论文标题
可扩展的重置算法，用于在有向图上同步脉冲耦合振荡器
Scalable Resetting Algorithms for Synchronization of Pulse-Coupled Oscillators over Rooted Directed Graphs
论文作者
论文摘要
我们研究了脉冲耦合振荡器（PCOS）在有向图上的鲁棒全局同步的问题。众所周知，当挖掘距离紧密连接时，可以使用一类确定性设置值值的复位控制器来实现全局同步。但是，对于大规模网络，这些算法是不可扩展的，因为它们的某些调谐参数具有O（1/N）的上限，其中N是代理的数量。本文通过使用确定性和随机混合动力学系统的更通用的网络拓扑结合PCOS的全局同步，通过在PCOS的全局同步中提出几个新结果来解决此可伸缩性问题。首先，我们确定类似的确定性重置算法可以在任何生根的无环挖掘物中实现稳健，全局和固定时同步。此外，在这种情况下，我们表明同步动力学现在可以扩展，因为算法的调谐参数是独立于网络的，即O（1）顺序。但是，算法不能进一步扩展到所有根生的挖掘物。我们通过引入具有特定根系的挖掘图的反例来建立这种新的不可能结果，而该图无法实现全局同步，而不论重置规则的调整如何。然而，我们表明，如果通过容纳ERDOS-RENYI型随机图模型来修改重置算法，那么所得的随机重置动力学将几乎可以肯定地确保所有根生根的图形全局同步，而且，对于所有动力学的可调节参数，动力学的可调参数都是独立的。使用设置值混合动力学系统的工具研究了重置算法的稳定性和鲁棒性。在本文的末尾提供了数值模拟，以证明主要结果。
We study the problem of robust global synchronization of pulse-coupled oscillators (PCOs) over directed graphs. It is known that when the digraphs are strongly connected, global synchronization can be achieved by using a class of deterministic set-valued reset controllers. However, for large-scale networks, these algorithms are not scalable because some of their tuning parameters have upper bounds of the order of O(1/N), where N is the number of agents. This paper resolves this scalability issue by presenting several new results in the context of global synchronization of PCOs with more general network topologies using deterministic and stochastic hybrid dynamical systems. First, we establish that similar deterministic resetting algorithms can achieve robust, global, and fixed-time synchronization in any rooted acyclic digraph. Moreover, in this case we show that the synchronization dynamics are now scalable as the tuning parameters of the algorithm are network independent, i.e., of order O(1). However, the algorithms cannot be further extended to all rooted digraphs. We establish this new impossibility result by introducing a counterexample with a particular rooted digraph for which global synchronization cannot be achieved, irrespective of the tuning of the reset rule. Nevertheless, we show that if the resetting algorithms are modified by accommodating an Erdos-Renyi type random graph model, then the resulting stochastic resetting dynamics will guarantee global synchronization almost surely for all rooted digraphs and, moreover, the tunable parameters of the dynamics are network independent. Stability and robustness properties of the resetting algorithms are studied using the tools from set-valued hybrid dynamical systems. Numerical simulations are provided at the end of the paper for demonstration of the main results.
