Consensus and Cooperative Output Regulation of Linear Multi-agent Systems

Over the past decade, the extensive applications of wireless sensor networks, cooperative robotics, unmanned aerial vehicle formations and so on have made the cooperative control of the multi-agent system a trendy topic. This thesis will concentrate on two basic cooperative control problems: consensus and cooperative output regulation.;In the first part of this thesis, we will consider these two consensus problems for both continuous-time and discrete-time general linear multi-agent systems subject to the switching network topology under the jointly connected assumption. Our problem formulation includes the consensus of many typical physical multi-agent systems such as single-integrators and harmonic oscillators as special cases. The main results of this part are summarized as follows:;1. Two consensus problems of continuous-time marginally stable linear multi-agent systems under switching network topology are studied. We first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is intriguing in that the system matrix does not have to be Hurwitz at any time instant. We then establish the main stability result by a combination of the Lyapunov stability analysis and a generalized Barbalat’s Lemma applicable to piecewise continuous linear systems.;2. Two consensus problems of linear discrete-time multi-agent systems under switching network topology are studied. We combine the common Lyapunov function approach with some novel technique to complete such stability analysis. Our result contains several existing results as special cases.;The second part of this thesis addresses the cooperative output regulation of linear multi-agent systems. The direct objective of this problem is to handle the asymptotic tracking and disturbance rejection problem in an uncertain multi-agent system via a distributed control approach. The main contributions of this part are summarized as follows:;1. The cooperative output regulation of linear multi-agent systems under both static and switching communication network topologies is studied. For the static network case, we present the sufficient and necessary solvability conditions via distributed dynamic state feedback control law and the distributed dynamic measurement output feedback control law. For the switching network case, we give the sufficient solvability condition via distributed dynamic state feedback control law and the distributed dynamic measurement output feedback with feedforward control law. This result can be viewed as a generalization of some leader-following consensus problems of multi-agent systems.;2. The cooperative robust output regulation problem of linear uncertain multi-agent systems under static network topology is studied. Using the LQR design method, we present the sufficient and necessary solvability conditions of this problem via both distributed dynamic state feedback control law and distributed dynamic output feedback control law. Due to the robustness of eigenvalue placement, such control laws can tolerate small plant uncertainty. This result also contains the leader-following consensus problem for several systems as special cases.;3. The cooperative robust output regulation of a class of heterogeneous linear multi-agent systems with parameter uncertainties under static network topology is studied. We introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi-agent system. We then solve this problem via distributed dynamic output feedback control law by combining a simultaneous high gain state feedback control technique and a distributed high gain observer technique. The sufficient and necessary solvability conditions are also given. A special case of our result leads to the solution of the leader-following robust consensus problem for a large class of uncertain multi-agent systems. (Abstract shortened by UMI.).