Distributed Average Tracking Problem Under Directed Networks: A Distributed Estimator-Based Design

This article considers the distributed average tracking (DAT) problem that a group of agents aims to track the average of local reference signals. The communication network is strongly connected but not required to be weight balanced. A framework of distributed estimator-based algorithm design without any initialization requirement is presented. For agents with nominal first-order (FO) dynamics, a class of distributed estimators is proposed to estimate the average of local reference signals within fixed time, with which each agent finally achieves the DAT within fixed time. For agents with second-order dynamics subject to modeling uncertainty, unmodeled dynamics, as well as external disturbances, a class of distributed estimator is proposed to estimate the average of local reference signals within fixed time, and then a local disturbance-observer-based control protocol is proposed for each agent to achieve DAT asymptotically. Different from most of the existing DAT results under general directed networks that DAT error can only be made globally ultimately bounded, the exact DAT can be achieved within fixed time or asymptotically here. Further, the idea of distributed estimator is applied to solve a class of distributed optimization problems within finite time. Finally, two simulation examples are given to show the effectiveness of the theoretical results.