Topological Hierarchy Structure Design Of Distributed Network System

Over the years,with the widespread use of distributed network systems,research on collaborative control issues has become more in-depth.The research of traditional cooperative control problems is generally discussed in the single-layer topology.Although the distributed algorithm used by each individual in the system is relatively simple,the whole system's convergence process involves a large number of individuals,making the system collaboratively controlled.The convergence speed is limited.Considering the fact that there is a hierarchical organization structure in the engineering system,the large-scale systems can be organized more rationally and efficiently under the hierarchical structure,and then it can deal with more complicated and huge problems,the multi-agent distributed consistency problem is the basis of cooperative control of multi-autonomous systems and the research on multi-level hierarchical structure is of great value.Therefore,this paper aims to design a hierarchical topology,and improve the consistency of system convergence speed as a design index of multi-layer topology.Then,the optimization problem of single-layer topology is transformed into the optimization of system eigenvalues.First,this paper proposes a topological hierarchical design based on ergodic algorithm and adopts ergodic algorithm to optimize the laplacian matrix of multi-agent topology,so as to obtain the single-layer topology decomposition structure of the system,and then convert the multi-level hierarchical structure design problem of multi-agent system into a single-layer topology structural optimization issues.This is,the second small eigenvalue of Laplacian matrix is optimized.This verifies the effectiveness of the algorithm.The accuracy of this algorithm is high,however,with the increase in the size of multi-agent systems,the more time it takes to run,the more it does not apply to large-scale systems.Furthermore,this paper proposes a hierarchical topology design based on the Improved Laplace And K-means algorithm(ILAK algorithm),and proposes a hierarchical consistency algorithm based on hierarchical structure to study the consensus convergence speed of multi-agents.In this paper,the ILAK algorithm is based on the Laplacian matrix,and the number of communities is determined by the distance and density distribution of the elements in the first nontrivial eigenvector of the Laplacian matrix.Then the clusters are clustered by the K-means and then the system topology is decomposed into different subgraphs.By using the ILAK algorithm several times,the single-layer topology is converted into a multi-layer topology.The convergence of multilevel hierarchical structure of multi-agent system is studied.Simulation results show that this algorithm can effectively improve the consistency of multi-agent system.Comparing with traversal algorithm,it can make up for the shortcomings of high time complexity and the inability to determine the number of communities in advance.