Synchronization of networked higher-order nonlinear systems with unknown dynamics

Synchronization of networked higher-order nonlinear systems with an active leader is considered. For each node, the system has unknown dynamics and unknown external disturbances. The non-autonomous nonlinear dynamics of the leader node is unknown to all the other nodes. The communication network studied in this paper is a weighted directed graph with fixed topology, and it is assumed to be strongly connected. Using neural network technique for controllers of each node to compensate the unknown dynamics, and introducing sliding mode errors to lower the order of the system, we propose a robust adaptive control law, which is totally distributed. Under this control law, all nodes are ultimately synchronized to the leader node with residual errors. Rigorous proof and simulation results justify the effectiveness of the designed control law.