Fully-Heterogeneous Containment Control of a Network of Leader-Follower Systems

💡 Research Summary

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This paper addresses the fully‑heterogeneous containment control problem (FHCCP) for linear multi‑agent systems in which both leaders and followers have distinct dynamics. The objective is to design distributed control protocols for the followers so that their outputs converge to the convex hull spanned by the leaders’ outputs. The authors first reformulate FHCCP by introducing a virtual exo‑system for each follower. This virtual system is generated from the dynamics of all leaders that influence the follower, weighted by a set of coefficients called normalized levels of influence (NLIs).

A key contribution is a fully distributed algorithm for computing the NLIs. By defining a local graph from the perspective of each follower—obtained by removing nodes that have no directed path to the follower—the authors construct local adjacency, degree, and Laplacian matrices. Using iterative set‑exchange procedures (Algorithm 1 and Algorithm 2), each follower discovers the labels of its influential leaders and followers and the corresponding edge weights. After a number of iterations bounded by the longest directed path in the overall graph, the follower obtains the exact row of (