Containment control for heterogeneous multi-agent systems with asynchronous updates

This paper is concerned with the asynchronous containment control problem for heterogeneous multi-agent systems with time-varying delays. Here, asynchrony means that each agent updates the state information by its own clock that is independent of the other agents’ update times, and the update intervals of each agent are not necessarily equispaced. It is assumed that the leaders are stationary, and the followers can be classified into two generic categories: the followers with the first-order dynamics and the followers with second-order dynamics. For different kinds of followers, two distributed containment control protocols are presented to guarantee that all the followers can asymptotically converge into the convex hull formed by the leaders. The properties of the product of infinite nonnegative matrices are explored to arrive at that the asynchronous containment control can be achieved under the proposed protocols if and only if the communication topology among the agents contains a directed spanning forest rooted at the leaders. At last, simulation results are given to demonstrate the validity of the theoretical findings.