IEEE Trans Cybern. 2023 Jun;53(6):3926-3938. doi: 10.1109/TCYB.2022.3190413. Epub 2023 May 17.
This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic relationship), which is more pluralistic and practical. Second, a hybrid impulsive controller is designed, which is composed of the feedback control part and the impulsive control part to realize the exponential bipartite synchronization objective. Both positive and negative impulsive effects are considered and the ranges of the impulsive control gain related to the order of Caputo fractional derivative are discussed. In addition, some sufficient conditions for exponential bipartite synchronization of fractional-order multilayer signed networks are obtained by using the signed graph theory, Lyapunov method, and average impulsive interval method. Furthermore, in order to illustrate the practicability of the theoretical results, fractional-order coupled Chua's circuits model and fractional-order power systems built on multilayer signed networks are established and the exponential bipartite synchronization issues are analyzed. Numerical examples and simulations are provided to show the effectiveness of the obtained results.
本文通过混合脉冲控制研究了分数阶双层有向网络的指数偶同步问题。首先，通过整合节点分数动力学、多层网络边以及正负权重（对抗关系），建立了更具多元性和实用性的网络数学模型。其次，设计了一种混合脉冲控制器，由反馈控制部分和脉冲控制部分组成，以实现指数偶同步目标。同时考虑了正负脉冲效应，并讨论了与 Caputo 分数导数阶数相关的脉冲控制增益的范围。此外，利用符号图理论、Lyapunov 方法和平均脉冲间隔方法，获得了分数阶双层有向网络指数偶同步的充分条件。进一步地，为了说明理论结果的实用性，建立了分数阶耦合 Chua 电路模型和基于多层有向网络的分数阶电力系统，并分析了指数偶同步问题。通过数值实例和仿真验证了所得结果的有效性。
