Distributed adaptive consensus and synchronization in complex networks of dynamical systems

In this paper we propose novel distributed adaptive controllers for leaderless synchronization in networks of identical discrete-time dynamical systems. Separate algorithms are developed for the cases of known and unknown control directions. Assuming that the directed network graph is strongly connected, it is proved that all agent outputs converge toward an emerging, unknown in advance, synchronization trajectory. This trajectory is not available for use by the agent's controllers, and its pattern is determined by the internal model built-in in the distributed adaptation mechanism. It is also shown that for each agent the controller parameter estimates are convergent sequences, and the inputs are uniformly bounded signals. The key to obtaining presented results is to construct adaptive algorithms providing l1-boundedness of certain error signals driving the local parameter estimators. The proposed estimators have a non-vanishing step-size.