Asynchronous formation-containment flocking of multi-agent systems

This paper develops an asynchronous distributed protocol for formation-containment flocking of discrete-time multi-agent systems, addressing moving leaders, cooperative-competitive interactions modeled by signed digraphs, and nonuniform private update schedules within a single design. Using only local neighbor information, each follower is driven to a prescribed barycentric position inside the translating convex hull of the leaders while aligning its velocity with the common leader velocity. The protocol couples absolute-value weighted velocity averaging for flocking with signed relative-position feedback for formation-containment. Convergence is analyzed through the theory of infinite products of sub-stochastic matrices, which yields explicit conditions linking the network topology (positive-path reachability), the control gains, the signed interaction weights, and the inter-update bound, and guarantees geometric convergence. Numerical examples with diamond and pentagram formations confirm the theoretical results and demonstrate scalability.