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Consensus Problem In Multi-Agent Systems

Posted on:2010-09-11Degree:DoctorType:Dissertation
Country:ChinaCandidate:W YangFull Text:PDF
GTID:1118360275954676Subject:Control theory and control engineering
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In recent years, with the fast development of distributed networks and multi-agent systems, the cooperative and coordinated control has been a hot area of research. As the basis of the cooperative control of multi-agents, consensus problem attracts much attention from many different fields. In a multi-agent system,"consensus"means that some of the agents'states reach at the same values, and consensus algorithm is a protocol for agents reach consensus based on local information. This thesis focuses on consensus algorithms with time delay and estimation problem based on consensus. Moreover, we investigate the consensus problem in complex networks.The main contributions of this dissertation are summarized as follows:Investigation on consensus algorithms with time delay.Unlike the methods in literatures, we firstly adopt a method in frequency domain to analyze the second order non-commensurate consensus algorithm with time delay by transferring the time delay system to a feedback interconnection of a linear time-invariant plant and a bounded operator. We get the time-invariant and time-varying delay bound, respectively, and we also obtain the conditions for guaranteeing the system stability. The results show that if the network contains a spanning tree and the system gain satisfies a certain condition with the time delay is less than the derived bound, then the whole system reaches on consensus. Moreover, we get another time-independent stability result for the time-invariant delay system. Finally, we extend all the results of second order consensus algorithms to higher order systems.Investigation on consensus estimation. Existing works on estimation over sensor networks assume the network needs to be complete connected. As a result, many communications between the sensors are needed. Here, we focus on studying distributed estimation problem in sensor network, and designing optimal control laws to help the optimal estimation with minimal energy consumption. Based on the classic LQG control, we propose a distributed estimation algorithm based on consensus, and furthermore design the algorithm for the case that only some of the sensors can measure the state of the underlying process. We get an upper bound for system estimation error covariance matrix which depends on the network Laplacian matrix and noise covariance matries. The results show that, when the network is connected, and the ratio of the maximal eigenvalue to the second smallest eigenvalue of the Laplacian matrix is less than a certain value, the error converges to a finite value. Furthermore, the simulation results show that the measurement noises have much more influence on the estimation error than the system noises. Moreover, the network topologies have different influences on the estimation error, and the period graph has the largest estimation error since its ratio of the maximal eigenvalue to the second smallest eigenvalue of the Laplacian matrix is the largest.Investigation on the consensus filter in complex networks. We implement the consensus filter into complex networks and find that the convergence speed of consensus algorithms can be largely enhanced by randomly rewiring a very small number of links during the network evolution from the regular lattice to the small world network, and finally the complete network. The simulation result also shows that the convergence speed of the algorithm has close relationship to the second smallest eigenvalue of the network Laplacian but rarely influenced by the system noises.Investigation on the consensus algorithm in heterogeneous networks. The existing work all considers the uniform agents. However, the agents are heterogeneous in reality. We propose a heterogeneous network model which is closer to the real life based on the classic Vicsek model. The simulation results show that the heterogeneity is benefit for the consensus, and only those"leaders"in the heterogeneous network can reach consensus, then the remaining agents can converge to consensus. Moreover, we adopt two pinning control schemes (random pinning and specific pinning) to the heterogeneous network to make the whole network converges to a designed value. We find that when the heterogeneity of the network is very strong, the convergence effect of specific pinning is much better than the random one. However, when the heterogeneity is weak, both pinning schemes act almost the same.
Keywords/Search Tags:consensus, multi-agent system, cooperative control, time delay, estimation, heterogeneity, complex network
PDF Full Text Request
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