Asymptotic Consensus for a Nonlinear Multi‐Agent System Modeled by the Wave Partial Differential Equations

ABSTRACT This study addresses the challenge of achieving asymptotic consensus for a nonlinear multi‐agent system described by wave equations. Firstly, a consensus control scheme is designed using only the boundary information of the multi‐agent system. Next, by means of operator semi‐group theory, the existence and uniqueness of the solution for the closed‐loop multi‐agent system are analyzed and proved. A distributed protocol is introduced to approximate the multi‐agent consensus realization to the exponential stability achievement of an error system. Then, the stability of the error system is proven using the Lyapunov stability theory. Finally, the effectiveness of the designed control scheme is verified by a simulation example.