Distributed synchronization control of multi-agent systems with unknown nonlinearities: The case of fixed directed communication topology

This paper revisits the distributed adaptive control problem for synchronization of multi-agent systems where the dynamics of the agents are nonlinear, nonidentical, unknown and subject to external disturbances. The communication topology under consideration is represented by a fixed strongly-connected directed graph. Distributed neural networks are used to approximate the uncertain dynamics and decentralized control protocols using local neighborhood information are proposed to solve the cooperative tracker problem, the problem of synchronization of all follower agents to a leader agent. In particular, we show that, under the proposed decentralized control protocols, the synchronization errors are ultimately bounded and their ultimate bounds can be reduced arbitrarily by choosing the control parameter appropriately.