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Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer 被引量:1
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作者 Chi Ma Dianbiao Dong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期1039-1050,共12页
This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eli... This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm. 展开更多
关键词 Finite-time control multi-agent systems neural network prescribed performance control time-varying formation control
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Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach
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作者 张晓娇 吴祥 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期137-145,共9页
This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theor... This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results. 展开更多
关键词 contraction theory virtual system bipartite consensus Lurie multi-agent systems
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Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information
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作者 Honghai Wang Qing-Long Han 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第4期878-892,共15页
This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consens... This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems. 展开更多
关键词 Consensus protocol Hurwitz stability multi-agent systems quasi-polynomials time delay
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Hyperbolic Tangent Function-Based Protocols for Global/Semi-Global Finite-Time Consensus of Multi-Agent Systems
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作者 Zongyu Zuo Jingchuan Tang +1 位作者 Ruiqi Ke Qing-Long Han 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第6期1381-1397,共17页
This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global ... This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols. 展开更多
关键词 Consensus protocol finite-time consensus hyper-bolic tangent function multi-agent systems.
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Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems
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作者 Xia Li Zhanyou Ma +3 位作者 Zhibao Mian Ziyuan Liu Ruiqi Huang Nana He 《Computers, Materials & Continua》 SCIE EI 2024年第3期4129-4152,共24页
Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as s... Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system. 展开更多
关键词 Model checking multi-agent systems fuzzy epistemic interpreted systems fuzzy computation tree logic transformation algorithm
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Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem
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作者 Yangyang Qian Lu Liu 《Journal of Automation and Intelligence》 2024年第2期119-127,共9页
This paper investigates the robust cooperative output regulation problem for a class of heterogeneousuncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizingthe in... This paper investigates the robust cooperative output regulation problem for a class of heterogeneousuncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizingthe internal model approach and the adaptive control technique, a distributed adaptive internal model isconstructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed ofa distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggeringmechanism is proposed, in which each agent updates its control input at its own triggering time instants. It isshown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solvedwithout requiring either the global information associated with the communication topology or the bounds ofthe uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided toillustrate the effectiveness of the proposed control strategy. 展开更多
关键词 Adaptive control Event-triggered control Internal model multi-agent systems Output regulation
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Robust adaptive leaderless consensus of unknown non-minimum phase linear multi-agent systems subject to disturbances and/or unmodeled dynamics
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作者 Wenji Cao Gang Feng 《Journal of Automation and Intelligence》 2024年第2期92-100,共9页
This article investigates the problem of robust adaptive leaderless consensus for heterogeneous uncertain nonminimumphase linear multi-agent systems over directed communication graphs. Each agent is assumed tobe of un... This article investigates the problem of robust adaptive leaderless consensus for heterogeneous uncertain nonminimumphase linear multi-agent systems over directed communication graphs. Each agent is assumed tobe of unknown nominal dynamics and also subject to external disturbances and/or unmodeled dynamics. Anovel distributed robust adaptive control strategy is proposed. It is shown that the robust adaptive leaderlessconsensus problem is solved with the proposed control strategy under some sufficient conditions. Two examplesare provided to demonstrate the efficacy of the proposed control strategy. 展开更多
关键词 Cooperative control Non-minimum phase Leaderless consensus multi-agent systems Robust adaptive control
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Distributed Adaptive Predefined-Time Bipartite Containment Algorithm for Nonlinear Multi-Agent Systems with Actuator Faults
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作者 Honghao Wu 《Journal of Electronic Research and Application》 2024年第6期15-25,共11页
Distributed adaptive predefined-time bipartite containment for a class of second-order nonlinear multi-agent systems are studied with actuator faults.The communication topology of multi-agent systems is fixed and dire... Distributed adaptive predefined-time bipartite containment for a class of second-order nonlinear multi-agent systems are studied with actuator faults.The communication topology of multi-agent systems is fixed and directed.To ensure that followers can reach the convex hull spanned by leaders under the conditions of actuator faults,the sliding mode method is introduced.Control protocol for multi-agent systems demonstrates its effectiveness.Finally,simulations are provided to verify the effectiveness of the proposed algorithm. 展开更多
关键词 Actuator faults Adaptive bipartite containment control Nonlinear multi-agent systems Predefined-time
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Robust Consensus Tracking Control of Uncertain Multi-Agent Systems With Local Disturbance Rejection 被引量:3
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作者 Pan Yu Kang-Zhi Liu +3 位作者 Xudong Liu Xiaoli Li Min Wu Jinhua She 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第2期427-438,共12页
