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Resilience Against Replay Attacks:A Distributed Model Predictive Control Scheme for Networked Multi-Agent Systems 被引量:5
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作者 Giuseppe Franzè Francesco Tedesco Domenico Famularo 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第3期628-640,共13页
In this paper,a resilient distributed control scheme against replay attacks for multi-agent networked systems subject to input and state constraints is proposed.The methodological starting point relies on a smart use ... In this paper,a resilient distributed control scheme against replay attacks for multi-agent networked systems subject to input and state constraints is proposed.The methodological starting point relies on a smart use of predictive arguments with a twofold aim:1)Promptly detect malicious agent behaviors affecting normal system operations;2)Apply specific control actions,based on predictive ideas,for mitigating as much as possible undesirable domino effects resulting from adversary operations.Specifically,the multi-agent system is topologically described by a leader-follower digraph characterized by a unique leader and set-theoretic receding horizon control ideas are exploited to develop a distributed algorithm capable to instantaneously recognize the attacked agent.Finally,numerical simulations are carried out to show benefits and effectiveness of the proposed approach. 展开更多
关键词 Distributed model predictive control leader-follower networks multi-agent systems replay attacks resilient control
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Pinning synchronization of networked multi-agent systems: spectral analysis
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作者 Linying XIANG Fei CHEN Guanrong CHEN 《Control Theory and Technology》 EI CSCD 2015年第1期45-54,共10页
Pinning synchronization of a networked multi-agent system with a directed communication topology is investigated from a spectral analysis approach. Some new types of synchronized regions for networked systems with dif... Pinning synchronization of a networked multi-agent system with a directed communication topology is investigated from a spectral analysis approach. Some new types of synchronized regions for networked systems with different nonlinear agent dynamics and inner coupling structures are discovered. The eigenvalue distributions of the coupling and control matrices for different types of directed networks are obtained. The effects of the network topology, pinning density and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing pinning density and pinning strength for some types of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other types. It is found that directed random networks are not always easier to synchronize than directed small-world networks, and a denser eigenvalue distribution may not always imply better synchronizability. 展开更多
关键词 multi-agent system directed network pinning control spectral analysis SYNCHRONIZABILITY synchronized region
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Finite-time fault-tolerant tracking control for multi-agent systems based on neural observer
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作者 Junzhe Cheng Shitong Zhang +1 位作者 Qing Wang Bin Xin 《Control Theory and Technology》 2026年第1期10-23,共14页
This paper investigates the consensus tracking control problem for high order nonlinear multi-agent systems subject to non-affine faults,partial measurable states,uncertain control coefficients,and unknown external di... This paper investigates the consensus tracking control problem for high order nonlinear multi-agent systems subject to non-affine faults,partial measurable states,uncertain control coefficients,and unknown external disturbances.Under the directed topology conditions,an observer-based finite-time control strategy based on adaptive backstepping and is proposed,in which a neural network-based state observer is employed to approximate the unmeasurable system state variables.To address the complexity explosion problem associated with the backstepping method,a finite-time command filter is incorporated,with error compensation signals designed to mitigate the filter-induced errors.Additionally,the Butterworth low-pass filter is introduced to avoid the algebraic ring problem in the design of the controller.The finite-time stability of the closed-loop system is rigorously analyzed with the finite-time Lyapunov stability criterion,validating that all closed-loop signals of the system remain bounded within a finite time.Finally,the effectiveness of the proposed control strategy is verified through a simulation example. 展开更多
关键词 multi-agent systems Command filtered backstepping Finite-time control Neural observer Non-affine faults
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Leader-following positive consensus of heterogeneous switched multi-agent systems with average dwell time switching
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作者 Kaiming Li Wei Xing +1 位作者 Haoyue Yang Junfeng Zhang 《Control Theory and Technology》 2026年第1期66-81,共16页
This paper focuses on the leader-following positive consensus problems of heterogeneous switched multi-agent systems.First,a state-feedback controller with dynamic compensation is introduced to achieve positive consen... This paper focuses on the leader-following positive consensus problems of heterogeneous switched multi-agent systems.First,a state-feedback controller with dynamic compensation is introduced to achieve positive consensus under average dwell time switching.Then sufficient conditions are derived to guarantee the positive consensus.The gain matrices of the control protocol are described using a matrix decomposition approach and the corresponding computational complexity is reduced by resorting to linear programming and co-positive Lyapunov functions.Finally,two numerical examples are provided to illustrate the results obtained. 展开更多
