基于线性矩阵不等式的牵制控制策略分析

研究复杂动力学网络的同步牵制控制问题.通过引入牵制控制,对具有大规模节点网络中的小部分节点实施线性反馈控制策略,使得整个网络的所有节点均达到同步.针对一类一致连结的耦合复杂网络模型,采用线性矩阵不等式的方法给出了实施牵制控制达到同步的充分条件.该条件表明,选择牵制异质网络中度较大的节点可能更容易使得网络实现同步.特别地,对于特定的内部耦合矩阵和足够大的耦合强度,只要对网络中任一节点实施牵制控制就可以保证整个网络同步的实现.数值仿真验证了上述结论的有效性.

Analysis of pinning control strategies based on linear matrix inequality

The synchronization control problem of complex dynamical networks is considered by means of pinning strategy,that is,applying local linear feedback control to a small fraction of a large-scale network to ensure synchronization of the whole network.For a uniform complex dynamical network,linear matrix inequality(LMI) is adopted to derive a sufficient condition of synchronization.Analytical result shows that synchronization of heterogeneous networks may be easily reached by pinning nodes with big degree.Specifically,for a particular inner-coupling matrix,a sufficiently large coupling strength will ensure the whole network to achieve synchronization by pinning any one node of the network.Numerical simulations verify the analytical results.