Research On Second-order Consensus Of Multi-agent Systems With Impulse And Time-delays

With the rapid development of information technology and economic globalization, the human civilization comes into the era of complex networks. In nature and human society, there are a large number of complex systems, and complex networks are recognized as one of the most effective ways in researching complex systems. Multi-agent systems is a class of complex systems, which widely exist in various groups of organisms in nature. The consistency problem of multi-agent systems is an important problem to be researched, and it has been widespread concerned in various fields, such as distributed computing, biological systems, the sensor networks and so on. Therefore, undertaking an extensive and in-depth study on the consistency of multi-agent systems has become an important contemporary topic.In this paper, we study the second-order consensus of multi-agent systems with pulse and time-delays. Firstly, we give a brief description of the basic concepts about complex networks, multi-agent systems and the consistency. Meanwhile, their development status and tendency and other related issues are also introduced. Next, the main body portion of this paper is presented. It includes two parts, one is the second-order consensus of multi-agent systems with pulse, the other is the second-order consensus of multi-agent systems with pulse and time-delays. The pulse and time-delays affect the multi-agent systems. According to pulse and time-delays respectively, vector matrix and Laplace matrix are both used to transform them to their corresponding deviation cases. Though studying their deviation, we analyze the evolution of these agents in the system indirect-ly. By means of the relevant theoretical knowledge of algebraic graph, matrix analysis, impulsive control and differential equations, the consistency conditions are achieved suc-cessfully. The results show that, when the time intervals of impulses are small, at the same time, some conditions are satisfied for these intervals and the control matrixes which occur at the moment of impulses, then these conditions will guarantee the second-order consensus. Following, the simulation results are presented to validate the effectiveness of these theoretical analyses. Finally, this paper summarizes the main work, and the prospective about the consensus of multi-agent is also discussed.