Adaptive consensus design for swarm systems with Lipschitz nonlinear dynamics

Adaptive consensus design problems for swarm systems with Lipschitz nonlinear dynamics are investigated. An adaptive consensus protocol based on state errors is proposed to obtain adaptive consensus. By using a state decomposition method, adaptive consensus problems of a swarm system are transformed into the asymptotic stabilization problems of a reduced-order subsystem. Then, the structure property of a transformation matrix and the Laplacian matrix, and the Lipschitz condition are utilized to deal with the Lipschitz nonlinear dynamics. Furthermore, an explicit expression of the consensus function of this swarm system and its initial state are presented. Finally, a numerical simulation is proposed to demonstrate the effectiveness of theoretical results.