具有时滞的混合阶多智能体系统的组一致性
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摘要
针对由离散时间一阶和二阶智能体组成的混合阶多智能体系统,研究其在固定和切换拓扑结构下受通信时滞影响时的组一致性问题。分别为两类智能体提出组一致性协议,引入模型变换,将闭环系统转化为等价系统。在一定假设条件下,以代数图论、矩阵理论为主要研究工具,分别在固定和切换拓扑结构下给出了混合阶多智能体系统实现渐近组一致性的条件。采用数值仿真对所得结果的有效性进行了验证。
In this paper, the group consensus problem for mixed-order multi-agent systems is studied, where the multiagent system is composed of discrete-time first-and second-order agents under fixed and switching topologies with communication delays. Firstly, group consensus protocols are proposed for two kinds of agents. Then model transformation is introduced to transform the closed-loop system into an equivalent system. Under certain assumptions, algebraic graph theory and matrix theory are utilized to derive conditions under which multi-agent systems with fixed and switching topologies will reach group consensus asymptotically, respectively. Finally, the effectiveness of the results obtained in the paper is validated by numerical simulations.
In this paper, the group consensus problem for mixed-order multi-agent systems is studied, where the multiagent system is composed of discrete-time first-and second-order agents under fixed and switching topologies with communication delays. Firstly, group consensus protocols are proposed for two kinds of agents. Then model transformation is introduced to transform the closed-loop system into an equivalent system. Under certain assumptions, algebraic graph theory and matrix theory are utilized to derive conditions under which multi-agent systems with fixed and switching topologies will reach group consensus asymptotically, respectively. Finally, the effectiveness of the results obtained in the paper is validated by numerical simulations.
引文
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[4]Lin P,Jia Y.Consensus of second-order discrete-time multiagent systems with nonuniform time-delays and dynamically changing topologies[J].Automatica,2009,45(9):2154-2158.
[5]Liu C,Liu F.Stationary consensus of heterogeneous multiagent systems with bounded communication delays[J].Automatica,2011,47(9):2130-2133.
[6]Liu C,Liu F.Dynamical consensus seeking of heterogeneousmulti-agent systems under input delays[J].International Journal of Communication Systems,2012,26(10):1243-1258.
[7]Zhao H,Park J H.Group consensus of discrete-time multiagent systems with fixed and stochastic switching topologies[J].Nonlinear Dynamics,2014,77(4):1297-1307.
[8]Miao G,Ma Q.Group consensus of the first-order multiagent systems with nonlinear input constraints[J].Neurocomputing,2015,161:113-119.
[9]Hu H,Yu W,Xuan Q,et al.Group consensus for heterogeneous multi-agent systems with parametric uncertainties[J].Neurocomputing,2014,142:383-392.
[10]Zheng Y,Wang L.A novel group consensus protocol for heterogeneous multi-agent systems[J].International Journal of Control,2015,88(11):2347-2353.
[11]Feng Y,Zheng W X.Group consensus control for discretetime heterogeneous first-and second-order multiagent systems[J].IET Control Theory&Applications,2018,12(6):753-760.
[12]Yu J,Wang L.Group consensus in multi-agent systems with switching topologies and communication delays[J].Systems&Control Letters,2010,59(6):340-348.
[13]Xia H,Huang T,Shao J,et al.Group consensus of multiagent systems with communication delays[J].Neurocomputing,2016,171:1666-1673.
[14]Wen G,Yu Y,Peng Z,et al.Dynamical group consensus of heterogeneous multiagent systemswith input time delays[J].Neurocomputing,2016,175:278-286.
[15]刘聪,周强,胡晓光.离散时间异质多智能体系统的一致性控制[J].工程科学学报,2016,38(1):143-148.
[16]Wolfowitz J.Products of indecomposable,aperiodic,stochastic matrices[J].Proceedings of the American Mathematical Society,1963,14(5):733-736.
[17]Horn R,Johnson C.Matrix analysis[M].Cambridge,UK:Cambridge University Press,1985.
[18]Xiao F,Wang L.State consensus for multi-agent systems with switching topologies and time-varying delays[J].International Journal of Control,2006,79(10):1277-1284.
[2]Ren W,Beard R W.Consensus seeking in multiagent systems under dynamically changing interaction topologies[J].IEEE Transactions on Automatic Control,2005,50(5):655-661.
[3]Xie G,Wang L.Consensus control for a class of networks of dynamic agents[J].International Journal of Robust and Nonlinear Control,2007,17(10/11):941-959.
[4]Lin P,Jia Y.Consensus of second-order discrete-time multiagent systems with nonuniform time-delays and dynamically changing topologies[J].Automatica,2009,45(9):2154-2158.
[5]Liu C,Liu F.Stationary consensus of heterogeneous multiagent systems with bounded communication delays[J].Automatica,2011,47(9):2130-2133.
[6]Liu C,Liu F.Dynamical consensus seeking of heterogeneousmulti-agent systems under input delays[J].International Journal of Communication Systems,2012,26(10):1243-1258.
[7]Zhao H,Park J H.Group consensus of discrete-time multiagent systems with fixed and stochastic switching topologies[J].Nonlinear Dynamics,2014,77(4):1297-1307.
[8]Miao G,Ma Q.Group consensus of the first-order multiagent systems with nonlinear input constraints[J].Neurocomputing,2015,161:113-119.
[9]Hu H,Yu W,Xuan Q,et al.Group consensus for heterogeneous multi-agent systems with parametric uncertainties[J].Neurocomputing,2014,142:383-392.
[10]Zheng Y,Wang L.A novel group consensus protocol for heterogeneous multi-agent systems[J].International Journal of Control,2015,88(11):2347-2353.
[11]Feng Y,Zheng W X.Group consensus control for discretetime heterogeneous first-and second-order multiagent systems[J].IET Control Theory&Applications,2018,12(6):753-760.
[12]Yu J,Wang L.Group consensus in multi-agent systems with switching topologies and communication delays[J].Systems&Control Letters,2010,59(6):340-348.
[13]Xia H,Huang T,Shao J,et al.Group consensus of multiagent systems with communication delays[J].Neurocomputing,2016,171:1666-1673.
[14]Wen G,Yu Y,Peng Z,et al.Dynamical group consensus of heterogeneous multiagent systemswith input time delays[J].Neurocomputing,2016,175:278-286.
[15]刘聪,周强,胡晓光.离散时间异质多智能体系统的一致性控制[J].工程科学学报,2016,38(1):143-148.
[16]Wolfowitz J.Products of indecomposable,aperiodic,stochastic matrices[J].Proceedings of the American Mathematical Society,1963,14(5):733-736.
[17]Horn R,Johnson C.Matrix analysis[M].Cambridge,UK:Cambridge University Press,1985.
[18]Xiao F,Wang L.State consensus for multi-agent systems with switching topologies and time-varying delays[J].International Journal of Control,2006,79(10):1277-1284.