Some Topics On Distributed Coordination For Multi-Agent Systems

Consensus on multi-agent systems is a hot topic in biology, physics, control engi-neering even applied mathematics since its widespread applications such as satellites (Unmanned Air Vehicle) formation control, wireless sensor networks, biological sys-tems and social networks, etc. Normally, a multi-agent system consists of a group of nodes (agents) and a graph characterized the interaction among them. Recent decade, numerous work on consensus have been done mainly via Lyapunov stability theory, matrix theory and algebraic theory. Consensus problem of multi-agent systems is still a important topic even though it is difficult. One of a fundamental reason is how to design a consensus scheme when the communication graph is directed, even uncon-nected? Compared to prototypical model on control theory, which can be viewed as a single node under multi-agent systems framework point of view, can not be generated or applied to multi-agent systems directly; Besides, the communication among nodes are nonlinear such as the famous Kuramoto model and so on.In this paper, we consider the consensus of multi-agent systems under several constrains utilizing both algebraic and Lyapunov stability theory, as well,as matrix theory:Consensus of multi-agent systems under data missing; Observe based consensus of multi-agent systems under communication failure; Gain based consensus of nonlinear multi-agent systems under intermittent control; Gain based consensus on second-order multi-agent systems without velocity measurements. The mainly concerned problems and contributions are described as follows:Packet dropout is inevitable since obstacles, unreliable communication equipments and complex communication setting, etc. Moreover, sampled-data control is widely adopted due to its low cost, ease maintenance and flexible usage. In chapter 2, we concern with the consensus problem of multi-agent systems under sampled-data con-trol with data missing, in which the coupling gain among agents is time-varying. The relationship between data missing rate and consensus is built, and the coupling gain converges to a fixed constant. Furthermore, tracking problem is also explicitly inves- tigated to obtain sufficient condition. Finally, simulation examples are presented to support these derived results.The key issue of consensus in multi-agent systems is:How to project a consensus algorithm such that consensus problem on multi-agent systems is solved? The case that all of the control inputs are lost in some communication intervals is considered in last chapter. However, it is unreasonable for distributed networks in a certain sense. Hence, could we design a more economical consensus protocol is the paramount work in this chapter. In chapter 3, sufficient conditions on nonlinear multi-agent systems are obtained utilizing relative output measurements via intermittent control to establish the relationship between data missing rate and consensus. Additionally, the case that arbitrarily switched topologies is also investigated, so does tracking problem. Finally, two examples are presented to show the effectiveness of these theoretical findings.Notice that, coupling gains in chapter 3 are all the constants. However, only local information is available for distributed systems (networks). Hence, a natural question is:could we design a more general consensus scheme such that consensus is guaranteed via local information. In chapter 4, consensus is ensured employing local output information with time-varying coupling gain. Furthermore, these results are extended to the scenario that under arbitrarily switching topologies. Similarly, tracking problem is also considered. However, compared to these results in chapter 3, the assumption on communication graph in this part is that the communication graph contains a directed spanning tree. It is a mild hypothesis and quite general. All of these results are supported via simulation examples.It should be pointed that consensus in aforementioned chapters focus on general case. However, second-order dynamical systems is a important topic in both theory and practical applications, for example pendulum model, tunnel diode circuit, even the famous Van der Pol equation and the damping of the single machine infinite bus system which is useful in applications, to name just a few. In chapter 5, consensus of second-order multi-agent systems without velocity information is considered to obtain a necessary and sufficient condition. Moreover, two consensus algorithm design meth-ods related to coupling gains among agents are explicitly presented, i.e., node and edge based schemes, respectively. Some sufficient consensus conditions are theoretical de- rived and all coupling gains are shown to converge to a fixed set with positive elements. In additionally, edge based scheme can be extended to switching setting while does not the node based case. Finally, these results are supported via pendulum models.