Resilient Synchronization of Pulse-Coupled Oscillators Under Stealthy Attacks

This paper studies a clock synchronization problem for wireless sensor networks employing pulse-based communication when some of the nodes are faulty or even adversarial. The objective is to design resilient distributed algorithms for the nonfaulty nodes to keep the influence of the malicious nodes minimal and to arrive at synchronization in a safe manner. Compared with conventional approaches, our algorithms are more capable in the sense that they are applicable to networks taking noncomplete graph structures. Our approach is to extend the class of mean subsequence reduced (MSR) algorithms from the area of multi-agent consensus. First, we provide a simple detection method to find malicious nodes that transmit pulses irregularly. Then, we demonstrate that in the presence of adversaries avoiding to be detected, the normal nodes can reach synchronization by ignoring suspicious pulses. Two extensions of this algorithm are further presented, which can operate under more adversarial attacks and also with relaxed conditions on the initial phases. We illustrate the effectiveness of our results by numerical examples.