Distributed leaderless synchronisation control for non-linear MASs with both parameter and non-parameter uncertainty terms

In this study, the authors first discuss the adaptive synchronisation control for discrete-time non-linear multi-agent systems (MASs) with parameter and non-parameter uncertainty terms under leaderless strongly connected digraph, which has not been mentioned in the existing literature. To cope with these two kinds of uncertainties, a state variable is used as an auxiliary tool to compensate for the non-parameter uncertainties, meanwhile, a new dead zone is constructed to ensure the boundedness of the estimated values of the unknown parameters. Based on the local information within the neighbourhood, distributed adaptive synchronisation protocols are designed. Moreover, they strictly prove that the designed adaptive control protocols can harmonise all agents' dynamics to achieve their synchronisation in theory. At the end of this study, an example is provided to indicate the validness of the proposed control protocols.