IEEE Trans Cybern. 2022 Sep;52(9):9490-9503. doi: 10.1109/TCYB.2021.3061700. Epub 2022 Aug 18.
In nature and human society, successive lag synchronization (SLS) is an important synchronization phenomenon. Compared with other synchronization patterns, the control theory of SLS is very lacking. To this end, we first introduce a complex dynamical network model with distributed delayed couplings, and design both the linear feedback pinning control and adaptive feedback pinning control to push SLS to the desired trajectories. Second, we obtain a series of sufficient conditions to achieve SLS to a desired trajectory with global stability. What is more, the control flow of SLS is given to show how to pick the pinned nodes accurately and set the feedback gains as well. Finally, since time-varying delay is common, we extend the constant time delay in SLS to be time varying. We find that the proposed pinning control schemes are still feasible if the coupling terms are appropriately adjusted. The theoretical results are verified on a neural network and the coupled Chua's circuits.
在自然界和人类社会中，连续滞后同步（SLS）是一种重要的同步现象。与其他同步模式相比，SLS 的控制理论非常缺乏。为此，我们首先引入了一个具有分布式时滞耦合的复杂动力网络模型，并设计了线性反馈钉扎控制和自适应反馈钉扎控制，以将 SLS 推向期望的轨迹。其次，我们得到了一系列实现 SLS 到期望轨迹的全局稳定性的充分条件。更重要的是，给出了 SLS 的控制流程，以展示如何准确地选择固定节点以及设置反馈增益。最后，由于时变延迟很常见，我们将 SLS 中的常时滞扩展为时变。我们发现，如果适当调整耦合项，所提出的钉扎控制方案仍然是可行的。理论结果在神经网络和耦合 Chua 电路上得到了验证。
