Quantitative Parameters And Controllability Under A Simple Topology

The controllability of multi-agent systems is a fundamental and important concept in research of multi-agent systems.In this paper,the main contents include:This paper introduces the background and significance of the research on the controllability of multi-agent systems,and summarizes the current situation of domestic and foreign development.Aiming at the controllability problem of multi-agent systems,the relevant knowledge of graph theory,matrix theory and linear system theory for solving the problems has been summarized.On the consensus protocol of multi-agent systems,the Laplacian matrix of system is divided into blocks.And a quantitative parameter is proposed based on the condition number of the system controllability matrix.This parameter can affect the controllability of multi-agent systems,and then this paper analyzes the controllability of multi-agent systems based on the value of the parameter.The controllability of the multi-agent system is related to the value of the parameter.The value of this parameter not only can be used to determine whether the system is controllable,but also to measure the degree of controllability of the multi-agent system.In the end,the effect of this parameter on controllability is verified by concrete examples.The multi-agent systems model,the complex network system model and the interconnected network system model have been summarized.And the controllability of these kinds of system models are studied under the same system topology structure(directed path graph and directed tree graph),then the generality of controllability is summarized.