Distributed Average Tracking over Directed Communication Networks: A Nonsmooth Surplus Approach

In the distributed average tracking (DAT) problem for multi-agent systems, a general yet challenging as sumption from the perspective of topological structure is the directed but not necessarily balanced communication networks, which has been rarely considered. This article is dedicated to realizing DAT over weight-unbalanced directed communication networks. Specifically: i) A new concept of “nonsmooth surplus” is developed to assist in designing DAT algorithms properly over unbalanced directed networks. Such a variable overcomes the inefficiency of conventional surplus-based method in the presence of non smooth components; ii) Considering the inadequacy of traditional analytical methods for the nonsmooth surplus-based approaches, a new analytical framework combining matrix perturbation theory and the graph theoretic minimum cut is properly developed to establish the algorithm's stability. A feasible condition on the control gain is also derived by utilizing the minimum cut; iii) Based on the non smooth surplus concept and the corresponding analytical framework, a class of nonsmooth surplus DAT algorithms is designed under unbalanced directed communication networks to re alize exact DAT, which seems to be the first time in the literature. The proposed algorithm is robust to the initialization mismatch and suitable for cases where the communication topology suffers from sudden changes. Finally, as a potential application of the proposed algorithm, the problem of distributed formation encirclement of multiple dynamic targets is studied over a diversified exploration network. Additionally, a new mapping structure is further designed to generalize agent-target interactions from strictly one-to one pairings to diverse modes. This extension effectively captures the diversified agent detection capabilities in real world scenarios. Some simulations are conducted to testify the validity of the proposed algorithms.