Model reference adaptive control of networked systems with state and input delays

Adaptive control strategies have been developed in response to more advanced complex systems and to deal with uncertain systems while maintaining the desired conditions. This paper addresses the networked unknown and unstable heterogeneous systems following a stable reference (leader), which is related to network synchronization. We deliver two different scenarios; each agent both fully communicates to the leader and shares communication among neighborhood agents and the leader. The communication among agents and the leader are weighted using Laplacian-like matrix and the model weight matrix in turn. Also, the state and input delays are induced to the systems to capture the real limited communication while the prediction of the reference signals and the augmented systems are proposed to deal with them. Moreover, the rigorous mathematical foundations of two adaptive laws, the stability analysis, the threshold of network, and the communication network are thoroughly presented. Also, the numerical illustrations of the two scenarios are given to show the effectiveness of the proposed method in the networked system. The results show that for both scenarios working on the required setting, the perfect tracking to the leader is guaranteed. Beyond that, the future research would implement the distributed adaptive control-oriented learning of networked system under some faults.