Resilient Consensus via Weight Learning and Its Application in Fault-Tolerant Clock Synchronization

This article addresses the distributed consensus problem in the presence of faulty nodes. A novel weight learning algorithm (WLA) is introduced such that neither the network connectivity nor a sequence of history records is required to achieve resilient consensus. The critical idea is to dynamically update the interaction weights among neighbors learnt from their credibility measurement. Basically, we define a reward function that is inversely proportional to the state difference to its neighbor, and then adjust the credibility based on the reward derived at the present step and the previous credibility. In such a way, the interaction weights are updated at every step, which integrates the historic information and degrades the influences from faulty nodes. Four classes of faulty nodes are considered, and both fixed and stochastic topologies are involved in this article. Furthermore, we apply this novel approach in a clock synchronization problem. By updating the logical clock skew and offset via the corresponding weight learning algorithms (WLA), the logical clock synchronization is eventually achieved regardless of faulty nodes. Simulations are provided to illustrate the effectiveness of the strategy.