The Evolution of the Distributed Observer and Its Applications

Abstract

A typical multi-agent system is composed of a follower system consisting of multiple subsystems called followers and a leader system whose output is to be tracked by the followers. What makes the control of a multi-agent system challenging is that the control law needs to be distributed in the sense that it must satisfy time-varying communication constraints. A special case of distributed control is where all the followers can access the information of the leader. For this special case, one can design, for each follower, a conventional control law based on the information of the leader. The collection of these conventional control laws constitutes the so-called purely decentralized control law for the multi-agent system. Nevertheless, the purely decentralized control law is not feasible due to the communication constraints. In this talk, we will introduce a framework for designing a distributed control law by cascading a purely decentralized control law and a so-called distributed observer for the leader system, which is a dynamic compensator that estimates and transmits the leader’s information to each follower over a communication network. Such a control law is called the distributed observer-based control law and has found its applications to such problems as consensus, synchronization, flocking, formation, and distributed Nash equilibrium seeking. The core of this design framework is the distributed observer for a linear leader system, which was initiated in 2010 for dealing with the cooperative output regulation problem, and has experienced three phases of developments. In the first phase, the distributed observer is only capable of estimating and transmitting the leader’s state to every follower assuming every follower knows the dynamics of the leader. In the second phase which started in 2015, the distributed observer is rendered the capability of estimating and transmitting not only the leader’s state but also the dynamics of the leader to every follower provided that the leader’s children know the information of the leader. Such a dynamic compensator is called an adaptive distributed observer for a known leader system. The distributed observer was further developed in 2017 for linear leader systems containing unknown parameters, thus entering its third phase of the development. Such a dynamic compensator is called an adaptive distributed observer for an unknown leader as it not only estimates the state but also the unknown parameters of the leader. We will start with an overview on the development of the distributed observer and then highlight the recent results on establishing an output-based adaptive distributed observer for an unknown leader system over jointly connected communication networks. Extensions, variants and applications of the distributed observer will also be touched.