Distributed Adaptive Consensus Disturbance Rejection: a Directed-spanning-tree Perspective

In this paper, we revisit the problem of consensus disturbance rejection for multiagent systems over a digraph, but from a different perspective, i.e., the perspective of a directed spanning tree (DST). When the minimum nonzero real part of the Laplacian eigenvalues is available, we reproduce the sufficient lower bound for a static homogeneous coupling gain in the literature, by exploring a DST structure of the digraph. The major novelty arises when it is shown that by adaptively tuning the coupling gains along a DST, consensus disturbance rejection can be achieved when the above eigenvalue information is not available. Numerical examples on networks of second-order oscillators and UAVs are included to validate the theoretical results.