关键词 Heterogeneous switched multi-agent systems Positive consensus Linear programming
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Improved Event-Triggered Adaptive Neural Network Control for Multi-agent Systems Under Denial-of-Service Attacks 被引量:2
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作者 Huiyan ZHANG Yu HUANG +1 位作者 Ning ZHAO Peng SHI 《Artificial Intelligence Science and Engineering》 2025年第2期122-133,共12页
This paper addresses the consensus problem of nonlinear multi-agent systems subject to external disturbances and uncertainties under denial-ofservice(DoS)attacks.Firstly,an observer-based state feedback control method... This paper addresses the consensus problem of nonlinear multi-agent systems subject to external disturbances and uncertainties under denial-ofservice(DoS)attacks.Firstly,an observer-based state feedback control method is employed to achieve secure control by estimating the system's state in real time.Secondly,by combining a memory-based adaptive eventtriggered mechanism with neural networks,the paper aims to approximate the nonlinear terms in the networked system and efficiently conserve system resources.Finally,based on a two-degree-of-freedom model of a vehicle affected by crosswinds,this paper constructs a multi-unmanned ground vehicle(Multi-UGV)system to validate the effectiveness of the proposed method.Simulation results show that the proposed control strategy can effectively handle external disturbances such as crosswinds in practical applications,ensuring the stability and reliable operation of the Multi-UGV system. 展开更多
关键词 multi-agent systems neural network DoS attacks memory-based adaptive event-triggered mechanism
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Time-Varying Formation Tracking Control of Heterogeneous Multi-Agent Systems With Intermittent Communications and Directed Switching Networks
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作者 Yuhan Wang Zhuping Wang +1 位作者 Hao Zhang Huaicheng Yan 《IEEE/CAA Journal of Automatica Sinica》 2025年第1期294-296,共3页
Dear Editor,This letter is concerned with the problem of time-varying formation tracking for heterogeneous multi-agent systems(MASs) under directed switching networks. For this purpose, our first step is to present so... Dear Editor,This letter is concerned with the problem of time-varying formation tracking for heterogeneous multi-agent systems(MASs) under directed switching networks. For this purpose, our first step is to present some sufficient conditions for the exponential stability of a particular category of switched systems. 展开更多
关键词 switched systems time varying formation tracking directed switching networks heterogeneous multi agent systems intermittent communications exponential stability
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Consensus of networked control multi-agent systems using a double-layer encryption scheme 被引量:3
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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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Tracking Control of Multi-Agent Systems Using a Networked Predictive PID Tracking Scheme 被引量:3
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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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Constrained Networked Predictive Control for Nonlinear Systems Using a High-Order Fully Actuated System Approach 被引量:1
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作者 Yi Huang Guo-Ping Liu +1 位作者 Yi Yu Wenshan Hu 《IEEE/CAA Journal of Automatica Sinica》 2025年第2期478-480,共3页
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv... Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system. 展开更多
关键词 optimal control problem constrained networked predictive control strategy Performance Optimization present upper bound Nonlinear systems NOISES Constrained networked Predictive Control High Order Fully Actuated systems
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Nonconvex Constrained Consensus of Discrete-Time Heterogeneous Multi-Agent Systems with Arbitrarily Switching Topologies
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作者 Honghao Wu 《Journal of Electronic Research and Application》 2025年第1期14-22,共9页
This paper mainly focuses on the velocity-constrained consensus problem of discrete-time heterogeneous multi-agent systems with nonconvex constraints and arbitrarily switching topologies,where each agent has first-ord... This paper mainly focuses on the velocity-constrained consensus problem of discrete-time heterogeneous multi-agent systems with nonconvex constraints and arbitrarily switching topologies,where each agent has first-order or second-order dynamics.To solve this problem,a distributed algorithm is proposed based on a contraction operator.By employing the properties of the stochastic matrix,it is shown that all agents’position states could converge to a common point and second-order agents’velocity states could remain in corresponding nonconvex constraint sets and converge to zero as long as the joint communication topology has one directed spanning tree.Finally,the numerical simulation results are provided to verify the effectiveness of the proposed algorithms. 展开更多
