The Controllability And Consistency Analysis Of The Edge Dynamic Multi-agent System

The edge dynamics multi-agent systems is an emerging research direction in recent years.The controllability and consensus of the system are a hot topic in the research process.It is very important to analyze the coupling relationship between agents.This paper mainly studies the controllability and consensus of the systems when the coupling relationship between agents changes dynamically.The main contents and contributions of this paper include:Firstly,the system models(the first-order neighbor agreement Laplacian model,the edge dynamics multi-agent systems model and the first-order edge dynamics multi-agent systems model)are introduced and defined in detail,and the preparation knowledge for the controllability and consensus of systems is fully prepared.Secondly,based on the PBH criterion and the Kalman criterion,the controllability of the edge dynamics multi-agent systems is analyzed in detail.Under the first-order dynamics multi-agent systems model,the relationship between eigenvalues and zero,eigenvalues and the decay rates are analyzed respectively,the necessary and sufficient conditions for the controllability of system are given.At the same time,the controllability matrix of the system is computed respectively.The necessary and sufficient conditions for the controllability of system are given related to the number of nodes and edges.In addition,it is possible to intervene the system by designing the decay rates and the leader nodes set to show the desired behavior,completing more complex tasks,and realize the overall function of the system.At the same time,through a power network system,the two methods of analyzing whether the system can be controlled are compared.It is found that the system based on the Kalman criterion determines that the amount of controllable calculation is relatively small and saves resources.But for some special eigenvalues in the system,the PBH criterion can be selected for the preliminary determination.Eventually,under the continuous time condition,the edge dynamics multi-agent systems edges consensus algorithm is designed,and the consensus of the edge dynamics multi-agent systems is analyzed.According to the topological connection relationship of the system,the edge consensus of the system is explored and analyzed through the line graph tool,the system convergence theorem is established for a special topological structure graph.The effectiveness of the conclusions is verified by an example of two sets of digital simulation results.In this paper,under the edge dynamics multi-agent systems model,the controllability and consensus of the systems are analyzed.Through analysis,the system leader nodes set and decay rates of the system can be changed to intervene the system to achieve the controllability and stability,so that the desired behavior can be exhibited and the overall function of the system can be realized.