多重连接网络的有限时间广义同步

Finite-Time Generalized Synchronization of Multi-Linked Networks

针对一类多重连接复杂动态网络,提出了一种实现有限时间广义同步的分散自适应控制策略。值得指出的是,本文的网络模型是由不同状态维数的相似节点组成的且外部耦合矩阵是时变的、非对称的、非耗散的。此外,需要强调的是,与现存的同步策略相比,有限时间广义同步不仅能减少控制成本和估计达到同步的时间,还可描述不同维数节点间的同步现象,这将提高控制策略的可操作性。基于有限时间稳定性理论,严格证明了网络有限时间广义同步控制策略的有效性,并通过数值仿真实例验证了所提结果的可行性和正确性。

The article proposes decentralized adaptive control strategy to realize finite-time generalized syn-chronization for a class of multi-linked complex dynamical networks. It is worth pointing out that our network model is composed of similar nodes with different state dimensions and the outer cou-pling matrix can be time-varying, asymmetric, non-diffusively coupled. In addition, compared to the existing synchronization strategies, finite-time generalized synchronization can not only reduce control costs and estimate the time to achieve synchronization, but also can describe the synchro-nization phenomenon between nodes of different dimensions, which can improve the operability of control strategy. Based on finite-time stability theory, the validness of the control strategy for real-izing the finite-time generalized synchronization of our multi-linked networks is rigorously proved, and the numerical example is provided to illustrate the effectiveness and correctness of the pro-posed theoretical result.