关键词 HETEROGENEOUS multi-agent systems Nonconvex constraint CONSENSUS
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Group formation tracking for heterogeneous linear multi-agent systems under switching topologies
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作者 Shiyu Zhou Dong Sun 《Journal of Automation and Intelligence》 2025年第2期108-114,共7页
This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control s... This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control strategy that enables the outputs of the followers to form the desired sub-formations and track the outputs of the leader in each subgroup.Firstly,novel distributed observers are developed to estimate the states of the leaders under switching topologies.Then,GFTC protocols are designed based on the proposed observers.It is shown that with the distributed protocol,the GFTC problem for HMASs under switching topologies is solved if the average dwell time associated with the switching topologies is larger than a fixed threshold.Finally,an example is provided to illustrate the effectiveness of the proposed control strategy. 展开更多
关键词 Formation tracking Group division Switching topologies multi-agent systems
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Distributed optimal formation control of heterogeneous Euler–Lagrange multi-agent systems
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作者 Mengmeng Duan Fengping Huang +2 位作者 Shanying Zhu Ziwen Yang Cailian Chen 《Journal of Automation and Intelligence》 2025年第4期282-290,共9页
In this paper,the distributed optimal formation control problem of heterogeneous Euler–Lagrange multi-agent systems with generic formation constraints and inequality constraints is investigated.Based on the primal–d... In this paper,the distributed optimal formation control problem of heterogeneous Euler–Lagrange multi-agent systems with generic formation constraints and inequality constraints is investigated.Based on the primal–dual dynamics and the adaptive control technique,a distributed optimal formation controller consists of a velocity reference signal generator and a velocity tracking controller is proposed.By using the optimality condition,the relationship between the equilibrium point of the closed-loop system and the optimal solution of the optimization problem is established.Then,by utilizing Lyapunov stability analysis,it is rigorously proved that the optimal formation is reached with the proposed controller.Lastly,simulation examples are provided to substantiate the theoretical results. 展开更多
关键词 Formation control Distributed optimization multi-agent systems
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Recent Advancement in Formation Control of Multi-Agent Systems:A Review
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作者 Aamir Farooq Zhengrong Xiang +1 位作者 Wen-Jer Chang Muhammad Shamrooz Aslam 《Computers, Materials & Continua》 2025年第6期3623-3674,共52页
Formation control in multi-agent systems has become a critical area of interest due to its wide-ranging applications in robotics,autonomous transportation,and surveillance.While various studies have explored distribut... Formation control in multi-agent systems has become a critical area of interest due to its wide-ranging applications in robotics,autonomous transportation,and surveillance.While various studies have explored distributed cooperative control,this review focuses on the theoretical foundations and recent developments in formation control strategies.The paper categorizes and analyzes key formation types,including formation maintenance,group or cluster formation,bipartite formations,event-triggered formations,finite-time convergence,and constrained formations.A significant portion of the review addresses formation control under constrained dynamics,presenting both modelbased and model-free approaches that consider practical limitations such as actuator bounds,communication delays,and nonholonomic constraints.Additionally,the paper discusses emerging trends,including the integration of eventdriven mechanisms and AI-enhanced coordination strategies.Comparative evaluations highlight the trade-offs among various methodologies regarding scalability,robustness,and real-world feasibility.Practical implementations are reviewed across diverse platforms,and the review identifies the current achievements and unresolved challenges in the field.The paper concludes by outlining promising research directions,such as adaptive control for dynamic environments,energy-efficient coordination,and using learning-based control under uncertainty.This review synthesizes the current state of the art and provides a road map for future investigation,making it a valuable reference for researchers and practitioners aiming to advance formation control in multi-agent systems. 展开更多
关键词 Cooperative control multi-agent systems formation control formation containment group formation bipartite formation
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Dynamic Decoupling-Driven Cooperative Pursuit for Multi-UAV Systems:A Multi-Agent Reinforcement Learning Policy Optimization Approach
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作者 Lei Lei Chengfu Wu Huaimin Chen 《Computers, Materials & Continua》 2025年第10期1339-1363,共25页
