奇异Lur'e网络的自适应牵制聚类同步控制

本文分别研究了由奇异和非奇异Lur''e系统组成的具有多种耦合方式时滞复杂动态网络的聚类同步问题. 通过设计一类牵制反馈控制器, 仅控制当前聚类中与其它聚类有直接连接的Lur''e系统, 从而有效减少控制器个数同时降低控制成本. 考虑到网络具有多种耦合方式, 本文合理构造Lyapunov 泛函, 并有效利用扇形条件、非线性函数类概念、S过程以及Lyapunov 稳定性定理等方法, 分别给出奇异和非奇异Lur''e 动态网络实现聚类同步的判定条件. 此外, 为有效节省控制成本, 针对控制强度设计一类自适应更新定律, 从而得到网络实现聚类同步的最优控制强度. 最后, 为了验证所得聚类同步判定条件和控制器的有效性, 对一类典型Lur''e网络聚类同步问题进行了数值仿真.

Cluster synchronization of heterogeneous Lur'e networks via pinning adaptive control

In this paper, the cluster synchronization problem for a kind of delayed complex dynamical networks with multiple couplings composed of heterogeneous and homogeneous Lur''e systems is investigated. By designing a kind of pinning negative feedback controllers, only the Lur''e systems in current clusters which have direct connections with the Lur''e systems in the other clusters are controlled. Considering different types of coupling patterns in the Lur''e networks, an effective Lyapunove functional is constructed and then sufficient conditions for the cluster synchronization of the heterogeneous and homogeneous Lur''e dynamical networks are obtained respectively, according to the sector conditions, the NCF function class, S-procedure and the Lyapunov stability theorem. Furthermore, to decrease the control costs, an adaptive updating law for the pinning feedback control strength is designed. Finally, the effectiveness of the proposed cluster synchronization conditions and the control schemes are verified by a numerical simulation.