Adaptive fuzzy control for synchronization of second-order nonlinear systems with prescribed performance

In this paper, an adaptive fuzzy control scheme is presented for synchronization of second-order nonlinear systems with prescribed transient and steady synchronization error bounds. Fuzzy logical systems (FLSs) are employed to approximate the unknown nonlinear functions. By using dynamic surface control (DSC) and prescribed performance control techniques, distributed adaptive fuzzy controllers are developed to guarantee that the outputs of all followers synchronize to that of the leader under directed graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SUUB), and the synchronization errors remain in a neighborhood of the origin with the prescribed bounds. Simulation results are presented to show the validity of the proposed approach.