This paper proposes a Multi-Agent Attention Proximal Policy Optimization(MA2PPO)algorithm aiming at the problems such as credit assignment,low collaboration efficiency and weak strategy generalization ability existing... This paper proposes a Multi-Agent Attention Proximal Policy Optimization(MA2PPO)algorithm aiming at the problems such as credit assignment,low collaboration efficiency and weak strategy generalization ability existing in the cooperative pursuit tasks of multiple unmanned aerial vehicles(UAVs).Traditional algorithms often fail to effectively identify critical cooperative relationships in such tasks,leading to low capture efficiency and a significant decline in performance when the scale expands.To tackle these issues,based on the proximal policy optimization(PPO)algorithm,MA2PPO adopts the centralized training with decentralized execution(CTDE)framework and introduces a dynamic decoupling mechanism,that is,sharing the multi-head attention(MHA)mechanism for critics during centralized training to solve the credit assignment problem.This method enables the pursuers to identify highly correlated interactions with their teammates,effectively eliminate irrelevant and weakly relevant interactions,and decompose large-scale cooperation problems into decoupled sub-problems,thereby enhancing the collaborative efficiency and policy stability among multiple agents.Furthermore,a reward function has been devised to facilitate the pursuers to encircle the escapee by combining a formation reward with a distance reward,which incentivizes UAVs to develop sophisticated cooperative pursuit strategies.Experimental results demonstrate the effectiveness of the proposed algorithm in achieving multi-UAV cooperative pursuit and inducing diverse cooperative pursuit behaviors among UAVs.Moreover,experiments on scalability have demonstrated that the algorithm is suitable for large-scale multi-UAV systems. 展开更多
关键词 multi-agent reinforcement learning multi-UAV systems pursuit-evasion games
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Unified Output Feedback Based Prescribed Performance Consensus Tracking Control of Heterogeneous Multi-Agent Systems
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作者 Dahui Luo Yujuan Wang +1 位作者 Frank L.Lewis Yongduan Song 《IEEE/CAA Journal of Automatica Sinica》 2025年第8期1636-1647,共12页
This paper proposes an output-feedback based prescribed performance consensus tracking control methodology for a class of heterogeneous multi-agent systems(HMASs)with inconsistent system structure,where the performanc... This paper proposes an output-feedback based prescribed performance consensus tracking control methodology for a class of heterogeneous multi-agent systems(HMASs)with inconsistent system structure,where the performance behavior is allowed to be different from that of each other.Both the heterogeneous system structures and the nonidentical performance requirements make the control problem much more challenging than that of MASs with identical structure and performance requirement.This is mainly due to the coupling effect of the system dynamics and performance restriction of each agent in the cooperative control action.The key to solve this problem is to introduce a dual-phase performance-guaranteed method,in which the consensus tracking error is decomposed into auxiliary tracking error and filter tracking error and then the whole performance control is decomposed into two phases.By confining the two errors respectively,the practical tracking error can be proved to be explicitly confined within an arbitrarily given performance envelope by merely adjusting the design parameters rather than modifying control structure.Moreover,the prescribed performance control(PPC)result is not only uniform with any initial conditions and design parameters,allowing it to be global,but also unifying both the global and semi-global result into one frame,distinguishing itself from most existing PPC works where either only global or only semi-global result is guaranteed.Finally,the effectiveness of the proposed control scheme is confirmed by the simulation conducted on a group of tunnel-diode circuits(TDC). 展开更多
关键词 Auxiliary filter heterogeneous multi-agent systems(HMASs) OUTPUT-FEEDBACK prescribed performance
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Observer-based prescribed-time time-varying output formation-containment control of heterogeneous multi-agent systems
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作者 Haiyang Hu Tao Li +3 位作者 Xiaowen Zhao Yuanmei Wang Jialong Tian Zijie Jiang 《Chinese Physics B》 2025年第10期366-375,共10页
This paper investigates the observer-based prescribed-time time-varying output formation-containment(PT-TV-OFC)control problem for heterogeneous multi-agent systems in which the different agents have different state d... This paper investigates the observer-based prescribed-time time-varying output formation-containment(PT-TV-OFC)control problem for heterogeneous multi-agent systems in which the different agents have different state dimensions.The system comprises one tracking leader,multiple formation leaders,and followers,where two types of leaders are used to generate a reference trajectory for movement and achieve specific formation,respectively.Firstly,a prescribed-time dynamics observer is constructed for the formation leaders to estimate the tracking leader's dynamic model and state.On this basis,a prescribed-time control protocol is designed for the formation leaders to achieve time-varying output formation.Then,a prescribed-time convex hull observer is designed for the followers to estimate information regarding the convex hull formed by the formation leaders.Using the estimated convex hull information,a prescribed-time containment control protocol is designed to ensure the followers converge into the convex hull.Furthermore,using Lyapunov stability theory,the stability of systems is proved in detail,which implies that the heterogeneous multi-agent systems can achieve PT-TV-OFC control.Finally,numerical simulations validate the feasibility of the theoretical results. 展开更多
