial for modem ship design. Compared with traditional methods, multidisciplinary design optimization (MDO) is a more promising approach. For this reason, Collaborative Optimization (CO) is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method. 展开更多
关键词 multidisciplinary design optimization (MDO) collaborative optimization (CO) optimal Latin hypercube design radial basis function network APPROXIMATION
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Application of artificial neural networks in optimal tuning of tuned mass dampers implemented in high-rise buildings subjected to wind load 被引量:9
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作者 Meysam Ramezani Akbar Bathaei Amir K.Ghorbani-Tanha 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2018年第4期903-915,共13页
High-rise buildings are usually considered as flexible structures with low inherent damping. Therefore, these kinds of buildings are susceptible to wind-induced vibration. Tuned Mass Damper(TMD) can be used as an ef... High-rise buildings are usually considered as flexible structures with low inherent damping. Therefore, these kinds of buildings are susceptible to wind-induced vibration. Tuned Mass Damper(TMD) can be used as an effective device to mitigate excessive vibrations. In this study, Artificial Neural Networks is used to find optimal mechanical properties of TMD for high-rise buildings subjected to wind load. The patterns obtained from structural analysis of different multi degree of freedom(MDF) systems are used for training neural networks. In order to obtain these patterns, structural models of some systems with 10 to 80 degrees-of-freedoms are built in MATLAB/SIMULINK program. Finally, the optimal properties of TMD are determined based on the objective of maximum displacement response reduction. The Auto-Regressive model is used to simulate the wind load. In this way, the uncertainties related to wind loading can be taken into account in neural network’s outputs. After training the neural network, it becomes possible to set the frequency and TMD mass ratio as inputs and get the optimal TMD frequency and damping ratio as outputs. As a case study, a benchmark 76-story office building is considered and the presented procedure is used to obtain optimal characteristics of the TMD for the building. 展开更多
关键词 artificial neural networks tuned mass damper wind load auto-regressive model optimal frequency anddamping
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Optimal distributed resource allocation in a wireless sensor network for control systems 被引量:7
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作者 MAO Jian-lin WU Zhi-ming 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第1期106-112,共7页
Wireless technology is applied increasingly in networked control systems. A new form of wireless network called wireless sensor network can bring control systems some advantages, such as flexibility and feasibility of... Wireless technology is applied increasingly in networked control systems. A new form of wireless network called wireless sensor network can bring control systems some advantages, such as flexibility and feasibility of network deployment at low costs, while it also raises some new challenges. First, the communication resources shared by all the control loops are limited. Second, the wireless and multi-hop character of sensor network makes the resources scheduling more difficult. Thus, how to effectively allocate the limited communication resources for those control loops is an important problem. In this paper, this problem is formulated as an optimal sampling frequency assignment problem, where the objective function is to maximize the utility of control systems, subject to channel capacity constraints. Then an iterative distributed algorithm based on local buffer information is proposed. Finally, the simulation results show that the proposed algorithm can effectively allocate the limited communication resource in a distributed way. It can achieve the optimal quality of the control system and adapt to the network load changes. 展开更多
关键词 Wireless sensor networks (WSN) Distributed resource allocation Control systems optimization.
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Reactive Power Optimization Model of Active Distribution Network with New Energy and Electric Vehicles 被引量:1
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作者 Chenxu Wang Jing Bian Rui Yuan 《Energy Engineering》 2025年第3期985-1003,共19页
Considering the uncertainty of grid connection of electric vehicle charging stations and the uncertainty of new energy and residential electricity load,a spatio-temporal decoupling strategy of dynamic reactive power o... Considering the uncertainty of grid connection of electric vehicle charging stations and the uncertainty of new energy and residential electricity load,a spatio-temporal decoupling strategy of dynamic reactive power optimization based on clustering-local relaxation-correction is proposed.Firstly,the k-medoids clustering algorithm is used to divide the reduced power scene into periods.Then,the discrete variables and continuous variables are optimized in the same period of time.Finally,the number of input groups of parallel capacitor banks(CB)in multiple periods is fixed,and then the secondary static reactive power optimization correction is carried out by using the continuous reactive power output device based on the static reactive power compensation device(SVC),the new energy grid-connected inverter,and the electric vehicle charging station.According to the characteristics of the model,a hybrid optimization algorithm with a cross-feedback mechanism is used to solve different types of variables,and an improved artificial hummingbird algorithm based on tent chaotic mapping and adaptive mutation is proposed to improve the solution efficiency.The simulation results show that the proposed decoupling strategy can obtain satisfactory optimization resultswhile strictly guaranteeing the dynamic constraints of discrete variables,and the hybrid algorithm can effectively solve the mixed integer nonlinear optimization problem. 展开更多
关键词 Active distribution network new energy electric vehicles dynamic reactive power optimization kmedoids clustering hybrid optimization algorithm
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Modelling and Multi-Objective Optimal Control of Batch Processes Using Recurrent Neuro-fuzzy Networks 被引量:2
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作者 Jie Zhang 《International Journal of Automation and computing》 EI 2006年第1期1-7,共7页
In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range pre... In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range prediction model through the fuzzy conjunction of a number of "local" linear dynamic models. Network output is fed back to network input through one or more time delay units, which ensure that predictions from the recurrent neuro-fuzzy network are long-range. In building a recurrent neural network model, process knowledge is used initially to partition the processes non-linear characteristics into several local operating regions, and to aid in the initialisation of corresponding network weights. Process operational data is then used to train the network. Membership functions of the local regimes are identified, and local models are discovered via network training. Based on a recurrent neuro-fuzzy network model, a multi-objective optimal control policy can be obtained. The proposed technique is applied to a fed-batch reactor. 展开更多
关键词 optimal control batch processes neural networks multi-objective optimisation.
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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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Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks 被引量:3
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作者 罗续鹏 蒋海军 +1 位作者 陈珊珊 李佳容 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期710-723,共14页
On the multilingual online social networks of global information sharing,the wanton spread of rumors has an enormous negative impact on people's lives.Thus,it is essential to explore the rumor-spreading rules in m... On the multilingual online social networks of global information sharing,the wanton spread of rumors has an enormous negative impact on people's lives.Thus,it is essential to explore the rumor-spreading rules in multilingual environment and formulate corresponding control strategies to reduce the harm caused by rumor propagation.In this paper,considering the multilingual environment and intervention mechanism in the rumor-spreading process,an improved ignorants–spreaders-1–spreaders-2–removers(I2SR)rumor-spreading model with time delay and the nonlinear incidence is established in heterogeneous networks.Firstly,based on the mean-field equations corresponding to the model,the basic reproduction number is derived to ensure the existence of rumor-spreading equilibrium.Secondly,by applying Lyapunov stability theory and graph theory,the global stability of rumor-spreading equilibrium is analyzed in detail.In particular,aiming at the lowest control cost,the optimal control scheme is designed to optimize the intervention mechanism,and the optimal control conditions are derived using the Pontryagin's minimum principle.Finally,some illustrative examples are provided to verify the effectiveness of the theoretical results.The results show that optimizing the intervention mechanism can effectively reduce the densities of spreaders-1 and spreaders-2 within the expected time,which provides guiding insights for public opinion managers to control rumors. 展开更多
关键词 rumor propagation heterogeneous network nonlinear incidence optimal control
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