A stochastic hybrid algorithm for robust global almost sure synchronization on the circle: All-to-all communication

A stochastic hybrid algorithm for guaranteeing global almost sure synchronization of a finite number of agents evolving on the circle is presented. We assume all-to-all communication where every agent has access to the same aggregate quantity corresponding to an average of the position of the agents. The lack of robustness of deterministic algorithms to adversaries and slow convergence properties of stochastic gossip algorithms are overcome by using a stochastic hybrid feedback.