Study On Hierarchical Consensus Of Multi-agent Systems Based On Community Decomposition

In recent years, with the wide-range applications of multi-agent system and the depth study of cooperative control problem the research on consensus problem develops quickly and has achieved fruitful results not only in theories but also in applications. As an importam research aspect of the multi-agent system (MAS), consensus control of multi-agents has received more and more attention since last decade. The problem of consensus is prevalent in distributed multi-agent cooperative control, in which the "consistency" mainly refers to multi-agent tends to be the same on some states. In a MAS,"consensus" means that some of the agents’states reach consensus based on local information. The traditional consensus algorithm is generally discussed on the single-layer topology and the optimization of collaborative performance is conducted by the method of devising edge weights or connecting edges, such that approach is constrained in some circumstance. So it is considered in this paper to the convergence speed of the multi-agent system by converting the single-layer consensus problem of the multi-agent system to multi-layers consensus problem.It is proposed a hierarchical consensus algorithm based on the community decomposition aimed at the convergence speed of multi-agent system in the paper. The community structure detection algorithm of the complex network was applied to the optimum decomposition problem of the multi-agent topology. Firstly, the spectral partitioning algorithm of the complex network was applied to the optimal decomposition problem of the multi-agent topology. Then the single-layer consensus problem of the multi-agent system is converted to multi-layers consensus problem. The convergence speed is effectively improved on the premise of maintaining the original topology constraints. The effectiveness of the algorithm is demonstrated by simulations compared with the classic model.Secondly, NF algorithm of Newman was applied to the optimal decomposition problem of the multi-agent topology. It is similar that the singic-iayer consensus problem of the multi-agent system is converted to multi-layers consensus problem. The effectiveness of the algorithm is demonstrated by simulations compared with the classic model. And then the comparison between the spectral partitioning method and NF algorithm applied to the optimal decomposition problem is proposed. The conclusion is below:the two algorithms have their advantages. The spectral partitioning algorithm is better than NF algorithm for the divided results in some cases, but the opposite result is obtained in some other cases.Finally, the new community decomposition method named MACD algorithm is put forward. The convergence rate of multi-agent is studied with making use of hierarchical consensus algorithm based on the new decomposition method. It is defined its modular density function D corresponding to the topology graph of multi-agent system. The MACD algorithm is used to decompose the topology graph into some different sub-graph, and then the single topology graph of the multi-agent system is converted to multi-layers. The effectiveness of the algorithm is demonstrated by simulations and analysis compared with the classic model. Moreover, it can avoid some defects of t the spectral partitioning algorithm and NF algorithm.