Prescribed performance projective synchronization for unknown complex networks with mismatched dimensions via event-triggered mechanism

In this article, we mainly address the function matrix projective synchronization (FMPS) problem with prescribed performance (PP) between a drive network (DN) with time-varying uncertain coupling, and its corresponding response network (RN) with mismatched dimensions. A new hybrid adaptive learning law is proposed, which consists of a discrete adaptive law designed for unknown time-varying coupling coefficients, and a continuous adaptive law designed for time-invariant coefficients. The proposed work extends the adaptive synchronization control that is originally applicable only with the constant coupling coefficient to the case where the coefficients are time-varying. To ensure the state trajectories of the RN are projectively synchronized to those of the DN while complying with PP constraints, a PP controller is designed. Meanwhile, to reduce the communication load, the event-triggered communication (ETC) mechanism is implemented. Finally, the effectiveness of the designed control scheme, adaptive laws and ETC protocol is validated through simulation.