Leaderless Synchronization of Heterogeneous Oscillators by Adaptively Learning the Group Model

This note addresses the problem of leaderless synchronization in a network of linear heterogeneous oscillators. It is well known that a synchronizing controller can be constructed when a common reference model is available to (some of) the agents. In this note, we show that synchronization can also be achieved without any access to such reference, by letting the agents cooperatively learn a suitable common model, which we refer to as group model. We show that there exists a group model that has the same structure as the oscillators and that the agents can learn its parameters and synchronize to it, by using a combination of consensus dynamics and adaptive regulation. This learning is even possible if the agents do not know their own dynamics, by using adaptive state observers. The distinguishing feature of this approach is making the agents collectively self-organize to their natural group model, instead of making them synchronize to an external reference.