Leader-Following Discrete Group Consistency for multi-agent systems with Smart Leaders

This paper provides insights into the conditions under which a multi-agent system equipped with the smart leader achieves leader-following group consensus, with a particular emphasis on the advantages of this mechanism in a discrete-time framework. Under the discrete-time setting, the system is able to more precisely control the time points for information updating and decision making, while the grouping consistency mechanism allows agents within groups to quickly reach a consistent state at discrete time points through local information exchanges, thus facilitating efficient collaboration within subgroups. At the same time, the smart leader, as the hub of the whole system, is able to instantly obtain and process the feedback information from each subgroup, dynamically adjust its behaviour and decision-making with the help of precise control at discrete time points, and provide more accurate and timely guidance direction for the followers. Numerical simulations are used to visualise the validity and feasibility of the aforementioned theoretical results.