In this paper,a new distributed consensus tracking protocol incorporating local disturbance rejection is devised for a multi-agent system with heterogeneous dynamic uncertainties and disturbances over a directed graph... In this paper,a new distributed consensus tracking protocol incorporating local disturbance rejection is devised for a multi-agent system with heterogeneous dynamic uncertainties and disturbances over a directed graph.It is of two-degree-of-freedom nature.Specifically,a robust distributed controller is designed for consensus tracking,while a local disturbance estimator is designed for each agent without requiring the input channel information of disturbances.The condition for asymptotic disturbance rejection is derived.Moreover,even when the disturbance model is not exactly known,the developed method also provides good disturbance-rejection performance.Then,a robust stabilization condition with less conservativeness is derived for the whole multi-agent system.Further,a design algorithm is given.Finally,comparisons with the conventional one-degree-of-freedombased distributed disturbance-rejection method for mismatched disturbances and the distributed extended-state observer for matched disturbances validate the developed method. 展开更多
关键词 Directed graph distributed control disturbance rejection dynamic uncertainties multi-agent systems robust control
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Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems 被引量:2
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作者 Wenji Cao Lu Liu Gang Feng 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第4期997-1008,共12页
This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs.The dynamics of followers are allowed to be non-mini... This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs.The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees.This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree.A distributed adaptive pole placement control scheme is developed,which consists of a distributed observer and an adaptive pole placement control law.It is shown that under the proposed distributed adaptive control scheme,all signals in the closed-loop system are bounded and the outputs of all the followers track the output of the leader asymptotically.The effectiveness of the proposed scheme is demonstrated by one practical example and one numerical example. 展开更多
关键词 Adaptive pole placement control heterogeneous multi-agent systems leader-following output consensus non-minimum phase
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Practical bipartite consensus for multi-agent systems:A barrier function-based adaptive sliding-mode control approach 被引量:3
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作者 Boda Ning Qing-Long Han Xiaohua Ge 《Journal of Automation and Intelligence》 2023年第1期14-19,共6页
This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite stead... This paper is concerned with bipartite consensus tracking for multi-agent systems with unknown disturbances.A barrier function-based adaptive sliding-mode control(SMC)approach is proposed such that the bipartite steady-state error is converged to a predefined region of zero in finite time.Specifically,based on an error auxiliary taking neighboring antagonistic interactions into account,an SMC law is designed with an adaptive gain.The gain can switch to a positive semi-definite barrier function to ensure that the error auxiliary is constrained to a predefined neighborhood of zero,which in turn guarantees practical bipartite consensus tracking.A distinguished feature of the proposed controller is its independence on the bound of disturbances,while the input chattering phenomenon is alleviated.Finally,a numerical example is provided to verify the effectiveness of the proposed controller. 展开更多
关键词 Barrier functions Practical bipartite consensus multi-agent systems Signed graphs Sliding-mode control
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Lyapunov-Based Output Containment Control of Heterogeneous Multi-Agent Systems With Markovian Switching Topologies and Distributed Delays 被引量:1
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作者 Haihua Guo Min Meng Gang Feng 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第6期1421-1433,共13页
This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topolog... This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller. 展开更多
关键词 Heterogeneous multi-agent systems Lyapunov method Markovian switching topologies output containment control time delays
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Consensus of networked control multi-agent systems using a double-layer encryption scheme 被引量:1
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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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Group-Consensus of Hierarchical Containment Control for Linear Multi-Agent Systems
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作者 Jingshu Sang Dazhong Ma Yu Zhou 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第6期1462-1474,共13页
The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection a... The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection and maintenance. Therefore, this paper is concerned with an extensional containment control issue, hierarchical containment control. It aims to enable a multitude of followers achieving a novel cooperation in the convex hull shaped by multiple leaders. Firstly, by constructing the three-layer topology, large-scale networks are decoupled. Then,under the condition of directed spanning group-tree, a class of dynamic hierarchical containment control protocol is designed such that the novel group-consensus behavior in the convex hull can be realized. Moreover, the definitions of coupling strength coefficients and the group-consensus parameter in the proposed dynamic hierarchical control protocol enhance the adjustability of systems. Compared with the existing containment control strategy, the proposed hierarchical containment control strategy improves dynamic control performance. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed hierarchical control protocol. 展开更多
关键词 Group-consensus behavior hierarchical containment control linear multi-agent systems three-layer topology
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Team-based fixed-time containment control for multi-agent systems with disturbances
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作者 赵小文 王进月 +1 位作者 赖强 刘源 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期281-292,共12页
We investigate the fixed-time containment control(FCC)problem of multi-agent systems(MASs)under discontinuous communication.A saturation function is used in the controller to achieve the containment control in MASs.On... We investigate the fixed-time containment control(FCC)problem of multi-agent systems(MASs)under discontinuous communication.A saturation function is used in the controller to achieve the containment control in MASs.One difference from using a symbolic function is that it avoids the differential calculation process for discontinuous functions,which further ensures the continuity of the control input.Considering the discontinuous communication,a dynamic variable is constructed,which is always non-negative between any two communications of the agent.Based on the designed variable,the dynamic event-triggered algorithm is proposed to achieve FCC,which can effectively reduce controller updating.In addition,we further design a new event-triggered algorithm to achieve FCC,called the team-trigger mechanism,which combines the self-triggering technique with the proposed dynamic event trigger mechanism.It has faster convergence than the proposed dynamic event triggering technique and achieves the tradeoff between communication cost,convergence time and number of triggers in MASs.Finally,Zeno behavior is excluded and the validity of the proposed theory is confirmed by simulation. 展开更多
