非连续Lur’e时滞网络的有限时间聚类同步与自适应控制

Adaptive finite-time cluster synchronization for discontinuous Lur’e networks with coupling time-delays

中文关键词  非连续Lur’e系统  有限时间稳定  聚类同步  自适应控制  非光滑控制

英文关键词  discontinuous Lur’e system  finite-time stable  cluster synchronization  adaptive control  nonsmooth control

中文摘要

      本文主要研究一类由非恒同非连续Lur’e系统耦合而成复杂动态网络的自适应有限时间聚类同步问题. 首 先, 通过引入Filippov微分包含理论和测度选择定理, 本文设计了一类有效的牵制反馈控制器, 该控制器只控制当前 聚类中与其他聚类有直接连接的部分节点. 为了有效节省控制成本, 本文基于反馈控制强度设计了一类自适应更新 定律以获取实现网络同步的最优控制强度. 其次, 利用有限时间稳定性理论和Lyapunov稳定性定理, 本文得到时变 时滞耦合和非线性耦合Lur’e网络实现有限时间聚类同步的判定条件, 并给出该网络达到聚类同步的收敛时间估计. 最后, 通过一个算例仿真验证了本控制方案和同步判据的有效性及正确性.

英文摘要

      This article investigates the problem of adaptive finite-time cluster synchronization of complex dynamic network which is coupled by nonidentical discontinuous Lur’e systems. Firstly, by introducing the Filippov differential inclusion theory and the measurable selection theorem, an effective pinning feedback controller is designed, which only imposed on the Lur’e systems in current cluster that are directly connected to the other clusters. In order to effectively save the control costs, a type of adaptive updating laws is designed so as to acquire some optimal control strengths for the network synchronization. Secondly, by applying the finite-time stability theory and Lyapunov stability theorem, the cluster synchronization criteria for the time-varying delay and nonlinearly coupled Lur’e network in finite time are obtained. In addition, the settling time for the cluster synchronization of the Lur’e network is intelligently estimated. Finally, a numerical simulation is given to verify the validity and correctness of the proposed control scheme and the synchronization criteria.