Couple-Group Consensus for Leader-Following Nonlinear Multi-Agent Systems under Network Attacks and Decay

In this article, the problem of couple-group consensus for the leader-following nonlinear multi-agent systems affected by network attacks and decay is investigated by adaptive state observer methods. Due to the different tasks of multiple subsystems of a multi-agent system, the long communication distance between different subsystems, and the frequent communication during the collaborative process of agents, it is necessary to consider the effects of external network attacks and decay. Firstly, a new control protocol is proposed by Lyapunov function and matrix theory. Based on algebraic graph theory, some sufficient conditions for the network topology are given to ensure that the nonlinear system reaches a group bounded consensus. Then, the nonlinear terms of the agents are approximated by an adaptive neural network algorithm and the network decay rate is obtained by the designed adaptive law. A state observer is designed based on the data obtained by the adaptive algorithm to recover the disturbed signals, thus bringing the system back to group consensus. Finally, a simulation example is given to verify the correctness of the theoretical results.