Ding Dong, Tang Ze, Park Ju H, Wang Yan, Ji Zhicheng
IEEE Trans Cybern. 2023 Feb;53(2):887-899. doi: 10.1109/TCYB.2022.3168854. Epub 2023 Jan 13.
Synchronization of complex networks with nonlinear couplings and distributed time-varying delays is investigated in this article. Since the mismatched parameters of individual systems, a kind of leader-following quasisynchronization issues is analyzed via impulsive control. To acquire appropriate impulsive intervals, the dynamic self-triggered impulsive controller is devoted to predicting the available instants of impulsive inputs. The proposed controller ensures the control effects while reducing the control costs. In addition, the updating laws of the dynamic parameter is settled in consideration of error bounds to adapt to the quasisynchronization. With the utilization of the Lyapunov stability theorem, comparison method, and the definition of average impulsive interval, sufficient conditions for realizing the synchronization within a specific bound are derived. Moreover, with the definition of average impulsive gain, the parameter variation scheme is extended from the fixed impulsive effects case to the time-varying impulsive effects case. Finally, three numerical examples are given to show the effectiveness and the superiority of proposed mathematical deduction.
本文研究了具有非线性耦合和分布式时变延迟的复杂网络的同步问题。由于各个系统的参数不匹配，通过脉冲控制分析了一种 leader-following 准同步问题。为了获得合适的脉冲间隔，动态自触发脉冲控制器致力于预测脉冲输入的可用时刻。所提出的控制器在降低控制成本的同时确保了控制效果。此外，考虑误差界来确定动态参数的更新律，以适应准同步。利用李雅普诺夫稳定性定理、比较方法和平均脉冲间隔的定义，导出了在特定界内实现同步的充分条件。此外，通过平均脉冲增益的定义，将参数变化方案从固定脉冲效应情况扩展到时变脉冲效应情况。最后，给出了三个数值例子，以说明所提出的数学推导的有效性和优越性。
