具有切换拓扑的动态复杂网络的同步控制

Synchronization Control for Complex Dynamical Networks with Switching Topology

针对一类耦合拓扑集合给定的动态复杂网络模型,研究在网络通过给定耦合拓扑集合中的任一拓扑进行耦合均不能实现同步时,如何通过在给定耦合拓扑集合中拓扑之间的切换来实现网络的同步。通过构建合适的Lyapunov函数给出了网络实现同步所需要满足的条件和相应的耦合拓扑切换规则。与已有的研究结果相比,本文所研究的动态复杂网络的耦合拓扑矩阵具有更为一般的形式,而且无需满足已有研究成果对耦合拓扑矩阵的限制条件(诸如可同时上三角化以及可同时对角化等条件)。数值仿真结果验证了所给结果的有效性和正确性。

For complex dynamical networks with a pre-given collection of coupled connection topologies, how to achieve synchronization by designing the topological switching law when synchronization cannot be achieved by using any topology alone in this collection is investigated. By constructing an appropriate Lyapunov function, the synchroni- zation criteria for the general connection topology is established and the switching law design is given. Compared with the existing results, the coupled topological matrices can be in more general forms without the restrictions on coupled topological matrices （such as simultaneous triangularizability or diagonalizability）. The simulation results indicate the effectiveness of the proposed results.