Scalable Resetting Algorithms for Synchronization of Pulse-Coupled Oscillators over Rooted Directed Graphs
Scalable Resetting Algorithms for Synchronization of Pulse-Coupled Oscillators over Rooted Directed Graphs
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DOI：
10.1016/j.automatica.2021.109807
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
M. Javed;J. Poveda;Xudong Chen
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文献类型：
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作者：
M. Javed;J. Poveda;Xudong Chen
研究了有向图上脉冲耦合振荡器的鲁棒全局同步问题。众所周知，当有向图强连接时，可以通过使用一类确定性二进制集值重置控制器来实现全局同步（Poveda和Teel， 2019）。然而，对于大规模网络，这些算法是不可扩展的，因为它们的一些调优参数的上界为O 1 N，其中N是代理的数量。本文利用确定性和随机混合动力系统的框架，提出了一些关于具有更一般网络拓扑的PCOs全局同步的新结果，从而解决了这一可扩展性问题。首先，我们建立了类似的确定性二进制重置算法可以在任何根无环有向图上实现鲁棒的全局固定时间同步。此外，在这种情况下，我们表明同步动态现在是可扩展的，因为算法的调谐参数是网络无关的，即O(1)阶。然而，该算法不能进一步扩展到所有有根图。我们通过引入一个反例来建立这个新的不可能结果，该反例具有一个特定的根有向图，无论调优参数如何，都无法实现全局同步。然而，我们表明，如果通过适应Erdös-Renýi类型的随机图模型来修改二进制重置算法，那么所得到的随机重置动态将几乎肯定地保证所有有根图的全局同步，并且动态的调整参数是网络无关的。利用集值混合动力系统的工具研究了复位算法的稳定性和鲁棒性。最后通过数值模拟对主要结果进行了验证。
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 binary set-valued resetting controllers (Poveda and Teel, 2019). However, for large-scale networks, these algorithms are not scalable because some of their tuning parameters have upper bounds of the order O 1 N, where N is the number of agents. This paper resolves this scalability issue by presenting several new results about global synchronization of PCOs with more general network topologies using the frameworks of deterministic and stochastic hybrid dynamical systems. First, we establish that similar deterministic binary 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, ie, of order O (1). However, the algorithms cannot be further extended to all rooted digraphs. We establish this new impossibility result by introducing a counter-example with a particular rooted digraph for which global synchronization cannot be achieved, irrespective of the tuning parameters. Nevertheless, we show that if the binary resetting algorithms are modified by accommodating an Erdös–Renýi type random graph model, then the resulting stochastic resetting dynamics will guarantee global synchronization almost surely for all rooted digraphs and, moreover, the tuning 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.