噪声下相互依存网络的自适应H∞异质同步

Adaptive H∞Heterogeneous Synchronization for Interdependent Networks With Noise

针对具有噪声的相互依存复杂动力网络,本文研究了它的局部自适应H∞异质同步问题.该网络由两个具有“一对一”相互依赖关系的子网构成,子网内部耦合和子网间的耦合均含有未知但有界的非线性函数.基于李雅普诺夫稳定性理论、线性矩阵不等式(Linear matrix inequality,LMI)技术和自适应以及H1控制方法,本文提出了使得相互依存网络在外部噪声的干扰下,两个子网各自达到一致的充分条件.这些条件不仅可以保证受扰动的网络获得鲁棒渐近同步而且可以让网络达到一个给定的鲁棒H∞水平.最后的数值模拟验证了提出的方法的有效性以及可行性.

In this paper,local adaptive H_∞ heterogeneous synchronization is investigated for interdependent networks with noise.The network considered consists of two sub-network,which are one-by-one inter-coupled.The unknown but bounded nonlinear functions exist both in the intra-coupling and inter-coupling between the two sub-networks.Based on the Lyapunov stability theory,linear matrix inequality(LMI),and adaptive H_∞ control technique,the sufficient conditions are established to lead the sub-networks of the interdependent networks with noise to respective heterogeneous synchronization,which guarantee not only robust asymptotical synchronization for networks with noise but also a prescribed robust H_∞ performance level.Finally,numerical simulations prove the effectiveness and feasibility of the method.