Scalable resetting algorithms for synchronization of pulse-coupled oscillators over rooted directed graphs

Javed, Muhammad Umar; Poveda, Jorge I.; Chen, Xudong

doi:10.1016/j.automatica.2021.109807

Cited by 5 publications

(12 citation statements)

References 37 publications

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“…The problem of global synchronization of PCOs using stochastic resetting algorithms has also been investigated in the literature [2], [3], [17]- [19]. Our study on the problem, as well as the main results established in the paper, are different from the ones in those existing works, as we elaborate below.…”

Section: Vertex-triggeringmentioning

confidence: 89%

“…See Figure 2 for an illustration of both models. Note that our previous work [2] has also considered edge-triggering. An advantage of "vertex-triggering" over "edge-triggering" is that the former requires a less number of Bernoulli random variables drawn at a time, making it easier for the agents to implement the resetting algorithm.…”

Section: Vertex-triggeringmentioning

confidence: 99%

“…Synchronization of PCOs using deterministic resetting algorithms has been widely investigated in the literature, and we refer the reader to [2], [4]- [16] and references therein. However, in none of these works global synchronization is shown to be achieved over all rooted digraphs using deterministic resetting algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…[4], [14], [15]) or almost global convergence (e.g. [12], [13], [16]) while other works have restrictions on the underlying digraphs [2], [5]- [11]. Recently, we have shown in [2] that a certain deterministic binary resetting algorithm cannot achieve global synchronization over all rooted digraphs.…”

Section: Introductionmentioning

confidence: 99%

“…[12], [13], [16]) while other works have restrictions on the underlying digraphs [2], [5]- [11]. Recently, we have shown in [2] that a certain deterministic binary resetting algorithm cannot achieve global synchronization over all rooted digraphs. Whether or not there exists a deterministic resetting algorithm that can achieve global synchronization of PCOs over all rooted digraphs still remains open.…”

Section: Introductionmentioning

confidence: 99%

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A Stochastic Binary Vertex-Triggering Resetting Algorithm for Global Synchronization of Pulse-Coupled Oscillators

Javed¹,

Poveda²,

Chen³

2022

Preprint

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In this paper, we propose a novel stochastic binary resetting algorithm for networks of pulse-coupled oscillators (or, simply, agents) to reach global synchronization. The algorithm is simple to state: Every agent in a network oscillates at a common frequency. Upon completing an oscillation, an agent generates a Bernoulli random variable to decide whether it sends pulses to all of its out-neighbours or it stays quite. Upon receiving a pulse, an agent resets its state by following a binary phase update rule. We show that such an algorithm can guarantee global synchronization of the agents almost surely as long as the underlying information flow topology is a rooted directed graph. The proof of the result relies on the use of a stochastic hybrid dynamical system approach. Toward the end of the paper, we present numerical demonstrations for the validity of the result and, also, numerical studies about the times needed to reach synchronization for various information flow topologies.

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