关键词 heterogeneous multi-agent systems prescribed-time control observers time-varying output formation-containment control
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Formation-containment control for nonholonomic multi-agent systems with a desired trajectory constraint
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作者 GU Xueqiang LU Lina +1 位作者 XIANG Fengtao ZHANG Wanpeng 《Journal of Systems Engineering and Electronics》 2025年第1期256-268,共13页
This paper addresses the time-varying formation-containment(FC) problem for nonholonomic multi-agent systems with a desired trajectory constraint, where only the leaders can acquire information about the desired traje... This paper addresses the time-varying formation-containment(FC) problem for nonholonomic multi-agent systems with a desired trajectory constraint, where only the leaders can acquire information about the desired trajectory. Input the fixed time-varying formation template to the leader and start executing, this process also needs to track the desired trajectory, and the follower needs to converge to the convex hull that the leader crosses. Firstly, the dynamic models of nonholonomic systems are linearized to second-order dynamics. Then, based on the desired trajectory and formation template, the FC control protocols are proposed. Sufficient conditions to achieve FC are introduced and an algorithm is proposed to resolve the control parameters by solving an algebraic Riccati equation. The system is demonstrated to achieve FC, with the average position and velocity of the leaders converging asymptotically to the desired trajectory. Finally, the theoretical achievements are verified in simulations by a multi-agent system composed of virtual human individuals. 展开更多
关键词 multi-agent systems nonholonomic dynamics formation-containment(FC)control desired trajectory constrains
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The Confluence of Evolutionary Computation and Multi-Agent Systems:A Survey
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作者 Tai-You Chen Wei-Neng Chen +5 位作者 Feng-Feng Wei Xiao-Qi Guo Wen-Xiang Song Rui Zhu Qiuzhen Lin Jun Zhang 《IEEE/CAA Journal of Automatica Sinica》 2025年第11期2175-2193,共19页
Both evolutionary computation(EC)and multiagent systems(MAS)study the emergence of intelligence through the interaction and cooperation of a group of individuals.EC focuses on solving various complex optimization prob... Both evolutionary computation(EC)and multiagent systems(MAS)study the emergence of intelligence through the interaction and cooperation of a group of individuals.EC focuses on solving various complex optimization problems,while MAS provides a flexible model for distributed artificial intelligence.Since their group interaction mechanisms can be borrowed from each other,many studies have attempted to combine EC and MAS.With the rapid development of the Internet of Things,the confluence of EC and MAS has become more and more important,and related articles have shown a continuously growing trend during the last decades.In this survey,we first elaborate on the mutual assistance of EC and MAS from two aspects,agent-based EC and EC-assisted MAS.Agent-based EC aims to introduce characteristics of MAS into EC to improve the performance and parallelism of EC,while EC-assisted MAS aims to use EC to better solve optimization problems in MAS.Furthermore,we review studies that combine the cooperation mechanisms of EC and MAS,which greatly leverage the strengths of both sides.A description framework is built to elaborate existing studies.Promising future research directions are also discussed in conjunction with emerging technologies and real-world applications. 展开更多
关键词 Distributed artificial intelligence distributed optimization evolutionary computation(EC) multi-agent systems(MAS)
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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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Stackelberg game-based optimal secure control against hybrid attacks for networked control systems
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作者 Wei Xiong Yi Dong Liubin Zhou 《Journal of Automation and Intelligence》 2025年第3期236-241,共6页
This paper investigates the problem of optimal secure control for networked control systems under hybrid attacks.A control strategy based on the Stackelberg game framework is proposed,which differs from conventional m... This paper investigates the problem of optimal secure control for networked control systems under hybrid attacks.A control strategy based on the Stackelberg game framework is proposed,which differs from conventional methods by considering both denial-of-service(DoS)and false data injection(FDI)attacks simultaneously.Additionally,the stability conditions for the system under these hybrid attacks are established.It is technically challenging to design the control strategy by predicting attacker actions based on Stcakelberg game to ensure the system stability under hybrid attacks.Another technical difficulty lies in establishing the conditions for mean-square asymptotic stability due to the complexity of the attack scenarios Finally,simulations on an unstable batch reactor system under hybrid attacks demonstrate the effectiveness of the proposed strategy. 展开更多
关键词 Stackelberg game networked control systems Hybrid attacks DoS attack FDI attack
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