On Consensus Speed Of The Leader-Following Multi-agent Systems

Comparing to conventional control systems, the multi-agent systems have many advantages such as reducing cost, improving system efficiency, flexibility, reliability, and so on. A consensus problem for the multi-agent systems is to design a simple control law for each agent, using local information from its neighbors, such that the networked system can achieve a consensus, namely all agents achieve a same state. In recent years, the consensus problem for the multi-agent systems has attracted more and more attentions, and the consensus problem for the leader-following multi-agent systems is an important part of it. Presently, the research of the consensus problem mainly focuses on the conditions of multi-agent systems achieving consensus, but the consensus speed (convergence rate of multi-agent systems) is less considered. This thesis studies the consensus speed of the leader-following multi-agent systems, and the main research contents and the results are shown as follows:1) The consensus speed problem for the second-order leader-following multi-agent systems in undirected network is studied, and the conditions of the second-order leader-following multi-agent systems achieving maximum consensus speed with three different control algorithms are given. The maximum consensus speed is related with the maximum eigenvalue and minimum eigenvalue of relevant matrix.2) An improved control algorithm for the leader-following multi-agent systems is given, and which can inevitably make the maximum consensus speed bigger in some specified networks.3) The conditions of the second-order leader-following multi-agent systems achieving maximum consensus speed are given in the directed network without directed loop.