Secure Synchronization of Heterogeneous Pulse-Coupled Oscillators

TL;DR

Two resilient synchronization protocols are developed in this paper by adapting the real-valued mean-subsequence reduced (MSR) algorithm to pulse-based interactions for synchronization of heterogeneous pulse-coupled oscillators (PCOs), where some oscillators might be faulty or malicious.

Abstract

In this paper, we consider the synchronization of heterogeneous pulse-coupled oscillators (PCOs), where some of the oscillators might be faulty or malicious. The oscillators interact through identical pulses at discrete instants and evolve continuously with different frequencies otherwise. Despite the presence of misbehaviors, benign oscillators aim to reach synchronization. To achieve this objective, two resilient synchronization protocols are developed in this paper by adapting the real-valued mean-subsequence reduced (MSR) algorithm to pulse-based interactions. The first protocol relies on packet-based communication to transmit absolute frequencies, while the second protocol operates purely with pulses to calculate relative frequencies. In both protocols, each normal oscillator periodically counts the received pulses to detect possible malicious behaviors. By disregarding suspicious pulses from its neighbors, the oscillator updates both its phases and frequencies. The paper establishes sufficient conditions on the initial states and graph structure under which resilient synchronization is achieved in the PCO network. Specifically, the normal oscillators can either detect the presence of malicious nodes or synchronize in both phases and frequencies. Additionally, a comparison between the two algorithms reveals a trade-off between relaxed initial conditions and reduced communication burden.

Figures (4)

• Figure 1: Possible cases if node $i$ emits a pulse at time $k$. The blue square represents the node emitting a pulse or making an update at the corresponding time, the gray squares represent other oscillators, and the dashed square is the virtual node $s$.
• Figure 2: A network that is $3$-robust ( leblanc2012resilient).
• Figure 3: The time responses of the phases of normal oscillators, where the red asterisks and blue circles indicate the timings when the attacking pulses are sent from malicious oscillators $1$ and $4$, respectively.
• Figure 4: Maximum difference in initial frequencies for varying initial phase differences among normal oscillators.

Theorems & Definitions (20)

• Definition 1
• Lemma 1: leblanc2013resilient
• Definition 2: Normal containing arc
• Definition 3: Resilient synchronization
• Remark 1
• Lemma 2
• proof
• Definition 4: Virtual containing arc
• Lemma 3
• proof