An Adaptive Distributed Observer for a Class of Uncertain Linear Leader Systems Over Jointly Connected Switching Networks and Its Application

The early results on the adaptive distributed observer for uncertain leader systems have three limitations. The adaptive distributed observer is state-based, the communications among the follower subsystems are undirected, and the communication network is static. Despite years of efforts, these issues have not been fully addressed. In this paper, we develop an output-based adaptive distributed observer for a class of uncertain linear leader systems over jointly connected switching networks. Our design consists of two steps. First, we develop an exponentially convergent estimator to estimate both the state and the unknown parameter vector of the leader system. Second, we design a state-based adaptive distributed observer for the exponentially convergent estimator over jointly connected switching networks. It turns out that such a two-step design overcomes all three obstacles. As an application, we solve the cooperative output regulation problem for linear multi-agent systems subject to an uncertain leader system.