一类离散时间异构多智能体系统有向图下的一致性分析
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摘要
研究了离散时间一阶二阶混合的异构多智能体系统有向通信下的一致性问题。首先,对该系统内的个体分别提出了相应的一致性协议。针对该异构系统不满足离散时间系统研究中凸性要求的问题,本文引入了一个非奇异变换,采用非负矩阵理论和一致性理论,分别分析得出了系统在固定和动态拓扑下实现一致性的充分条件。当通信拓扑包含生成树,采样时间和控制参数在一定范围内取值系统将获得一致性,该范围取决于通信拓扑的度矩阵。最后,通过仿真对该结论进行了验证。
The consensus problem for a class of discrete-time heterogeneous multi-agent system composed of first-order and second-order agents in directed topology is investigated.Firstly,two consensus protocols are constructed.Because the convexity conditions can not be satisfied in this system,a non-singular transformation is imposed on the system.Then,based on the theory of the nonnegative matrix and the consensus theory,the sufficient conditions for achieving consensus are obtained in fixed and dynamical switching topologies.When the communication topology contains the spanning tree,and sampling time and control parameters can satisfy some conditions,the system will achieve consensus.Finally,numerical simulations are shown to demonstrate the theoretical results.
The consensus problem for a class of discrete-time heterogeneous multi-agent system composed of first-order and second-order agents in directed topology is investigated.Firstly,two consensus protocols are constructed.Because the convexity conditions can not be satisfied in this system,a non-singular transformation is imposed on the system.Then,based on the theory of the nonnegative matrix and the consensus theory,the sufficient conditions for achieving consensus are obtained in fixed and dynamical switching topologies.When the communication topology contains the spanning tree,and sampling time and control parameters can satisfy some conditions,the system will achieve consensus.Finally,numerical simulations are shown to demonstrate the theoretical results.
引文
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[2]Olfati-Saber R,Murray R M.Consensus problems in networks of agents with switching topology and time-delays[J].IEEE Trans.on Automatic Control,2004,49(9):1520-1533.
[3]Ren W,Beard R W.Consensus seeking in multi-agent systems under dynamically changing interaction topologies[J].IEEE Trans.on Automatic Control,2005,50(5):655-661.
[4]Xiao F,Wang L.Consensus problems for high-dimensional multi-agent systems[J].IET Control Theory&Applications,2007,1(3):830-837.
[5]Zhu M,Martinez S.Discrete-time dynamic average consensus[J].Automatica,2010,46(2):322-329.
[6]He W,Cao H.Consensus control for high-order multi-agent systems[J].IET Control Theory and Applications,2011,5(1):231-239.
[7]Xi J X,Shi Z Y,Zhong Y S.Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems[J].Physica A,2012,391(7):5839-5849.
[8]You K Y,Li Z K,Xie L H.Consensus condition for linear multi-agent systems over randomly switching topologies[J].Automatica,2013,49(8):3125-3132.
[9]Zheng Y,Zhu Y,Wang L.Consensus of heterogeneous multi-agent systems[J].IET Control Theory and Application,2011,16(5):1881-1888.
[10]Zhu Y K,Guan X P,Luo X Y.Finite-time consensus of heterogeneous multi agent systems[J].Chinese Physics B,2013,22(3):0389011-0389016.
[11]Zheng Y S,Wang L.Finite-time consensus of heterogeneous multiagent systems with and without velocity measurements[J].Systems&Control Letters,2012,61(7):871-878.
[12]Liu C L,Liu F.Stationary consensus of heterogeneous multi-agent systems with bounded communication delays[J].Automatica,2011,47(5):2130-2133.
[13]Yin X X,Yue D,Hu S L.Distributed event-triggered control of discrete-time heterogeneous multi agent systems[J].Journal of the Franklin Institute,2013,350(1):651-669.
[14]Zhu M,Martinez S.Discrete time dynamic average consensus[J].Automatica,2010,46(2):322-329.
[15]Wolfowitz J.Products of indecomposable,aperiodic,stochastic matrices[J].Proc.of the Amer.Math.Soc,1963,15(6):733-736.
[16]Chen Y,Lv J,Yu X.Robust consensus of discrete time multiagent systems with time-varying delays[J].Science China Technological Sciences,2011:54(8):2014-2023.
[17]Chen Y,Lv J H,Lin Z L.Consensus of discrete-time multiagent systems with transmission nonlinearity[J].Automatica,2013,49(3):1768-1775.