Research On The Distributed Consensus Control Of Multi-Agent Systems

During the past decade, the cooperative control problems of multi-agent systems consisting of multiple autonomous agents have attracted much attention in a variety of research fields, such as biology, physics, robotics and computer sciences. One of the most important and fundamental issues of the cooperative control is the consensus problem that aims to design a distributed controller and drives the states or outputs of all agents to a common value. The cooperative control problems contain the consen-sus problem without a leader (i.e., the leaderless consensus problem), the consensus problem with a leader (i.e., the leader-following tracking problem) and the consensus problem with multiple leaders (i.e., the containment problem). This dissertation mainly focuses on the three consensus problems mentioned above for the nonlinear multi-agent systems. The main contents are summarized as follows:First of all, the consensus problem of a class of nonlinear multi-agent systems is investigated. The nonlinear function of each agent satisfies the Lipschitz condition and each agent subjects to the external disturbances which belong to L2[0,∞). By defining an appropriate controlled output, the consensus problem is transformed into an H∞ control problem. Based on the H∞ control theory, we design a distributed dynamic output feedback protocol to solve the consensus problem. Moreover, the consensus problem of multi-agent systems with nonlinear functions satisfying the sector condition is considered, and a distributed dynamic output feedback protocol is given to solve the consensus problem. Due to the convex property of LMIs, the parameters of the dynamic controller are obtained by solving three LMIs.Second, the cooperative output regulation and containment control problems for a class of heterogeneous nonlinear multi-agent systems are studied. We assume that each follower agent is in the output feedback form with the same relative degree with re-spect to its output. For the cooperative output regulation problem, we design a dynamic controller such that the outputs of follower agents track the desired trajectory which is the output of the leader agent. For the containment control problem, the control objec-tive is to design a distributed controller such that the outputs of follower agents enter the convex hull spanned by the outputs of leader agents. To this end, we convert the containment control problem into a cooperative output regulation problem.A recursive procedure and internal model are employed to design the distributed controller.Finally, we consider the finite-time tracking control of the linear and nonlinear multi-agent systems. For the linear multi-agent systems, we firstly study the finite-time tracking problem for the individual agent with single input, and we present a finite-time tracking protocol for the linear multi-agent systems. We prove that the tracking errors will not go to infinity in any finite-time internal and show that the whole multi-agent system will track the state of the leader agent in a finite time. We give a similar result for multi inputs case as well. For the nonlinear multi-agent systems, each agent is in the strict-feedback form and the communication topology is a directed graph. By using the homogeneous systems theory, we firstly give a finite-time tracking protocol for the high-order linear multi-agent systems, based on which we give a finite-time tracking protocol for nonlinear multi-agent systems in strict-feedback form. To deal with the un-measurable states, finite-time convergent observers are constructed to estimate the real states of agents, and we use the states of observers to construct the finite-time tracking protocol for nonlinear multi-agent systems.