时变复杂动力学网络的同步控制

Synchronization control of a time-varying complex dynamical network

中文关键词  同步  自适应控制  线性反馈  复杂网络  鲁棒性

英文关键词  synchronization  adaptive control  linear feedback  complex networks  robustness

中文摘要

      研究时变复杂动力学网络的同步控制问题. 假定网络模型中的同步轨迹及耦合配置矩阵、内部耦合矩阵的各元素均有界. 当这些界值可以预估或不确定时, 分别应用线性反馈控制和自适应反馈控制策略使该网络实现全局同步. 通过构造Lyapunov函数, 证明了对于任意初始状态的时变复杂动力学网络模型在相应的控制手段下总可以实现渐近同步. 特别是设计的自适应反馈控制策略对网络的拓扑结构、节点间的耦合强度及时滞等因素表现出较强的鲁棒性. 数值仿真证实了上述结论的有效性.

英文摘要

      Synchronization control of a time-varying complex dynamical network model is investigated. We assume that the synchronous trajectories, entries of the coupling configuration matrix and inner-coupling matrix of the model are all bounded. When those bounds are a priori known or uncertain, a linear feedback scheme and an adaptive scheme are applied to globally synchronize the network respectively. By constructing the adequate Lyapunov function, we can always let a dynamical network, no matter how it is initialized, achieve asymptotic synchronization under the corresponding control scheme. In particular, the proposed adaptive control scheme shows a high robustness to the uncertainties in topological structure of network, coupling strength between nodes, time delays, etc. Numerical simulations validate the effectiveness of the proposed approach.