Clock Synchronization With Unknown and Unmodeled Disturbances Over Distributed Networks

Abstract

The clock synchronization problem has garnered significant attention in the field of multiagent systems due to its aim of establishing a common and reliable framework for facilitating cooperation among different agents. In contrast to previous studies, our primary focus lies in addressing the following question: When we lack prior knowledge about disturbances, what synchronization performance can we achieve compared to a hindsight-based approach? To tackle this challenge, we introduce the concept of regret as a metric to model and quantify our problem, independent of any assumptions regarding disturbances. We define regret as the measure of deviation from an ideal synchronization outcome. Furthermore, we prove that the problem inherently possesses a lower bound of regret, which remains unaffected by disturbances. By appropriately setting the regret requirement, we can transform the problem into an $\mathcal {H}_\infty$ optimal control problem equivalently, which allows us to determine the corresponding synchronization strategy. Through simulations, we validate the effectiveness of our method, demonstrating its superiority over existing approaches.