Research On Bipartite Consistency Of Edge Dynamics In Multi-agent Systems

Multi-agent systems have become a hot subject in the field of control and artificial intelligence in recent years.Among them,the consensus of system has a wide range of applications and has been paid attention by a large number of researchers.Based on the study of consensus,this paper mainly considers the effect of the coupling relationship between the agents in the system,which named the effect of edge-dynamic.Furthermore,the analysis of edge-dynamic consensus of the multi-agent system is under the positive and negative mixed weighted directed graph.The main contents and contributions of this paper are as follows:First,the multi-agent system is introduced in detail,and the concepts of edge-dynamic,consensus and time-delay in systems are described in detail,besides the theoretical knowledge basic about graph theory,matrix theory and stability theory are fully introduced.In order to conduct research on related consensus.Secondly,the first-order and second-order edge-dynamic system models are constructed for the multi-agent system without time-delay under strongly connected directed graphs which is digon sign-symmetric.On this basis,the relevant protocol about edge-dynamic bipartite consensus is designed.The normal transformation matrix is used to construct the positive weight system corresponding to the positive and negative mixed weight system.The transformation is used to convert the problem of bipartite consensus of the positive and negative mixed weight system into the problem of consensus of the general system,and further to the stability problem of the system through matrix transformation.On the basis of stability theory,the stability of the system is researched.Then simulate the example by MATLAB.Finally,based on the research of multi-agent system without time-delay,the non-uniform fixed time-delay is added to the model to construct the first-order and second-order edgedynamic models of multi-agent system with time-delay.And the time-delay information of the system is designed.On this basis,a control protocol of edge-dynamic bipartite consensus with time-delay is designed.Similar to the system without time-delay,a new system is constructed using normal transformation and matrix transformation.Then the problem of bipartite consensus of the original system is transformed into stability problem of the new system.And use Lyapunov's second method to analyze the stability of the system,combined with the LMI toolbox in MATLAB to analyze time-delay of the system,further obtain the conditions for multi-agent system with time-delay of achieving the edge-dynamic bipartite consensus,then use MATLAB for example simulation.