Consensus Of Second-order Multi-agent Systems And Its Application

In recent years, multi-agent systems are widely used in the fields of computers, artificial intelligence, communications, communication engineering, traffic control, military exercises, social psychology, as well as e-commerce. Therefore the consensus of multi-agent systems becomes research focus in those areas. In this essay, the consensus of the second-order multi-agent systems are studied by using the Laplace transform, graph theory, matrix theory and control theory. This paper not only proves theoretically that the second-order multi-agent system could reach consensus, but also obtains position and velocity values of all agent when it achieves consensus. Furthermore some numerical simulations are given to verify that theoretical results. This article mainly focuses on three specific matters:1. We study the consensus in second-order continuous multi-agent system which is general topology. Appling the knowledge of graph theory and matrix theory, the model of the second-order multi-agent system is descried by matrix. Then the matrix model can translate into linear equation by applying the Laplace transform. Thereby we can obtain that each agent in the second-order multi-agent system could reach consensus under certain circumstance and derive the accurate solution of the model.2. We consider a second-order continuous multi-agent system with directed topology and investigate the consensus of its. We consider coupling strength in the model of the second-order multi-agent system. Currently the Lyapunov method is used in most of studies of the second-order multi-agent systems. However it only could determine the conditions of the system reach consensus, but could not obtain an exact solution of a system model by Lyapunov method. We introduced the Laplace transform to study the consensus. It not only avoids constructing a Lyapunov function, but also obtains exact solutions of the second-order multi-agent system model. Moreover theoretically and numerically prove that the second-order multi-agent system could reach consensus.3. We discuss consensus and time delay in second-order continuous multi-agent systems. Delay phenomenon realistically exists in communication and information transfer, therefore the study of the consistency of multi-agent systems with a time delay is practical significant. In this paper, the Laplace transform is used to study the consensus of second-order systems with time delay, then we expand the model and obtain the upper bound of the delays when the system reached consensus.