关键词 fixed-time containment control dynamic event-triggered strategy team-based triggered strategy multi-agent systems
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Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises
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作者 Chuanjian Li Xiaofeng Zong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第3期737-748,共12页
A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two s... A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples. 展开更多
关键词 Additive noises consensus control containment control group hybrid coordination control multi-agent systems(MASs) TIME-DELAYS
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A survey on multi-agent reinforcement learning and its application
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作者 Zepeng Ning Lihua Xie 《Journal of Automation and Intelligence》 2024年第2期73-91,共19页
Multi-agent reinforcement learning(MARL)has been a rapidly evolving field.This paper presents a comprehensive survey of MARL and its applications.We trace the historical evolution of MARL,highlight its progress,and di... Multi-agent reinforcement learning(MARL)has been a rapidly evolving field.This paper presents a comprehensive survey of MARL and its applications.We trace the historical evolution of MARL,highlight its progress,and discuss related survey works.Then,we review the existing works addressing inherent challenges and those focusing on diverse applications.Some representative stochastic games,MARL means,spatial forms of MARL,and task classification are revisited.We then conduct an in-depth exploration of a variety of challenges encountered in MARL applications.We also address critical operational aspects,such as hyperparameter tuning and computational complexity,which are pivotal in practical implementations of MARL.Afterward,we make a thorough overview of the applications of MARL to intelligent machines and devices,chemical engineering,biotechnology,healthcare,and societal issues,which highlights the extensive potential and relevance of MARL within both current and future technological contexts.Our survey also encompasses a detailed examination of benchmark environments used in MARL research,which are instrumental in evaluating MARL algorithms and demonstrate the adaptability of MARL to diverse application scenarios.In the end,we give our prospect for MARL and discuss their related techniques and potential future applications. 展开更多
关键词 Benchmark environments multi-agent reinforcement learning multi-agent systems Stochastic games
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The First Five Years of a Phase Theory for Complex Systems and Networks
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作者 Dan Wang Wei Chen Li Qiu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第8期1728-1743,共16页
In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical in... In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years. 展开更多
关键词 Consensus and synchronization matrix phases multi-agent systems phase theory sectored real lemma small phase theorem.
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Formation-Containment Control Using Dynamic Event-Triggering Mechanism for Multi-Agent Systems 被引量:21
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作者 Amir Amini Amir Asif Arash Mohammadi 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第5期1235-1248,共14页
The paper proposes a novel approach for formationcontainment control based on a dynamic event-triggering mechanism for multi-agent systems.The leader-leader and follower-follower communications are reduced by utilizin... The paper proposes a novel approach for formationcontainment control based on a dynamic event-triggering mechanism for multi-agent systems.The leader-leader and follower-follower communications are reduced by utilizing the distributed dynamic event-triggered framework.We consider two separate sets of design parameters:one set comprising control and dynamic event-triggering parameters for the leaders and a second set similar to the first one with different values for the followers.The proposed algorithm includes two novel stages of codesign optimization to simultaneously compute the two sets of parameters.The design optimizations are convex and use the weighted sum approach to enable a structured trade-off between the formation-containment convergence rate and associated communications.Simulations based on non-holonomic mobile robot multi-agent systems quantify the effectiveness of the proposed approach. 展开更多
关键词 Co-design convex optimization dynamic event-triggered schemes formation-containment control multi-agent systems
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Secure Impulsive Synchronization in Lipschitz-Type Multi-Agent Systems Subject to Deception Attacks 被引量:16
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作者 Wangli He Zekun Mo +1 位作者 Qing-Long Han Feng Qian 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第5期1326-1334,共9页
Cyber attacks pose severe threats on synchronization of multi-agent systems.Deception attack,as a typical type of cyber attack,can bypass the surveillance of the attack detection mechanism silently,resulting in a heav... Cyber attacks pose severe threats on synchronization of multi-agent systems.Deception attack,as a typical type of cyber attack,can bypass the surveillance of the attack detection mechanism silently,resulting in a heavy loss.Therefore,the problem of mean-square bounded synchronization in multi-agent systems subject to deception attacks is investigated in this paper.The control signals can be replaced with false data from controllerto-actuator channels or the controller.The success of the attack is measured through a stochastic variable.A distributed impulsive controller using a pinning strategy is redesigned,which ensures that mean-square bounded synchronization is achieved in the presence of deception attacks.Some sufficient conditions are derived,in which upper bounds of the synchronization error are given.Finally,two numerical simulations with symmetric and asymmetric network topologies are given to illustrate the theoretical results. 展开更多
关键词 Deception attacks impulsive control multi-agent systems(MASs) SYNCHRONIZATION
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